Chapter 3 Spiral Bevel Gear and Herringbone Gear Spiral

Revised Edition: 2016
ISBN 978-1-283-49166-2
© All rights reserved.
Published by:
Research World
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New York, NY 10036, United States
Email: Table of Contents
Chapter 1 – Gear
Chapter 2 - Bevel Gear
Chapter 3 - Spiral Bevel Gear and Herringbone Gear
Chapter 4 - Worm Drive
Chapter 5 - Epicyclic Gearing
Chapter 6 - Harmonic Drive and Non-Circular Gear
Chapter 7 - Backlash (Engineering)
Chapter 8 - Derailleur Gears
Chapter 9 - Hub Gear
Chapter 10 - Manual Transmission
Chapter 11 - Automatic Transmission
Chapter 12 - List of Gear Nomenclature
Chapter 1
Two meshing gears transmitting rotational motion. Note that the smaller gear is rotating
faster. Although the larger gear is rotating less quickly, its torque is proportionally
A gear or more correctly a "gear wheel" is a rotating machine part having cut teeth, or
cogs, which mesh with another toothed part in order to transmit torque. Two or more
gears working in tandem are called a transmission and can produce a mechanical
advantage through a gear ratio and thus may be considered a simple machine. Geared
devices can change the speed, magnitude, and direction of a power source. The most
common situation is for a gear to mesh with another gear, however a gear can also mesh a
non-rotating toothed part, called a rack, thereby producing translation instead of rotation.
The gears in a transmission are analogous to the wheels in a pulley. An advantage of
gears is that the teeth of a gear prevent slipping.
When two gears of unequal number of teeth are combined a mechanical advantage is
produced, with both the rotational speeds and the torques of the two gears differing in a
simple relationship.
In transmissions which offer multiple gear ratios, such as bicycles and cars, the term
gear, as in first gear, refers to a gear ratio rather than an actual physical gear. The term is
used to describe similar devices even when gear ratio is continuous rather than discrete,
or when the device does not actually contain any gears, as in a continuously variable
The earliest known reference to gears was circa A.D. 50 by Hero of Alexandria, but they
can be traced back to the Greek mechanics of the Alexandrian school in the 3rd century
B.C. and were greatly developed by the Greek polymath Archimedes (287–212 B.C.).
The Antikythera mechanism is an example of a very early and intricate geared device,
designed to calculate astronomical positions. Its time of construction is now estimated
between 150 and 100 BC.
Comparison with other drive mechanisms
The definite velocity ratio which results from having teeth gives gears an advantage over
other drives (such as traction drives and V-belts) in precision machines such as watches
that depend upon an exact velocity ratio. In cases where driver and follower are in close
proximity gears also have an advantage over other drives in the reduced number of parts
required; the downside is that gears are more expensive to manufacture and their
lubrication requirements may impose a higher operating cost.
The automobile transmission allows selection between gears to give various mechanical
External vs. internal gears
Internal gear
An external gear is one with the teeth formed on the outer surface of a cylinder or cone.
Conversely, an internal gear is one with the teeth formed on the inner surface of a
cylinder or cone. For bevel gears, an internal gear is one with the pitch angle exceeding
90 degrees. Internal gears do not cause direction reversal.
Spur gear
Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder
or disk with the teeth projecting radially, and although they are not straight-sided in form,
the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears
can be meshed together correctly only if they are fitted to parallel shafts.
Helical gears
Top: parallel configuration
Bottom: crossed configuration
Helical gears offer a refinement over spur gears. The leading edges of the teeth are not
parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this
angling causes the tooth shape to be a segment of a helix. Helical gears can be meshed in
a parallel or crossed orientations. The former refers to when the shafts are parallel to
each other; this is the most common orientation. In the latter, the shafts are non-parallel,
and in this configuration are sometimes known as "skew gears".
The angled teeth engage more gradually than do spur gear teeth causing them to run more
smoothly and quietly. With parallel helical gears, each pair of teeth first make contact at a
single point at one side of the gear wheel; a moving curve of contact then grows
gradually across the tooth face to a maximum then recedes until the teeth break contact at
a single point on the opposite side. In spur gears teeth suddenly meet at a line contact
across their entire width causing stress and noise. Spur gears make a characteristic whine
at high speeds and can not take as much torque as helical gears. Whereas spur gears are
used for low speed applications and those situations where noise control is not a problem,
the use of helical gears is indicated when the application involves high speeds, large
power transmission, or where noise abatement is important. The speed is considered to be
high when the pitch line velocity exceeds 25 m/s.
A disadvantage of helical gears is a resultant thrust along the axis of the gear, which
needs to be accommodated by appropriate thrust bearings, and a greater degree of sliding
friction between the meshing teeth, often addressed with additives in the lubricant.
For a crossed configuration the gears must have the same pressure angle and normal
pitch, however the helix angle and handedness can be different. The relationship between
the two shafts is actually defined by the helix angle(s) of the two shafts and the
handedness, as defined:
E = β1 + β2 for gears of the same handedness
E = β1 − β2 for gears of opposite handedness
Where β is the helix angle for the gear. The crossed configuration is less mechanically
sound because there is only a point contact between the gears, whereas in the parallel
configuration there is a line contact.
Quite commonly helical gears are used with the helix angle of one having the negative of
the helix angle of the other; such a pair might also be referred to as having a right-handed
helix and a left-handed helix of equal angles. The two equal but opposite angles add to
zero: the angle between shafts is zero – that is, the shafts are parallel. Where the sum or
the difference (as described in the equations above) is not zero the shafts are crossed. For
shafts crossed at right angles the helix angles are of the same hand because they must add
to 90 degrees.
Double helical
Double helical gears
Double helical gears, or herringbone gear, overcome the problem of axial thrust
presented by "single" helical gears by having two sets of teeth that are set in a V shape.
Each gear in a double helical gear can be thought of as two standard mirror image helical
gears stacked. This cancels out the thrust since each half of the gear thrusts in the
opposite direction. Double helical gears are more difficult to manufacture due to their
more complicated shape.
For each possible direction of rotation, there are two possible arrangements of two
oppositely-oriented helical gears or gear faces. In one possible orientation, the helical
gear faces are oriented so that the axial force generated by each is in the axial direction
away from the center of the gear; this arrangement is unstable. In the second possible
orientation, which is stable, the helical gear faces are oriented so that each axial force is
toward the mid-line of the gear. In both arrangements, when the gears are aligned
correctly, the total (or net) axial force on each gear is zero. If the gears become
misaligned in the axial direction, the unstable arrangement generates a net force for
disassembly of the gear train, while the stable arrangement generates a net corrective
force. If the direction of rotation is reversed, the direction of the axial thrusts is reversed,
a stable configuration becomes unstable, and vice versa.
Stable double helical gears can be directly interchanged with spur gears without any need
for different bearings.
Bevel gear
A bevel gear is shaped like a right circular cone with most of its tip cut off. When two
bevel gears mesh their imaginary vertices must occupy the same point. Their shaft axes
also intersect at this point, forming an arbitrary non-straight angle between the shafts.
The angle between the shafts can be anything except zero or 180 degrees. Bevel gears
with equal numbers of teeth and shaft axes at 90 degrees are called miter gears.
The teeth of a bevel gear may be straight-cut as with spur gears, or they may be cut in a
variety of other shapes. Spiral bevel gear teeth are curved along the tooth's length and set
at an angle, analogously to the way helical gear teeth are set at an angle compared to spur
gear teeth. Zerol bevel gears have teeth which are curved along their length, but not
angled. Spiral bevel gears have the same advantages and disadvantages relative to their
straight-cut cousins as helical gears do to spur gears. Straight bevel gears are generally
used only at speeds below 5 m/s (1000 ft/min), or, for small gears, 1000 r.p.m.
Hypoid gear
Hypoid gears resemble spiral bevel gears except the shaft axes do not intersect. The pitch
surfaces appear conical but, to compensate for the offset shaft, are in fact hyperboloids of
revolution. Hypoid gears are almost always designed to operate with shafts at 90 degrees.
Depending on which side the shaft is offset to, relative to the angling of the teeth, contact
between hypoid gear teeth may be even smoother and more gradual than with spiral bevel
gear teeth. Also, the pinion can be designed with fewer teeth than a spiral bevel pinion,
with the result that gear ratios of 60:1 and higher are feasible using a single set of hypoid
gears. This style of gear is most commonly found driving mechanical differentials; which
are normally straight cut bevel gears; in motor vehicle axles.
Crown gear
Crown gears or contrate gears are a particular form of bevel gear whose teeth project at
right angles to the plane of the wheel; in their orientation the teeth resemble the points on
a crown. A crown gear can only mesh accurately with another bevel gear, although crown
gears are sometimes seen meshing with spur gears. A crown gear is also sometimes
meshed with an escapement such as found in mechanical clocks.
Worm gear
4-start worm and wheel
Worm gears resemble screws. A worm gear is usually meshed with an ordinary looking,
disk-shaped gear, which is called the gear, wheel, or worm wheel.
Worm-and-gear sets are a simple and compact way to achieve a high torque, low speed
gear ratio. For example, helical gears are normally limited to gear ratios of less than 10:1
while worm-and-gear sets vary from 10:1 to 500:1. A disadvantage is the potential for
considerable sliding action, leading to low efficiency.
Worm gears can be considered a species of helical gear, but its helix angle is usually
somewhat large (close to 90 degrees) and its body is usually fairly long in the axial
direction; and it is these attributes which give it its screw like qualities. The distinction
between a worm and a helical gear is made when at least one tooth persists for a full
rotation around the helix. If this occurs, it is a 'worm'; if not, it is a 'helical gear'. A worm
may have as few as one tooth. If that tooth persists for several turns around the helix, the
worm will appear, superficially, to have more than one tooth, but what one in fact sees is
the same tooth reappearing at intervals along the length of the worm. The usual screw
nomenclature applies: a one-toothed worm is called single thread or single start; a worm
with more than one tooth is called multiple thread or multiple start. The helix angle of a
worm is not usually specified. Instead, the lead angle, which is equal to 90 degrees minus
the helix angle, is given.
In a worm-and-gear set, the worm can always drive the gear. However, if the gear
attempts to drive the worm, it may or may not succeed. Particularly if the lead angle is
small, the gear's teeth may simply lock against the worm's teeth, because the force
component circumferential to the worm is not sufficient to overcome friction. Worm-andgear sets that do lock are called self locking, which can be used to advantage, as for
instance when it is desired to set the position of a mechanism by turning the worm and
then have the mechanism hold that position. An example is the machine head found on
some types of stringed instruments.
If the gear in a worm-and-gear set is an ordinary helical gear only a single point of
contact will be achieved. If medium to high power transmission is desired, the tooth
shape of the gear is modified to achieve more intimate contact by making both gears
partially envelop each other. This is done by making both concave and joining them at a
saddle point; this is called a cone-drive.
Worm gears can be right or left-handed following the long established practice for screw
Non-circular gears
Non-circular gears are designed for special purposes. While a regular gear is optimized to
transmit torque to another engaged member with minimum noise and wear and maximum
efficiency, a non-circular gear's main objective might be ratio variations, axle
displacement oscillations and more. Common applications include textile machines,
potentiometers and continuously variable transmissions.
Rack and pinion
Rack and pinion gearing
A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely
large radius of curvature. Torque can be converted to linear force by meshing a rack with
a pinion: the pinion turns; the rack moves in a straight line. Such a mechanism is used in
automobiles to convert the rotation of the steering wheel into the left-to-right motion of
the tie rod(s). Racks also feature in the theory of gear geometry, where, for instance, the
tooth shape of an interchangeable set of gears may be specified for the rack (infinite
radius), and the tooth shapes for gears of particular actual radii then derived from that.
The rack and pinion gear type is employed in a rack railway.
Epicyclic gearing
In epicyclic gearing one or more of the gear axes moves. Examples are sun and planet
gearing and mechanical differentials.
Sun and planet
Sun (yellow) and planet (red) gearing
Sun and planet gearing was a method of converting reciprocal motion into rotary motion
in steam engines. It played an important role in the Industrial Revolution. The Sun is
yellow, the planet red, the reciprocating crank is blue, the flywheel is green and the
driveshaft is grey.
Harmonic drive
Harmonic drive gearing
A harmonic drive is a specialized proprietary gearing mechanism.
Cage gear
Cage gear in Pantigo Windmill, Long Island
A cage gear, also called a lantern gear or lantern pinion has cylindrical rods for teeth,
parallel to the axle and arranged in a circle around it, much as the bars on a round bird
cage or lantern. The assembly is held together by disks at either end into which the tooth
rods and axle are set.
General nomenclature
Rotational frequency, n
Measured in rotation over time, such as RPM.
Angular frequency, ω
Measured in radians per second. 1RPM = π / 30 rad/second
Number of teeth, N
How many teeth a gear has, an integer. In the case of worms, it is the number of
thread starts that the worm has.
Gear, wheel
The larger of two interacting gears or a gear on its own.
The smaller of two interacting gears.
Path of contact
Path followed by the point of contact between two meshing gear teeth.
Line of action, pressure line
Line along which the force between two meshing gear teeth is directed. It has the
same direction as the force vector. In general, the line of action changes from
moment to moment during the period of engagement of a pair of teeth. For
involute gears, however, the tooth-to-tooth force is always directed along the
same line—that is, the line of action is constant. This implies that for involute
gears the path of contact is also a straight line, coincident with the line of action—
as is indeed the case.
Axis of revolution of the gear; center line of the shaft.
Pitch point, p
Point where the line of action crosses a line joining the two gear axes.
Pitch circle, pitch line
Circle centered on and perpendicular to the axis, and passing through the pitch
point. A predefined diametral position on the gear where the circular tooth
thickness, pressure angle and helix angles are defined.
Pitch diameter, d
A predefined diametral position on the gear where the circular tooth thickness,
pressure angle and helix angles are defined. The standard pitch diameter is a basic
dimension and cannot be measured, but is a location where other measurements
are made. Its value is based on the number of teeth, the normal module (or normal
diametral pitch), and the helix angle. It is calculated as:
in metric units or
in imperial units.
Module, m
A scaling factor used in metric gears with units in millimeters who's effect is to
enlarge the gear tooth size as the module increases and reduce the size as the
module decreases. Module can be defined in the normal (mn), the transverse (mt),
or the axial planes (ma) depending on the design approach employed and the type
of gear being designed. Module is typically an input value into the gear design
and is seldom calculated.
Operating pitch diameters
Diameters determined from the number of teeth and the center distance at which
gears operate. Example for pinion:
Pitch surface
In cylindrical gears, cylinder formed by projecting a pitch circle in the axial
direction. More generally, the surface formed by the sum of all the pitch circles as
one moves along the axis. For bevel gears it is a cone.
Angle of action
Angle with vertex at the gear center, one leg on the point where mating teeth first
make contact, the other leg on the point where they disengage.
Arc of action
Segment of a pitch circle subtended by the angle of action.
Pressure angle, θ
The complement of the angle between the direction that the teeth exert force on
each other, and the line joining the centers of the two gears. For involute gears,
the teeth always exert force along the line of action, which, for involute gears, is a
straight line; and thus, for involute gears, the pressure angle is constant.
Outside diameter, Do
Diameter of the gear, measured from the tops of the teeth.
Root diameter
Diameter of the gear, measured at the base of the tooth.
Addendum, a
Radial distance from the pitch surface to the outermost point of the tooth. a = (Do
− D) / 2
Dedendum, b
Radial distance from the depth of the tooth trough to the pitch surface. b = (D −
rootdiameter) / 2
Whole depth, ht
The distance from the top of the tooth to the root; it is equal to addendum plus
dedendum or to working depth plus clearance.
Distance between the root circle of a gear and the addendum circle of its mate.
Working depth
Depth of engagement of two gears, that is, the sum of their operating addendums.
Circular pitch, p
Distance from one face of a tooth to the corresponding face of an adjacent tooth
on the same gear, measured along the pitch circle.
Diametral pitch, pd
Ratio of the number of teeth to the pitch diameter. Could be measured in teeth per
inch or teeth per centimeter.
Base circle
In involute gears, where the tooth profile is the involute of the base circle. The
radius of the base circle is somewhat smaller than that of the pitch circle.
Base pitch, normal pitch, pb
In involute gears, distance from one face of a tooth to the corresponding face of
an adjacent tooth on the same gear, measured along the base circle.
Contact between teeth other than at the intended parts of their surfaces.
Interchangeable set
A set of gears, any of which will mate properly with any other.
Helical gear nomenclature
Helix angle, ψ
Angle between a tangent to the helix and the gear axis. It is zero in the limiting
case of a spur gear, albeit it can considered as the hypotenuse angle as well.
Normal circular pitch, pn
Circular pitch in the plane normal to the teeth.
Transverse circular pitch, p
Circular pitch in the plane of rotation of the gear. Sometimes just called "circular
pitch". pn = pcos(ψ)
Several other helix parameters can be viewed either in the normal or transverse planes.
The subscript n usually indicates the normal.
Worm gear nomenclature
Distance from any point on a thread to the corresponding point on the next turn of
the same thread, measured parallel to the axis.
Linear pitch, p
Distance from any point on a thread to the corresponding point on the adjacent
thread, measured parallel to the axis. For a single-thread worm, lead and linear
pitch are the same.
Lead angle, λ
Angle between a tangent to the helix and a plane perpendicular to the axis. Note
that it is the complement of the helix angle which is usually given for helical
Pitch diameter, dw
Same as described earlier in this list. Note that for a worm it is still measured in a
plane perpendicular to the gear axis, not a tilted plane.
Subscript w denotes the worm, subscript g denotes the gear.
Tooth contact nomenclature
Line of contact
Path of action
Line of action
Plane of action
Lines of contact (helical gear)
Arc of action
Length of action
Limit diameter
Face advance
Zone of action
Point of contact
Any point at which two tooth profiles touch each other.
Line of contact
A line or curve along which two tooth surfaces are tangent to each other.
Path of action
The locus of successive contact points between a pair of gear teeth, during the
phase of engagement. For conjugate gear teeth, the path of action passes through
the pitch point. It is the trace of the surface of action in the plane of rotation.
Line of action
The path of action for involute gears. It is the straight line passing through the
pitch point and tangent to both base circles.
Surface of action
The imaginary surface in which contact occurs between two engaging tooth
surfaces. It is the summation of the paths of action in all sections of the engaging
Plane of action
The surface of action for involute, parallel axis gears with either spur or helical
teeth. It is tangent to the base cylinders.
Zone of action (contact zone)
For involute, parallel-axis gears with either spur or helical teeth, is the rectangular
area in the plane of action bounded by the length of action and the effective face
Path of contact
The curve on either tooth surface along which theoretical single point contact
occurs during the engagement of gears with crowned tooth surfaces or gears that
normally engage with only single point contact.
Length of action
The distance on the line of action through which the point of contact moves
during the action of the tooth profile.
Arc of action, Qt
The arc of the pitch circle through which a tooth profile moves from the
beginning to the end of contact with a mating profile.
Arc of approach, Qa
The arc of the pitch circle through which a tooth profile moves from its beginning
of contact until the point of contact arrives at the pitch point.
Arc of recess, Qr
The arc of the pitch circle through which a tooth profile moves from contact at the
pitch point until contact ends.
Contact ratio, mc, ε
The number of angular pitches through which a tooth surface rotates from the
beginning to the end of contact.In a simple way, it can be defined as a measure of
the average number of teeth in contact during the period in which a tooth comes
and goes out of contact with the mating gear.
Transverse contact ratio, mp, εα
The contact ratio in a transverse plane. It is the ratio of the angle of action to the
angular pitch. For involute gears it is most directly obtained as the ratio of the
length of action to the base pitch.
Face contact ratio, mF, εβ
The contact ratio in an axial plane, or the ratio of the face width to the axial pitch.
For bevel and hypoid gears it is the ratio of face advance to circular pitch.
Total contact ratio, mt, εγ
The sum of the transverse contact ratio and the face contact ratio.
εγ = εα + εβ
mt = mp + mF
Modified contact ratio, mo
For bevel gears, the square root of the sum of the squares of the transverse and
face contact ratios.
Limit diameter
Diameter on a gear at which the line of action intersects the maximum (or
minimum for internal pinion) addendum circle of the mating gear. This is also
referred to as the start of active profile, the start of contact, the end of contact, or
the end of active profile.
Start of active profile (SAP)
Intersection of the limit diameter and the involute profile.
Face advance
Distance on a pitch circle through which a helical or spiral tooth moves from the
position at which contact begins at one end of the tooth trace on the pitch surface
to the position where contact ceases at the other end.
Tooth thickness nomeclature
Tooth thickness
Thickness relationships
Chordal thickness
Tooth thickness measurement over pins
Span measurement
Long and short addendum teeth
Circular thickness
Length of arc between the two sides of a gear tooth, on the specified datum circle.
Transverse circular thickness
Circular thickness in the transverse plane.
Normal circular thickness
Circular thickness in the normal plane. In a helical gear it may be considered as
the length of arc along a normal helix.
Axial thickness
In helical gears and worms, tooth thickness in an axial cross section at the
standard pitch diameter.
Base circular thickness
In involute teeth, length of arc on the base circle between the two involute curves
forming the profile of a tooth.
Normal chordal thickness
Length of the chord that subtends a circular thickness arc in the plane normal to
the pitch helix. Any convenient measuring diameter may be selected, not
necessarily the standard pitch diameter.
Chordal addendum (chordal height)
Height from the top of the tooth to the chord subtending the circular thickness arc.
Any convenient measuring diameter may be selected, not necessarily the standard
pitch diameter.
Profile shift
Displacement of the basic rack datum line from the reference cylinder, made nondimensional by dividing by the normal module. It is used to specify the tooth
thickness, often for zero backlash.
Rack shift
Displacement of the tool datum line from the reference cylinder, made nondimensional by dividing by the normal module. It is used to specify the tooth
Measurement over pins
Measurement of the distance taken over a pin positioned in a tooth space and a
reference surface. The reference surface may be the reference axis of the gear, a
datum surface or either one or two pins positioned in the tooth space or spaces
opposite the first. This measurement is used to determine tooth thickness.
Span measurement
Measurement of the distance across several teeth in a normal plane. As long as the
measuring device has parallel measuring surfaces that contact on an unmodified
portion of the involute, the measurement will be along a line tangent to the base
cylinder. It is used to determine tooth thickness.
Modified addendum teeth
Teeth of engaging gears, one or both of which have non-standard addendum.
Full-depth teeth
Teeth in which the working depth equals 2.000 divided by the normal diametral
Stub teeth
Teeth in which the working depth is less than 2.000 divided by the normal
diametral pitch.
Equal addendum teeth
Teeth in which two engaging gears have equal addendums.
Long and short-addendum teeth
Teeth in which the addendums of two engaging gears are unequal.
Pitch nomenclature
Pitch is the distance between a point on one tooth and the corresponding point on an
adjacent tooth. It is a dimension measured along a line or curve in the transverse, normal,
or axial directions. The use of the single word pitch without qualification may be
ambiguous, and for this reason it is preferable to use specific designations such as
transverse circular pitch, normal base pitch, axial pitch.
Tooth pitch
Base pitch relationships
Principal pitches
Circular pitch, p
Arc distance along a specified pitch circle or pitch line between corresponding
profiles of adjacent teeth.
Transverse circular pitch, pt
Circular pitch in the transverse plane.
Normal circular pitch, pn, pe
Circular pitch in the normal plane, and also the length of the arc along the normal
pitch helix between helical teeth or threads.
Axial pitch, px
Linear pitch in an axial plane and in a pitch surface. In helical gears and worms,
axial pitch has the same value at all diameters. In gearing of other types, axial
pitch may be confined to the pitch surface and may be a circular measurement.
The term axial pitch is preferred to the term linear pitch. The axial pitch of a
helical worm and the circular pitch of its worm gear are the same.
Normal base pitch, pN, pbn
An involute helical gear is the base pitch in the normal plane. It is the normal
distance between parallel helical involute surfaces on the plane of action in the
normal plane, or is the length of arc on the normal base helix. It is a constant
distance in any helical involute gear.
Transverse base pitch, pb, pbt
In an involute gear, the pitch on the base circle or along the line of action.
Corresponding sides of involute gear teeth are parallel curves, and the base pitch
is the constant and fundamental distance between them along a common normal
in a transverse plane.
Diametral pitch (transverse), Pd
Ratio of the number of teeth to the standard pitch diameter in inches.
Normal diametral pitch, Pnd
Value of diametral pitch in a normal plane of a helical gear or worm.
Angular pitch, θN, τ
Angle subtended by the circular pitch, usually expressed in radians.
degrees or
Backlash is the error in motion that occurs when gears change direction. It exists because
there is always some gap between the trailing face of the driving tooth and the leading
face of the tooth behind it on the driven gear, and that gap must be closed before force
can be transferred in the new direction. The term "backlash" can also be used to refer to
the size of the gap, not just the phenomenon it causes; thus, one could speak of a pair of
gears as having, for example, "0.1 mm of backlash." A pair of gears could be designed to
have zero backlash, but this would presuppose perfection in manufacturing, uniform
thermal expansion characteristics throughout the system, and no lubricant. Therefore,
gear pairs are designed to have some backlash. It is usually provided by reducing the
tooth thickness of each gear by half the desired gap distance. In the case of a large gear
and a small pinion, however, the backlash is usually taken entirely off the gear and the
pinion is given full sized teeth. Backlash can also be provided by moving the gears
farther apart.
For situations, such as instrumentation and control, where precision is important,
backlash can be minimised through one of several techniques. For instance, the gear can
be split along a plane perpendicular to the axis, one half fixed to the shaft in the usual
manner, the other half placed alongside it, free to rotate about the shaft, but with springs
between the two halves providing relative torque between them, so that one achieves, in
effect, a single gear with expanding teeth. Another method involves tapering the teeth in
the axial direction and providing for the gear to be slid in the axial direction to take up
Shifting of gears
In some machines (e.g., automobiles) it is necessary to alter the gear ratio to suit the task.
There are several methods of accomplishing this. For example:
Manual transmission
Automatic transmission
Derailleur gears which are actually sprockets in combination with a roller chain
Hub gears (also called epicyclic gearing or sun-and-planet gears)
There are several outcomes of gear shifting in motor vehicles. In the case of vehicle noise
emissions, there are higher sound levels emitted when the vehicle is engaged in lower
gears. The design life of the lower ratio gears is shorter so cheaper gears may be used (i.e.
spur for 1st and reverse) which tends to generate more noise due to smaller overlap ratio
and a lower mesh stiffness etc than the helical gears used for the high ratios. This fact has
been utilized in analyzing vehicle generated sound since the late 1960s, and has been
incorporated into the simulation of urban roadway noise and corresponding design of
urban noise barriers along roadways.
Tooth profile
Profile of a spur gear
A profile is one side of a tooth in a cross section between the outside circle and the root
circle. Usually a profile is the curve of intersection of a tooth surface and a plane or
surface normal to the pitch surface, such as the transverse, normal, or axial plane.
The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the
bottom of the tooth space.2
As mentioned in the beginning, the attainment of a non fluctuating velocity ratio is
dependent on the profile of the teeth. Friction and wear between two gears is also
dependent on the tooth profile. There are a great many tooth profiles that will give a
constant velocity ratio, and in many cases, given an arbitrary tooth shape, it is possible to
develop a tooth profile for the mating gear that will give a constant velocity ratio.
However, two constant velocity tooth profiles have been by far the most commonly used
in modern times. They are the cycloid and the involute. The cycloid was more common
until the late 1800s; since then the involute has largely superseded it, particularly in drive
train applications. The cycloid is in some ways the more interesting and flexible shape;
however the involute has two advantages: it is easier to manufacture, and it permits the
center to center spacing of the gears to vary over some range without ruining the
constancy of the velocity ratio. Cycloidal gears only work properly if the center spacing
is exactly right. Cycloidal gears are still used in mechanical clocks.
An undercut is a condition in generated gear teeth when any part of the fillet curve lies
inside of a line drawn tangent to the working profile at its point of juncture with the fillet.
Undercut may be deliberately introduced to facilitate finishing operations. With undercut
the fillet curve intersects the working profile. Without undercut the fillet curve and the
working profile have a common tangent.
Gear materials
Wooden gears of a historic windmill
Numerous nonferrous alloys, cast irons, powder-metallurgy and even plastics are used in
the manufacture of gears. However steels are most commonly used because of their high
strength to weight ratio and low cost. Plastic is commonly used where cost or weight is a
concern. A properly designed plastic gear can replace steel in many cases because it has
many desirable properties, including dirt tolerance, low speed meshing, and the ability to
"skip" quite well. Manufacturers have employed plastic gears to make consumer items
affordable in items like copy machines, optical storage devices, VCRs, cheap dynamos,
consumer audio equipment, servo motors, and printers.
The module system
Countries which have adopted the metric system generally use the module system. As a
result, the term module is usually understood to mean the pitch diameter in millimeters
divided by the number of teeth. When the module is based upon inch measurements, it is
known as the English module to avoid confusion with the metric module. Module is a
direct dimension, whereas diametral pitch is an inverse dimension (like "threads per
inch"). Thus, if the pitch diameter of a gear is 40 mm and the number of teeth 20, the
module is 2, which means that there are 2 mm of pitch diameter for each tooth.
Gear Cutting simulation faster, high bitrate version.
Gears are most commonly produced via hobbing, but they are also shaped, broached,
cast, and in the case of plastic gears, injection molded. For metal gears the teeth are
usually heat treated to make them hard and more wear resistant while leaving the core
soft and tough. For large gears that are prone to warp a quench press is used.
Gear geometry can be inspected and verified using various methods such as industrial CT
scanning, coordinate-measuring machines, white light scanner or laser scanning.
Particularly useful for plastic gears, industrial CT scanning can inspect internal geometry
and imperfections such as porosity.
Gear model in modern physics
Modern physics adopted the gear model in different ways. In the nineteenth century,
James Clerk Maxwell developed a model of electromagnetism in which magnetic field
lines were rotating tubes of incompressible fluid. Maxwell used a gear wheel and called it
an "idle wheel" to explain the electrical current as a rotation of particles in opposite
directions to that of the rotating field lines.
More recently, quantum physics uses "quantum gears" in their model. A group of gears
can serve as a model for several different systems, such as an artificially constructed
nanomechanical device or a group of ring molecules.
The Three Wave Hypothesis compares the wave–particle duality to a bevel gear.
Chapter 2
Bevel Gear
Bevel gears are gears where the axes of the two shafts intersect and the tooth-bearing
faces of the gears themselves are conically shaped. Bevel gears are most often mounted
on shafts that are 90 degrees apart, but can be designed to work at other angles as well.
The pitch surface of bevel gears is a cone.
Bevel gear on roller shutter door.
Independently from the operating angle, the gear axes must intersect (at the point O)
Bevel gear lifts floodgate by means of central screw.
Bevel ring gear on the rear wheel of a shaft-driven bicycle
Spiral bevel gear - ZF Friedrichshafen
Two important concepts in gearing are pitch surface and pitch angle. The pitch surface
of a gear is the imaginary toothless surface that you would have by averaging out the
peaks and valleys of the individual teeth. The pitch surface of an ordinary gear is the
shape of a cylinder. The pitch angle of a gear is the angle between the face of the pitch
surface and the axis.
The most familiar kinds of bevel gears have pitch angles of less than 90 degrees and
therefore are cone-shaped. This type of bevel gear is called external because the gear
teeth point outward. The pitch surfaces of meshed external bevel gears are coaxial with
the gear shafts; the apexes of the two surfaces are at the point of intersection of the shaft
Bevel gears that have pitch angles of greater than ninety degrees have teeth that point
inward and are called internal bevel gears.
Bevel gears that have pitch angles of exactly 90 degrees have teeth that point outward
parallel with the axis and resemble the points on a crown. That's why this type of bevel
gear is called a crown gear.
Miter gears are mating bevel gears with equal numbers of teeth and with axes at right
Skew bevel gears are those for which the corresponding crown gear has teeth that are
straight and oblique.
There are two issues regarding tooth shape. One is the cross-sectional profile of the
individual tooth. The other is the line or curve on which the tooth is set on the face of the
gear: in other words the line or curve along which the cross-sectional profile is projected
to form the actual three-dimensional shape of the tooth. The primary effect of both the
cross-sectional profile and the tooth line or curve is on the smoothness of operation of the
gears. Some result in a smoother gear action than others.
Tooth line
The teeth on bevel gears can be straight, spiral or "zero".
Straight tooth lines
In straight bevel gears the teeth are straight and parallel to the generators of the cone.
This is the simplest form of bevel gear. It resembles a spur gear, only conical rather than
cylindrical. The gears in the floodgate picture are straight bevel gears. In straight, when
each tooth engages it impacts the corresponding tooth and simply curving the gear teeth
can solve the problem.
Spiral tooth lines
Spiral bevel gears have their teeth formed along spiral lines. They are somewhat
analogous to cylindrical type helical gears in that the teeth are angled; however with
spiral gears the teeth are also curved.
The advantage of the spiral tooth over the straight tooth is that they engage more
gradually. The contact between the teeth starts at one end of the gear and then spreads
across the whole tooth. This results in a less abrupt transfer of force when a new pair of
teeth come in to play. With straight bevel gears, the abrupt tooth engagement causes
noise, especially at high speeds, and impact stress on the teeth which makes them unable
to take heavy loads at high speeds without breaking. For these reasons straight bevel
gears are generally limited to use at linear speeds less than 1000 feet/min; or, for small
gears, under 1000 r.p.m.
Zero tooth lines
Zero bevel gears are an intermediate type between straight and spiral bevel gears. Their
teeth are curved, but not angled.
The bevel gear has many diverse applications such as locomotives, marine applications,
automobiles, printing presses, cooling towers, power plants, steel plants, railway track
inspection machines, etc.
For examples :
Bevel gears are used in differential drives, which can transmit power to two
axles spinning at different speeds, such as those on a cornering automobile.
Bevel gears are used as the main mechanism for a hand drill. As the handle of
the drill is turned in a vertical direction, the bevel gears change the rotation of the
chuck to a horizontal rotation. The bevel gears in a hand drill have the added
advantage of increasing the speed of rotation of the chuck and this makes it
possible to drill a range of materials.
The gears in a bevel gear planer permit minor adjustment during assembly and
allow for some displacement due to deflection under operating loads without
concentrating the load on the end of the tooth.
Spiral bevel gears are important components on rotorcraft drive systems. These
components are required to operate at high speeds, high loads, and for a large
number of load cycles. In this application, spiral bevel gears are used to redirect
the shaft from the horizontal gas turbine engine to the vertical rotor.
Bevel gears on grain mill at Dordrecht. Note wooden teeth inserts on one of the gears.
This gear makes it possible to change the operating angle.
Differing of the number of teeth (effectively diameter) on each wheel allows
mechanical advantage to be changed. By increasing or decreasing the ratio of
teeth between the drive and driven wheels one may change the ratio of rotations
between the two, meaning that the rotational drive and torque of the second wheel
can be changed in relation to the first, with speed increasing and torque
decreasing, or speed decreasing and torque increasing.
One wheel of such gear is designed to work with its complementary wheel and no
Must be precisely mounted.
The axes must be capable of supporting significant forces.
Chapter 3
Spiral Bevel Gear and Herringbone Gear
Spiral bevel gear
Spiral bevel handedness
Zerol handedness
A spiral bevel gear is a bevel gear with helical teeth. The main application of this is in a
vehicle differential, where the direction of drive from the drive shaft must be turned 90
degrees to drive the wheels. The helical design produces less vibration and noise than
conventional straight-cut or spur-cut gear with straight teeth.
A spiral bevel gear set should always be replaced in pairs i.e. both the left hand and right
hand gears should be replaced together since the gears are manufactured and lapped in
A right hand spiral bevel gear is one in which the outer half of a tooth is inclined in the
clockwise direction from the axial plane through the midpoint of the tooth as viewed by
an observer looking at the face of the gear.
A left hand spiral bevel gear is one in which the outer half of a tooth is inclined in the
counterclockwise direction from the axial plane through the midpoint of the tooth as
viewed by an observer looking at the face of the gear.
Note that a spiral bevel gear and pinion are always of opposite hand, including the case
when the gear is internal.
Also note that the designations right hand and left hand are applied similarly to other
types of bevel gear, hypoid gears, and oblique tooth face gears.
Hypoid gears
A hypoid is a type of spiral bevel gear whose axis does not intersect with the axis of the
meshing gear. The shape of a hypoid gear is a revolved hyperboloid (that is, the pitch
surface of the hypoid gear is a hyperbolic surface), whereas the shape of a spiral bevel
gear is normally conical. The hypoid gear places the pinion off-axis to the crown wheel
(ring gear) which allows the pinion to be larger in diameter and have more contact area.
In hypoid gear design, the pinion and gear are practically always of opposite hand, and
the spiral angle of the pinion is usually larger than that of the gear. The hypoid pinion is
then larger in diameter than an equivalent bevel pinion.
A hypoid gear incorporates some sliding and can be considered halfway between a
straight-cut gear and a worm gear. Special gear oils are required for hypoid gears because
the sliding action requires effective lubrication under extreme pressure between the teeth.
Hypoid gearings are used in power transmission products that are more efficient than
conventional worm gearing.
Spiral angle
Spiral angle
The spiral angle in a spiral bevel gear is the angle between the tooth trace and an element
of the pitch cone, and corresponds to the helix angle in helical teeth. Unless otherwise
specified, the term spiral angle is understood to be the mean spiral angle.
Mean spiral angle is the specific designation for the spiral angle at the mean cone
distance in a bevel gear.
Outer spiral angle is the spiral angle of a bevel gear at the outer cone distance.
Inner spiral angle is the spiral angle of a bevel gear at the inner cone distance.
Spiral angle relationships
Comparison of spiral bevel gears to hypoid gears
Hypoid gears are stronger, operate more quietly and can be used for higher reduction
ratios, however they also have some sliding action along the teeth, which reduces
mechanical efficiency, the energy losses being in the form of heat produced in the gear
surfaces and the lubricating fluid.
In older automotive designs, hypoid gears were typically used in rear-drive automobile
drivetrains, but modern designs have tended to substitute spiral bevel gears to increase
driving efficiency.
Hypoid gears are still common in larger trucks because they can transmit higher torque.
A higher hypoid offset allows the gear to transmit higher torque. However increasing the
hypoid offset results in reduction of mechanical efficiency and a consequent reduction in
fuel economy. For practical purposes, it is often impossible to replace low efficiency
hypoid gears with more efficient spiral bevel gears in automotive use because the spiral
bevel gear would need a much larger diameter to transmit the same torque. Increasing the
size of the drive axle gear would require an increase of the size of the gear housing and a
reduction in the ground clearance.
Another advantage of hypoid gear is that the ring gear of the differential and the input
pinion gear are both hypoid. In most passenger cars this allows the pinion to be offset to
the bottom of the crown wheel. This provides for longer tooth contact and allows the
shaft that drives the pinion to be lowered, reducing the "hump" intrusion in the passenger
compartment floor. However, the greater the displacement of the input shaft axis from the
crown wheel axis, the lower the mechanical efficiency.
Hypoid gear in a differential
Herringbone gear
A herringbone gear, also known as a double helical gear, is a special type of gear
which is a side to side (not face to face) combination of two helical gears of opposite
hands. Unlike helical gears they can sustain axial load smoothly. From the top the helical
grooves of this gear looks like letter V.
Like helical gears, they have the advantage of transferring power smoothly as multiple
gear teeth engage and disengage simultaneously. Their advantage over the helical gears is
that the side-thrust of one half is balanced by that of the other half. This means that
herringbone gears can be used in torque gearboxes without requiring a substantial thrust
bearing. Because of this herringbone gears were an important step in the introduction of
the steam turbine to marine propulsion.
Precision herringbone gears are more difficult to manufacture than equivalent spur or
helical gears and consequently are more expensive. They are used in heavy machinery.
Where the oppositely angled teeth meet in the middle of a herringbone gear, the
alignment may be such that tooth tip meets tooth tip, or the alignment may be staggered,
so that tooth tip meets tooth trough. The latter alignment is the unique defining
characteristic of a Wuest type herringbone gear, named after its inventor.
With the older method of fabrication, herringbone gears had a central channel separating
the two oppositely-angled courses of teeth. This was necessary to permit the shaving tool
to run out of the groove. The development of the Sykes gear shaper made it possible to
have continuous teeth, with no central gap. After the W.E. Sykes and Farrel Gear
Machine companies dissolved in 1983-84 there are no current production machines that
have this ability. It is standard industry practice to obtain an older machine and rebuild it
if necessary to create this unique type of gear. A disadvantage of the herringbone gear is
that it cannot be cut by simple gear hobbing machines, as the cutter would run into the
other half of the gear. Solutions to this have included assembling small gears by stacking
two helical gears together, cutting the gears with a central groove to provide clearance,
and (particularly in the early days) by casting the gears to an accurate pattern and without
further machining.
The logo of the car maker Citroën is a graphic representation of a herringbone gear, it
comes from Andre Citroën's early involvement in the manufacture of these gears.
Chapter 4
Worm Drive
Worm and worm gear
A worm drive is a gear arrangement in which a worm (which is a gear in the form of a
screw) meshes with a worm gear (which is similar in appearance to a spur gear, and is
also called a worm wheel). The terminology is often confused by imprecise use of the
term worm gear to refer to the worm, the worm gear, or the worm drive as a unit.
Like other gear arrangements, a worm drive can reduce rotational speed or allow higher
torque to be transmitted. The image shows a section of a gear box with a worm gear
being driven by a worm. A worm is an example of a screw, one of the six simple
Worm gear with 4-start worm
A gearbox designed using a worm and worm-wheel will be considerably smaller than one
made from plain spur gears and has its drive axes at 90° to each other. With a single start
worm, for each 360° turn of the worm, the worm-gear advances only one tooth of the
gear. Therefore, regardless of the worm's size (sensible engineering limits
notwithstanding), the gear ratio is the "size of the worm gear - to - 1". Given a single start
worm, a 20 tooth worm gear will reduce the speed by the ratio of 20:1. With spur gears, a
gear of 12 teeth (the smallest size permissible, if designed to good engineering practices)
would have to be matched with a 240 tooth gear to achieve the same ratio of 20:1.
Therefore, if the diametrical pitch (DP) of each gear was the same, then, in terms of the
physical size of the 240 tooth gear to that of the 20 tooth gear, the worm arrangement is
considerably smaller in volume.
A double bass features worm gears as tuning mechanisms
There are three different types of gears that can go in a worm drive.
The first are non-throated worm gears. These don't have a throat, or groove, machined
around the circumference around either the worm or worm wheel. The second are singlethroated worm gears,in which the worm wheel is throated. The final type are doublethroated worm gears, which have both gears throated. This type of gearing can support
the highest loading.
An enveloping (hourglass) worm has one or more teeth and increases in diameter from its
middle portion toward both ends.
Double-enveloping wormgearing comprises enveloping worms mated with fully
enveloping wormgears. It is also known as globoidal wormgearing.
Direction of transmission
Unlike with ordinary gear trains, the direction of transmission (input shaft vs output
shaft) is not reversible when using large reduction ratios, due to the greater friction
involved between the worm and worm-wheel, when usually a single start (one spiral)
worm is used. This can be an advantage when it is desired to eliminate any possibility of
the output driving the input. If a multistart worm (multiple spirals) then the ratio reduces
accordingly and the braking effect of a worm and worm-gear may need to be discounted
as the gear may be able to drive the worm.
Worm gear configurations in which the gear can not drive the worm are said to be selflocking. Whether a worm and gear will be self-locking depends on the lead angle, the
pressure angle, and the coefficient of friction; however, it is approximately correct to say
that a worm and gear will be self-locking if the tangent of the lead angle is less than the
coefficient of friction.
A worm drive controlling a gate. The position of the gate will not change after being set
In early 20th century automobiles prior to the introduction of power steering, the effect of
a flat or blowout on one of the front wheels will tend to pull the steering mechanism
toward the side with the flat tire. The employment of a worm screw reduced this effect.
Further development of the worm drive employs recirculating ball bearings to reduce
frictional forces, allowing some of the steering force to be felt in the wheel as an aid to
vehicle control and greatly reducing wear, which leads to difficulties in steering
Worm drives are a compact means of substantially decreasing speed and increasing
torque. Small electric motors are generally high-speed and low-torque; the addition of a
worm drive increases the range of applications that it may be suitable for, especially
when the worm drive's compactness is considered.
Worm drives are used in presses, in rolling mills, in conveying engineering, in mining
industry machines, and on rudders. In addition, milling heads and rotary tables are
positioned using high-precision duplex worm drives with adjustable backlash. Worm
gears are used on many lift- (in US English known as elevator) and escalator-drive
applications due to their compact size and the non-reversibility of the gear.
In the era of sailing ships, the introduction of a worm drive to control the rudder was a
significant advance. Prior to its introduction, a rope drum drive was used to control the
rudder, and rough seas could cause substantial force to be applied to the rudder, often
requiring several men to steer the vessel, with some drives having two large-diameter
wheels to allow up to four crewmen to operate the rudder.
Truck final drive of the 1930s
Worm drives have been used in a few automotive rear-axle final drives (although not the
differential itself at this time). They took advantage of the location of the gear being at
either the very top or very bottom of the differential crown wheel. In the 1910s they were
common on trucks; to gain the most clearance on muddy roads the worm gear was placed
on top. In the 1920s the Stutz firm used them on its cars; to have a lower floor than its
competitors, the gear was located on the bottom. An example from around 1960 was the
Peugeot 404. The worm gear carries the differential gearing, which protects the vehicle
against rollback. This ability has largely fallen from favour due to the higher-thannecessary reduction ratios.
A more recent exception to this is the Torsen differential, which uses worms and
planetary worm gears in place of the bevel gearing of conventional open differentials.
Torsen differentials are most prominently featured in the HMMWV and some
commercial Hummer vehicles, and as a center differential in some all wheel drive
systems, such as Audi's quattro. Very heavy trucks, such as those used to carry
aggregates, often use a worm gear differential for strength. The worm drive is not as
efficient as a hypoid gear, and such trucks invariably have a very large differential
housing, with a correspondingly large volume of gear oil, to absorb and dissipate the heat
Worm drives are used as the tuning mechanism for many musical instruments, including
guitars, double-basses, mandolins and bouzoukis, although not banjos, which use
planetary gears or friction pegs. A worm drive tuning device is called a machine head.
Plastic worm drives are often used on small battery-operated electric motors, to provide
an output with a lower angular velocity (fewer revolutions per minute) than that of the
motor, which operates best at a fairly high speed. This motor-worm-gear drive system is
often used in toys and other small electrical devices.
A worm drive is used on jubilee-type hose clamps or jubilee clamps; the tightening screw
has a worm thread which engages with the slots on the clamp band.
Occasionally a worm gear is designed to be run in reverse, resulting in the output shaft
turning much faster than the input. Examples of this may be seen in some hand-cranked
centrifuges or the wind governor in a musical box.
Left hand and right hand worm
Helical and worm handedness
A right hand helical gear or right hand worm is one in which the teeth twist clockwise as
they recede from an observer looking along the axis. The designations, right hand and left
hand, are the same as in the long established practice for screw threads, both external and
internal. Two external helical gears operating on parallel axes must be of opposite hand.
An internal helical gear and its pinion must be of the same hand.
A left hand helical gear or left hand worm is one in which the teeth twist
counterclockwise as they recede from an observer looking along the axis.
Worm wheels are first gashed to rough out the teeth and then hobbed to the final
Chapter 5
Epicyclic Gearing
Epicyclic gearing is used here for increasing output speed. The planet gear carrier (green)
is driven by an input torque. The sun gear (yellow) provides the output torque, while the
ring gear (red) is fixed. Note the red marks both before and after the input drive is rotated
45° clockwise.
Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer
gears, or planet gears, revolving about a central, or sun gear. Typically, the planet gears
are mounted on a movable arm or carrier which itself may rotate relative to the sun gear.
Epicyclic gearing systems also incorporate the use of an outer ring gear or annulus,
which meshes with the planet gears.
The axes of all gears are usually parallel, but for special cases like pencil sharpeners they
can be placed at an angle, introducing elements of bevel gear (see below). Further, the
sun, planet carrier and annulus axes are usually concentric.
Gear ratio
In this example, the carrier (green) is held stationary while the sun gear (yellow) is used
as input. The planet gears (blue) turn in a ratio determined by the number of teeth in each
gear. Here, the ratio is -24/16, or -3/2; each planet gear turns at 3/2 the rate of the sun
gear, in the opposite direction.
Reduction gears on Pratt & Whitney Canada PT6 gas turbine engine.
The gear ratio in an epicyclic gearing system is somewhat non-intuitive, particularly
because there are several ways in which an input rotation can be converted into an output
rotation. The three basic components of the epicyclic gear are:
Sun: The central gear
Planet carrier: Holds one or more peripheral planet gears, all of the same size,
meshed with the sun gear
Annulus: An outer ring with inward-facing teeth that mesh with the planet gear or
In many epicyclic gearing systems, one of these three basic components is held
stationary; one of the two remaining components is an input, providing power to the
system, while the last component is an output, receiving power from the system. The
ratio of input rotation to output rotation is dependent upon the number of teeth in each
gear, and upon which component is held stationary.
In other systems, such as hybrid vehicle transmissions, two of the components are used as
inputs with the third providing output relative to the two inputs.
One situation is when the planetary carrier is held stationary, and the sun gear is used as
input. In this case, the planetary gears simply rotate about their own axes at a rate
determined by the number of teeth in each gear. If the sun gear has Ns teeth, and each
planet gear has Np teeth, then the ratio is equal to -Ns/Np. For instance, if the sun gear
has 24 teeth, and each planet has 16 teeth, then the ratio is -24/16, or -3/2; this means that
one clockwise turn of the sun gear produces 1.5 counterclockwise turns of each of the
planet gear(s) about its axis.
This rotation of the planet gears can in turn drive the annulus, in a corresponding ratio. If
the annulus has Na teeth, then the annulus will rotate by Np/Na turns for each turn of the
planet gears. For instance, if the annulus has 64 teeth, and the planets 16, one clockwise
turn of a planet gear results in 16/64, or 1/4 clockwise turns of the annulus. Extending
this case from the one above:
One turn of the sun gear results in − Ns / Np turns of the planets
One turn of a planet gear results in Np / Na turns of the annulus
So, with the planetary carrier locked, one turn of the sun gear results in − Ns / Na turns of
the annulus.
The annulus may also be held fixed, with input provided to the planetary gear carrier;
output rotation is then produced from the sun gear. This configuration will produce an
increase in gear ratio, equal to 1+Na/Ns.
These are all described by the equation:
(2 + n)ωa + nωs − 2(1 + n)ωc = 0
where n is the form factor of the planetary gear, defined by:
n = Ns / Np
If the annulus is held stationary and the sun gear is used as the input, the planet carrier
will be the output. The gear ratio in this case will be 1/(1+Na/Ns). This is the lowest gear
ratio attainable with an epicyclic gear train. This type of gearing is sometimes used in
tractors and construction equipment to provide high torque to the drive wheels.
In bicycle hub gears, the sun is usually stationary, being keyed to the axle or even
machined directly onto it. The planetary gear carrier is used as input. In this case the gear
ratio is simply given by (Ns+Na)/Na. The number of teeth in the planet gear is irrelevant.
Compound planets of a Sturmey-Archer AM bicycle hub (gear ring removed)
Some designs use "compound planets" which have two differently-sized gears on either
end of a common casting. The large end engages the sun, while the small end engages the
annulus. This may be necessary to achieve smaller step changes in gear ratio when the
overall package size is limited. Compound planets have "timing marks" and must be
assembled in the correct initial orientation relative to each other, or their teeth will not
simultaneously engage the sun and annulus at opposite ends of the planet, leading to very
rough running and short life. The use of compound planets is like increasing the size of
the annulus; for example, compound planets with teeth in a 2:1 ratio with a 50T annulus
would give the same effect as a 100T annulus, but with half the actual diameter.
More planet and sun gear units can be placed in series in the same annulus housing
(where the output shaft of the first stage becomes the input shaft of the next stage)
providing a larger (or smaller) gear ratio. This is the way some automatic transmissions
During World War II, a special variation of epicyclic gearing was developed for portable
radar gear, where a very high reduction ratio in a small package was needed. This had
two outer annular gears, each half the thickness of the other gears. One of these two
annular gears was held fixed and had one tooth fewer than did the other. Therefore,
several turns of the "sun" gear made the "planet" gears complete a single revolution,
which in turn made the rotating annular gear rotate by a single tooth.
Split annulus, compound planet, epicyclic gears of a car rear-view mirror positioner
The mechanism of a pencil sharpener with stationary annulus and rotating planet carrier
as input. Planet gears are extended into cylindric cutters, rotating around the pencil that is
placed on the sun axis. The axis of planetary gears join at pencil sharpening angle.
Calculating the output from the input
It is first drawn simplified as the sun, a single planet, the annulus, and an arm holding the
planet. Any gear can be the input or output, including the arm.
Now, put in the known values and solve for ωring:
or you can use the other form of this equation:
where N is the number of teeth, ω is angular velocity of the element (sun, arm, or ring).
Since the angular velocity and rpm are directly proportional, you can use rpm instead.
However, if the arm is the input or output, say the ring is the output/input instead and
reverse the direction (since if the arm moves a certain speed relative to the ring, the ring
moves that same speed the other way relative to the arm, and obviously the arm does not
have a tooth count to plug in)
To derive this, just imagine the arm is locked, and calculate the gear ratio ωring / ωsun =
Nsun / Nring, then unlock the arm. From the arms reference frame the ratio is always
Nsun/Nring, but from your frame all the speeds are increased by the angular velocity of the
arm. So to write this relative relationship, you arrive at the equation from above.
Also, make sure Nsun+2Nplanet=Nring where N is the number of teeth. This simply says that
the gears will fit, since N is directly proportional to diameter.
Advantages and disadvantages
Advantages of planetary gears over parallel axis gears include high power density, large
reduction in a small volume, multiple kinematic combinations, pure torsional reactions,
and coaxial shafting. Disadvantages include high bearing loads, inaccessibility, and
design complexity. The planetary gearbox arrangement is an engineering design that
offers many advantages over traditional gearbox arrangements. One advantage is its
unique combination of both compactness and outstanding power transmission
efficiencies. A typical efficiency loss in a planetary gearbox arrangement is only 3% per
stage. This type of efficiency ensures that a high proportion of the energy being input is
transmitted through the gearbox, rather than being wasted on mechanical losses inside the
Another advantage of the planetary gearbox arrangement is load distribution. Because the
load being transmitted is shared between multiple planets, torque capability is greatly
increased. The more planets in the system, the greater load ability and the higher the
torque density.
The planetary gearbox arrangement also creates greater stability due to the even
distribution of mass and increased rotational stiffness.
Chapter 6
Harmonic Drive and Non-Circular Gear
Harmonic drive
Harmonic drive
A Harmonic Drive (also known as "Strain Wave Gearing") is a special type of
mechanical gear system that can improve certain characteristics compared to traditional
gearing systems (such as Helical Gears or Planetary Gears). It was invented in 1957 and
is now produced by Harmonic Drive LLC. The advantages include: no backlash,
compactness and light weight, high gear ratios, reconfigurable ratios within a standard
housing, good resolution and repeatability when repositioning inertial loads, high torque
capability, and coaxial input and output shafts. High gear reduction ratios are possible in
a small volume (a ratio of 100:1 is possible in the same space in which planetary gears
typically only produce a 10:1 ratio).
Disadvantages include a tendency for 'wind-up' (a torsional spring rate) and potential
degradation over time from mechanical shocks and environment.
They are typically used in industrial motion control, robotics and aerospace, for gear
reduction but may also be used to increase rotational speed, or for differential gearing.
The basic concept of Strain Wave Gearing (SWG) was introduced by C.W. Musser in his
1957 patent. It was first used successfully in 1964 by Hasegawa Gear Works, Ltd. and
USM Co., Ltd. Later, Hasegawa Gear Works, Ltd. became Harmonic Drive Systems Inc.
located in Japan and USM Co., Ltd. Harmonic Drive division became Harmonic Drive
Technologies Inc.
On January 1, 2006, Harmonic Drive Technologies/Nabtesco of Peabody, MA and HD
Systems of Hauppauge, NY, merged to form a new joint venture, Harmonic Drive LLC.
HD Systems, Inc. was a subsidiary company of Harmonic Drive System, Inc. Offices are
maintained in both Peabody and Hauppauge.
Cross-section of a Strain Wave Gearing.
A: circular spline (fixed)
B: flex spline (attached to output shaft, not shown)
C: wave generator (attached to input shaft, not shown)
The Strain Wave Gearing theory is based on elastic dynamics and utilizes the flexibility
of metal. The mechanism has three basic components: a wave generator, a flex spline,
and a circular spline. More complex versions have a fourth component normally used to
shorten the overall length or to increase the gear reduction within a smaller diameter, but
still follow the same basic principles.
The wave generator is made up of two separate parts: an elliptical disk called a wave
generator plug and an outer ball bearing. The gear plug is inserted into the bearing,
giving the bearing an elliptical shape as well.
The flex spline is like a shallow cup. The sides of the spline are very thin, but the bottom
is thick and rigid. This results in significant flexibility of the walls at the open end due to
the thin wall, but in the closed side being quite rigid and able to be tightly secured (to a
shaft, for example). Teeth are positioned radially around the outside of the flex spline.
The flex spline fits tightly over the wave generator, so that when the wave generator plug
is rotated, the flex spline deforms to the shape of a rotating ellipse but does not rotate
with the wave generator.
The circular spline is a rigid circular ring with teeth on the inside. The flex spline and
wave generator are placed inside the circular spline, meshing the teeth of the flex spline
and the circular spline. Because the flex spline has an elliptical shape, its teeth only
actually mesh with the teeth of the circular spline in two regions on opposite sides of the
flex spline, along the major axis of the ellipse.
Assume that the wave generator is the input rotation. As the wave generator plug rotates,
the flex spline teeth which are meshed with those of the circular spline change. The major
axis of the flex spline actually rotates with wave generator, so the points where the teeth
mesh revolve around the center point at the same rate as the wave generator. The key to
the design of the harmonic drive is that there are fewer teeth (for example two fewer) on
the flex spline than there are on the circular spline. This means that for every full rotation
of the wave generator, the flex spline would be required to rotate a slight amount (two
teeth, for example) backward relative to the circular spline. Thus the rotation action of the
wave generator results in a much slower rotation of the flex spline in the opposite
For a Strain Wave Gearing mechanism, the gearing reduction ratio can be calculated from
the number of teeth on each gear:
For example, if there are 202 teeth on the circular spline and 200 on the flex spline, the
reduction ratio is (200 − 202)/200 = −0.01
Thus the flex spline spins at 1/100 the speed of the wave generator plug and in the
opposite direction. This allows different reduction ratios to be set without changing the
mechanism's shape, increasing its weight, or adding stages. The range of possible gear
ratios is limited by teeth size limits for a given configuration.
Non-Circular gear
Non-circular gear example
Another non-circular gear
A non-circular gear (NCG) is a special gear design with special characteristics and
purpose. While a regular gear is optimized to transmit torque to another engaged member
with minimum noise and wear and with maximum efficiency, a non-circular gear's main
objective might be ratio variations, axle displacement oscillations and more. Common
applications include textile machines, potentiometers and CVTs (continuously variable
transmissions). Many bicycles have an elliptical gear, see, eg., Biopace.
A regular gear pair can be represented as two circles rolling together without slip. In the
case of non-circular gears, those circles are replaced with anything different from a circle.
This is also the reason NCG in most cases is not round, however round NCGs looking
like regular gears are possible too (small ratio variations result from meshing area
Generally NCG should meet all the requirements of regular gearing, but in some cases,
for example variable axle distance, could prove impossible to support and such gears
require very tight manufacturing tolerances and assembling problems arise. Because of
complicated geometry, NCGs are most likely spur gears and molding or electrical
discharge machining technology is used instead of generation.
Mathematical description
Ignoring the gear teeth for the moment (i.e. assuming the gear teeth are very small), let
r1(θ1) be the radius of the first gear wheel as a function of angle from the axis of rotation
θ1, and let r2(θ2) be the radius of the second gear wheel as a function of angle from its
axis of rotation θ2. If the axles remain fixed, the distance between the axles is also fixed:
Assuming that the point of contact lies on the line connecting the axles, in order for the
gears to touch without slipping, the velocity of each wheel must be equal at the point of
contact and perpendicular to the line connecting the axles, which implies that:
Of course, each wheel must be cyclic in its angular coordinates. If the shape of the first
wheel is known, the shape of the second can often be found using the above equations. If
the relationship between the angles is specified, the shapes of both wheels can often be
determined analytically as well.
It is more convenient to use the circular variable z = eiθ when analyzing this problem.
Assuming the radius of the first gear wheel is known as a function of z, and using the
, the above two equations can be combined to yield the
differential equation:
where z1 and z2 describe the rotation of the first and second gears respectively. This
equation can be formally solved as:
where ln(K) is a constant of integration.
Chapter 7
Backlash (Engineering)
In mechanical engineering, backlash, sometimes called lash or play, is clearance
between mating components, sometimes described as the amount of lost motion due to
clearance or slackness when movement is reversed and contact is re-established. For
example, in a pair of gears, backlash is the amount of clearance between mated gear
Theoretically, the backlash should be zero, but in actual practice some backlash must be
allowed to prevent jamming. It is unavoidable for nearly all reversing mechanical
couplings, although its effects can be negated. Depending on the application it may or
may not be desirable. Reasons for requiring backlash include allowing for lubrication,
manufacturing errors, deflection under load and thermal expansion.
Factors affecting the amount backlash required in a gear train include errors in profile,
pitch, tooth thickness, helix angle and center distance, and runout. The greater the
accuracy the smaller the backlash needed. Backlash is most commonly created by cutting
the teeth deeper into the gears than the ideal depth. Another way of introducing backlash
is by increasing the center distances between the gears.
Backlash due to tooth thickness changes is typically measured along the pitch circle and
is defined by:
= backlash due to tooth thickness modifications
= tooth thickness on the pitch circle for ideal gearing (no backlash)
= actual tooth thickness
Backlash, measured on the pitch circle, due to operating center modifications is defined
= backlash due to operating center distance modifications
= difference between actual and ideal operating center distances
= pressure angle
Standard practice is to make allowance for half the backlash in the tooth thickness of
each gear. However, if the pinion (the smaller of the two gears) is significantly smaller
than the gear it is meshing with then it is common practice to account for all of the
backlash in the larger gear. This maintains as much strength as possible in the pinion's
teeth. The amount of additional material removed when making the gears depends on the
pressure angle of the teeth. For a 14.5° pressure angle the extra distance the cutting tool is
moved in equals the amount of backlash desired. For a 20° pressure angle the distance
equals 0.73 times the amount of backlash desired.
As a rule of thumb the average backlash is defined as 0.04 divided by the diametral pitch;
the minimum being 0.03 and the maximum 0.05.
In a gear train, backlash is cumulative. When a gear-train is reversed the driving gear is
turned a short distance, equal to the total of all the backlashes, before the final driven gear
begins to rotate. At low power outputs, backlash results in inaccurate calculation from the
small errors introduced at each change of direction; at large power outputs backlash sends
shocks through the whole system and can damage teeth and other components.
Anti-backlash designs
In certain applications, backlash is an undesirable characteristic and should be
minimized; for example, a radio tuning dial where one may make precise tuning
movements both forwards and backwards. Specialised gear designs allow this. One of the
more common designs splits the gear into two gears, each half the thickness of the
original. One half of the gear is fixed to its shaft while the other half of the gear is
allowed to turn on the shaft, but pre-loaded in rotation by small coil springs that rotate the
free gear relative to the fixed gear. In this way, the spring tension rotates the free gear
until all of the backlash in the system has been taken out; the teeth of the fixed gear press
against one side of the teeth of the pinion while the teeth of the free gear press against the
other side of the teeth on the pinion. Loads smaller than the force of the springs do not
compress the springs and with no gaps between the teeth to be taken up, backlash is
High-precision main drives and positioning drives of CNC machine tools use duplex
worm gear sets for backlash adjustment.
In mechanical computers a more complex solution is required, namely a frontlash
gearbox. This works by turning slightly faster when the direction is reversed to 'use up'
the backlash slack.
Some motion controllers include backlash compensation. Compensation may be achieved
by simply adding extra compensating motion or by sensing the load's position in a closed
loop control scheme.The dynamic response of backlash itself, essentially a delay, makes
the position loop less stable and prone to oscillation.
Minimum backlash
Minimum backlash is the minimum transverse backlash at the operating pitch circle
allowable when the gear tooth with the greatest allowable functional tooth thickness is in
mesh with the pinion tooth having its greatest allowable functional tooth thickness, at the
tightest allowable center distance, under static conditions.
Difference between the maximum and minimum backlash occurring in a whole
revolution of the larger of a pair of mating gears.
Gear couplings use backlash to allow for angular misalignment.
Backlash is undesirable in precision positioning applications such as machine tool tables.
It can be minimized by tighter design features such as ball screws instead of leadscrews,
and by using preloaded bearings. A preloaded bearing uses a spring or other compressive
force to maintain bearing surfaces in contact despite reversal of direction.
There can be significant backlash in unsynchronized transmissions because of the
intentional gap between dog gears (also known as dog clutches). The gap is necessary so
that the driver or electronics can engage the gears easily while synchronizing the engine
speed with the driveshaft speed. If there was a small clearance, it would be nearly
impossible to engage the gears because the teeth would interfere with each other in most
configurations. In synchronized transmissions, synchromesh solves this problem.
Chapter 8
Derailleur Gears
Derailleur gears are a variable-ratio transmission system commonly used on bicycles,
consisting of a chain, multiple sprockets of different sizes, and a mechanism to move the
chain from one sprocket to another. Although referred to as gears in the bike world, these
bicycle gears, unlike the gears in an internally-geared hub, are technically sprockets since
they drive or are driven by a chain, and are not driven by one another.
Modern front and rear derailleurs typically consist of a moveable chain-guide that is
operated remotely by a Bowden cable attached to a shift lever mounted on the down tube,
handlebar stem, or handlebar. When a rider operates the lever while pedalling, the change
in cable tension moves the chain-guide from side to side, "derailing" the chain onto
different sprockets.
Various derailleur systems were designed and built in the late 1800s. The French bicycle
tourist, writer and cycling promoter Paul de Vivie (1853–1930), who wrote under the
name Velocio, invented a two speed rear derailleur in 1905 which he used on forays into
the Alps. Some early designs used rods to move the chain onto various gears. 1928 saw
the introduction of the "Super Champion Gear" (or "Osgear") from the company founded
by champion cyclist Oscar Egg, and the Vittoria Margherita; both employed chainstay
mounted 'paddles' and single lever chain tensioners mounted near or on the downtube.
However, these systems, along with the rod-operated Campagnolo Cambio Corsa were
eventually superseded by parallelogram derailleurs. In 1937, the derailleur system was
introduced to the Tour de France, allowing riders to change gears without having to
remove wheels. Previously, riders would have to dismount in order to change their wheel
from downhill to uphill mode. Derailleurs did not become common road racing
equipment until 1938 when Simplex introduced a cable-shifted derailleur.
In 1949 Campagnolo introduced the Gran Sport, a refined version of less commercially
successful cable-operated parallelogram rear derailleurs already existing.
A modern road bicycle drivetrain with front and rear derailleurs
In 1964, Suntour invented the slant-parallelogram rear derailleur, which let the jockey
pulley maintain a more constant distance from the different sized sprockets, resulting in
easier shifting. Once the patents expired, other manufacturers adopted this design, at least
for their better models, and the "slant parallelogram" remains the current rear derailleur
Before the 1990s many manufacturers made derailleurs, including Simplex, Huret, Galli,
Mavic, Gipiemme, Zeus, Suntour, and Shimano. However, the successful introduction
and promotion of indexed shifting by Shimano in 1985 required a compatible system of
shift levers, derailleur, cogset, chainrings, chain, shift cable, and shift housing. This need
for compatibility increased the use of groupsets made by one company, and was one of
the factors that drove the other manufacturers out of the market. Today Campagnolo and
Shimano are the two main manufacturers of derailleurs, with Campagnolo only making
road cycling derailleurs and Shimano making both road and offroad. American
manufacturer SRAM has been an important third, specializing in derailleurs for mountain
bikes, and in 2006 they introduced a drivetrain system for road bicycles.
Modern derailleur types
The major innovations since then have been the switch from friction to indexed shifting
and the gradual increase in the number of gears. With friction shifting, the rider first
moves the lever enough for the chain to jump to the next sprocket, and then adjusts the
lever a slight amount to center the chain on that sprocket. An indexed shifter has a detent
or ratchet mechanism which stops the gear lever, and hence the cable and the derailleur,
after moving a specific distances with each press or pull. Indexed shifters require recalibration when cables stretch and parts get damaged or swapped out. On racing
bicycles, 10-gear rear cassettes appeared in 2000, and 11-gear cassettes appeared in 2009.
Most current mountain bicycles have three front chainrings; while road bicycles may
have two or three.
Rear derailleurs
Campagnolo Super Record rear derailleur from 1983.
Shimano XT rear derailleur on a mountain bike
The rear derailleur serves double duty: moving the chain between rear sprockets and
taking up chain slack caused by moving to a smaller sprocket at the rear or a smaller
chainring by the front derailleur. In order to accomplish this second task, it is positioned
in the path of the bottom, slack portion of chain.
Although variations exist, as noted below, most rear derailleurs have several components
in common. They have a cage that holds two pulleys that guide the chain in an S-shaped
pattern. The pulleys are known as the jockey pulley or guide pulley (top) and the
tension pulley (bottom). The cage rotates in its plane and is spring-loaded to take up
chain slack. The cage is positioned under the desired sprocket by an arm that can swing
back and forth under the sprockets. The arm is usually implemented with a parallelogram
mechanism to keep the cage properly aligned with the chain as it swings back and forth.
The other end of the arm mounts to a pivot point attached to the bicycle frame. The arm
pivots about this point to maintain the cage at a nearly constant distance from the
different sized sprockets. There may be one or more adjustment screws that control the
amount of lateral travel allowed and the spring tension.
The components may be constructed of aluminum alloy, steel, plastic, or carbon fiber
composite. The pivot points may be bushings or ball bearings. These will require
moderate lubrication.
Relaxed position
High normal or top normal rear derailleurs return the chain to the smallest sprocket on
the cassette when no cable tension is applied. This is the regular pattern used on most
Shimano mountain, all Shimano road, and all SRAM and Campagnolo derailleurs. In this
condition, spring pressure takes care of the easier change to smaller sprockets. In road
racing the swiftest gear changes are required on the sprints to the finish line, hence highnormal types, which allow a quick change to a higher gear, remain the preference.
Low normal or rapid rise rear derailleurs return the chain to the largest sprocket on the
cassette when no cable tension is applied. While this was once a common design for rear
derailleurs, it is relatively uncommon today. In mountain biking and off-road cycling, the
most critical gear changes occur on uphill sections, where riders must cope with obstacles
and difficult turns while pedaling under heavy load. This derailleur type provides an
advantage over high normal derailleurs because gear changes to lower gears occur in the
direction of the loaded spring, making these shifts easier during high load pedaling.
Cage length
The distance between the upper and lower pulleys of a rear derailleur is known as the
cage length. Cage length determines the capacity of a derailleur to take up chain slack.
Cage length determines the total capacity of the derailleur, that is the size difference
between the largest and smallest chainrings, and the size difference between the largest
and smallest sprockets on the cogset added together. A larger sum requires a longer cage
length. Typical cross country mountain bikes with three front chainrings will use a long
cage rear derailleur. A road bike with only two front chainrings and close ratio sprockets
can operate with either a short or long cage derailleur, but will work better with a short
Manufacturer stated derailleur capacities are as follows: Shimano long = 45T; medium =
33T SRAM long = 43T; medium = 37T; short = 30T
Benefits of a shorter cage length:
more positive gear-changing due to less flex in the parallelogram
better gear-changing with good cable leverage
better obstruction clearance
less danger of catching spokes.
slight weight savings.
Cage positioning
There are at least two methods employed by rear derailleurs to maintain the appropriate
gap between the upper jockey wheel and the rear sprockets as the derailleur moves
between the large sprockets and the small sprockets.
One method, used by Shimano, is to use chain tension to pivot the cage.
This has the advantage of working with most sets of sprockets, if the chain
has the proper length. A disadvantage is that rapid shifts from small
sprockets to large over multiple sprockets at once can cause the cage to
strike the sprockets before the chain moves onto the larger sprockets and
pivots the cage as necessary.
Another method, used by SRAM, is to design the spacing into the
parallelogram mechanism of the derailleur itself. The advantage is that no
amount of rapid, multi-sprocket shifting can cause the cage to strike the
sprockets. The disadvantage is that there are limited options for sprocket
sizes that can be used with a particular derailleur.
Actuation ratio
Currently there are multiple conventions for the relationship between shifter travel and
rear derailleur travel, known as actuation ratios. The ratios, when given, are nominal,
and do not represent an exact ratio.
One convention, used by Shimano, is one-to-two (1:2). A unit of cable
moved in causes about twice as much movement of the derailleur.
Another convention, used by SRAM mountain bike rear derailleurs, is
one-to-one (1:1). A unit of cable moved in the shifter causes about an
equal amount to be moved in the derailleur. SRAM claims that this makes
their systems more robust: more accepting of contamination.
Exact Actuation, used by SRAM road bike rear derailleurs, similar but
different from the mountain ratio.
Campagnolo convention.
Suntour's convention.
Shifters employing one convention are generally not compatible with derailleurs
employing the other, although exceptions exist.
Front derailleurs
Shimano XT front derailleur (top pull, bottom swing, triple cage) on a mountain bike
Shimano E-type front derailleur (top pull, top swing, triple cage)
The front derailleur only has to move the chain side to side between the front chainrings,
but it has to do this with the top, taut portion of the chain. It also needs to accommodate
large differences in chainring size: from as many as 53 teeth to as few as 20 teeth.
As with the rear derailleur, the front derailleur has a cage through which the chain passes.
On a properly adjusted derailleur, the chain will only touch the cage while shifting. The
cage is held in place by a movable arm which is usually implemented with a
parallelogram mechanism to keep the cage properly aligned with the chain as it swings
back and forth. There are usually two adjustment screws controlling the limits of lateral
travel allowed.
The components may be constructed of aluminum alloy, steel, plastic, or carbon fiber
composite. The pivot points are usually bushings, and these will require lubrication.
Cable pull types
bottom pull
Commonly used on road and touring bikes, this type of derailleur is actuated by a
cable pulling downwards. The cable is often routed beneath the bottom bracket
shell on a plastic guide, which redirects the cable up the lower edge of the frame's
down tube. Full-suspension mountain bikes often have bottom pull routing as the
rear suspension prevents routing via the top tube .
top pull
This type is more commonly seen on mountain bikes without rear-suspension.
The derailleur is actuated by a cable pulling upwards, which is usually routed
along the frame's top tube, using cable stops and a short length of housing to
change the cable's direction. This arrangement keeps the cable away from the
underside of the bottom bracket/down tube which get pelted with dirt when offroad.
combination of both (dual pull)
There are some derailleurs available that have provisions for either top pull or
bottom pull, and can be used in either application.
Cage types
double (Standard)
These are intended to be used with cranksets having two chainrings. When
viewed from the side of the bicycle, the inner and outer plates of the cage have
roughly the same profile.
triple (Alpine)
Derailleurs designed to be used with cranksets having three chainrings, or with
two chainrings that differ greatly in size. When viewed from the side of the
bicycle, the inner cage plate extends further towards the bottom bracket's center of
rotation than the outer cage plate does. This is to help shift the chain from the
smallest ring onto the middle ring more easily.
Swing types
bottom swing
The derailleur cage is mounted to the bottom of the four-bar linkage that carries it.
This is the most common type of derailleur.
top swing
The derailleur cage is mounted to the top of the four-bar linkage that carries it.
This alternate arrangement was created as a way to get the frame clamp of the
derailleur closer to the bottom bracket to be able to clear larger suspension
components and allow different frame shapes. The compact construction of a top
swing derailleur can cause it to be less robust than its bottom swing counterpart.
Top swing derailleurs are typically only used in applications where a bottom
swing derailleur will not fit. An alternate solution would be to use an E-type front
derailleur, which does not clamp around the seat tube at all.
Mount types
The vast majority of front derailleurs are mounted to the frame by a clamp around
the frame's seat tube. Derailleurs are available with several different clamp
diameters designed to fit different types of frame tubing. Recently, there has been
a trend to make derailleurs with only one diameter clamp, and several sets of
shims are included to space the clamp down to the appropriate size.
An alternative to the clamp is the braze-on derailleur hanger, where the derailleur
is mounted by bolting a tab on the derailleur to a corresponding tab on the frame's
seat tube. This avoids any clamp size issues, but requires either a frame with the
appropriate braze-on, or an adapter clamp that simulates a braze-on derailleur tab.
This type front derailleurs do not clamp around the frame's seat tube, but instead
are attached to the frame by a plate mounted under the drive side bottom bracket
cup and a screw threaded into a boss on the seat tube. These derailleurs are
usually found on mountain bikes with rear suspension components that do not
allow space for a normal derailleur's clamp to go around the seat tube.
Direct-Mount-Derailleur - Initiated by Specialized Bicycles, this type of derailleur
is bolted directly to bosses on the chainstay of the bike. They are mostly used on
dual suspension mountain bikes, where suspension movement causes changes to
the chain angle as it enters the front derailleur cage. By utilizing a DMD system,
the chain and derailleur move together, allowing for better shifting when the
suspension is active. A DMD derailleur should not be confused with Shimano's
Direct Mount, which uses a different mounting system. However, SRAM's direct
mount front derailleurs are compatible with DMD, and certain Shimano E-type
derailleurs can be used with DMD if the e-type plate is removed.
Because of the possibility of the chain shifting past the smallest inner chainring,
especially when the inner chainring is very small, even on bikes adjusted by professional
race mechanics, and the problems such misshifts can cause, a small after-market of addon products, called chain deflectors, exists to help prevent them from occurring. Some
clamp around the seat tube, below the front derailleur, and at least one attaches to the
front derailleur mount.
Use of derailleurs
Derailleurs require the chain to be in movement, the rider pedalling, in order to change
ratio. This requires foresight in regular road-usage and commuting, changing down
(while still pedalling) on approaching a junction.
Chain-drive systems such as the derailleur systems work best if the chain is in line with
the sprockets, especially avoiding the biggest drive sprocket running with the biggest
driven sprocket (or the smallest with the smallest). The diagonal chain run produced by
these practices is less efficient and shortens the life of all components, with no advantage
from the middle of the range ratio obtained.
Hence, the change down should be one or two sprockets at the rear derailleur, followed
by a change at the front derailleur, followed by further changes at the rear. This advice
does not apply when forced to slow down quickly, when it is more convenient to change
down at the front derailleur first, getting a bigger difference in the easier direction, the
chain forced off a larger sprocket onto a smaller one.
Electronic gear-shifting system
Electrically actuated front derailleur
An electronic gear-shifting system is a derailleur system that uses electric motors
controlled by switches in place of traditional lever-and-cable actuation.
Chapter 9
Hub Gear
Hub gears or internal-gear hubs are gear ratio changing systems commonly used on
bicycles. Hub gear systems generally have a long and largely maintenance-free life
though some are not suitable for high-stress use in competitions or hilly, off-road
Many commuter or urban cycles such as European city bikes are now commonly fitted
with 7-speed gear-hubs and 8-speed systems are becoming increasingly available. Older
or less costly utility bicycles often use 3-speed gear-hubs, e.g. the public bicycle rental
programmes in Paris, Montreal, Lyon, London, and Washington, DC (Vélib', Bixi,
Vélo'v, Barclays Cycle Hire, and Capital Bikeshare). Many folding bicycles use 3-speed
gear-hubs. Modern developments with up to 14 gear ratios are available.
Gear-hubs use internal planetary or epicyclic gearing. Unlike derailleur gears, where the
gears and mechanism are exposed to the elements, hub gears and lubricants are sealed
within the hub-shell of the bicycle's rear wheel.
Changing the gear ratio was traditionally accomplished by a lever connected to the hub.
Twist-grip style shifters have become general.
In this simple epicyclic gear mechanism, the inner gear or "sun gear" (green) provides the
input rotation. The two "planet gears" (blue) rotate freely about the planet gear carrier
(yellow) which is fixed. As the planet gears rotate about the sun gear, they propel the
outer ring gear or "annulus" (red), which provides the output rotation
Before epicyclic gears were used in bicycle hubs, they were used on tricycles. Patents for
epicyclic hubs date from the mid-1880s. The first patent for a compact epicyclic hub gear
was granted in 1895 to the American machinist Seward Thomas Johnson of Noblesville,
Indiana, U.S.A. This was a 2-speed but was not commercially successful.
In 1896 William Reilly of Salford, England patented a 2-speed hub which went into
production in 1898 as 'The Hub'. It was a great success, remaining in production for a
decade. It rapidly established the practicality of compact epicyclic hub gears.
By 1902 Reilly had designed a 3-speed hub gear. He parted company with the
manufacturer of 'The Hub' but had signed away to them the intellectual rights to his
future gear designs. To circumvent this problem, the patents for Reilly's 3-speed were
obtained in the name of his colleague, James Archer. Meanwhile, well-known English
journalist and inventor Henry Sturmey had also invented a 3-speed hub. In 1903 Frank
Bowden, head of the Raleigh cycle company, formed The Three-Speed Gear Syndicate,
having obtained the rights to both the Reilly/Archer and Sturmey 3-speeds. Reilly's hub
went into production as the first Sturmey Archer 3-speed.
In 1902 Mikael Pedersen (who also produced the Dursley Pedersen bicycle) patented a 3speed hub gear and this was produced in 1903. This was said to be based on the "counter
shaft" principle but was arguably an unusual epicyclic gear, in which a second sun was
used in place of an annulus. In 1904 the Fichtel & Sachs company (Germany,
Schweinfurt) produced a hub gear under license to Wanderer, and by 1909 there were 14
different 3-speed hub gears on the British market.
By the 1930s hub gears were used on bicycles all over the world. They were particularly
popular in the UK, The Netherlands, the German speaking countries and Scandinavia.
Since the 1970s, they have become much less common in the English-speaking countries.
But in many parts of northern Europe, where bicycles are regularly used as daily
transport rather than merely for sport or leisure, hub gears are still widely used. The
cheaper and stronger (but less reliable) derailleur system now started to appear and offer
a wider gear range.
By 1987 Sturmey-Archer made only 3- and 5-speed hubs, and Fichtel & Sachs and
Shimano made only 2- and 3-speed hubs. In that year the first book (apart from service
manuals) for some 80 years dealing solely with epicyclic bicycle gears was published.
Since then there has been a slow but steady increase in interest in hub gears, reflected in
the wider range of products now available.
In 1995 Sachs introduced the Elan, the first hub gear with more than 12 speeds, and an
overall range of 339%. Three years later Rohloff came out with the Speedhub 500/14, a
gear hub with 14 speeds and a range of 526%, comparable to that of a 27 speed derailleur
gear system, and also sufficiently robust and light weight for mountain biking. In 2007
NuVinci started manufacturing stepless ∞-speed (CVT) hubs for commuter bicycles, with
a range of about 350%.
As of 2008, Sturmey-Archer makes 3-, 5- and 8-speed hubs, SRAM (successor to Fichtel
& Sachs) make 3-, 5-, 7- and 9-speeds and Shimano make 3-, 7- and 8-speeds. In
february 2010 Shimano announced the introduction of the Shimano Alfine 700, an 11speed model.
Though most hub gear systems use one rear sprocket, SRAM's DualDrive system
combines an epicyclic hub with a multi-speed rear derailleur system to provide a wideranging drivetrain concentrated at the rear wheel. In 2010 Canyon introduced the 1442, a
hybrid hub which uses a similar epicyclical/derailleur combination.
Brompton Bicycle have their own design, with a two-speed derailleur coupled to a special
three-speed wide-ratio Sturmey-Archer hub, the "BWR" (Brompton Wide Ratio). The
system is useful for folding bicycles (where a multiple front chainset could foul the bike's
folding mechanism) and in recumbent bicycles and freight bicycles (where small wheels
and/or increased weight require a wider range of gears with smaller steps). Hub gears
have in the past also been used on motorcycles, although this is now rare.
Principle of operation
The simplest 3-speed hubs use a single planetary epicyclic gearset. The sun gear is
mounted solidly to the axle and is thus fixed. In low gear, the sprocket drives the annulus,
while the planet carrier drives the hub, giving a gear reduction. In mid gear, the annulus
is connected to both the sprocket and hub, giving a direct drive. The planets cycle freely.
In high gear, the sprocket is switched to drive the planets, while the annulus remains
connected to the hub, giving an overdrive gear.
The hub axle of a hub-gear (unlike that of a derailleur system) must be securely braced
against rotation. While anti-rotation washers between the dropout and axle nut have often
proved adequate, better quality modern systems use a reaction arm affixed to the chain
stay. Rear wheels with drum brakes (another feature of better quality commuter bicycles)
require a reaction arm anyway.
This belt-drive on a Trek Soho is fitted with a sprocket too.
Hub-gear systems can change gear ratios when the rear wheel is stationary. This
can be useful for commuter cycling with frequent stops and for mountain biking
in rough terrain.
Hub-gear systems are simple to use for inexperienced riders, because there is
generally only a single shifter to operate and there are no overlapping gear ratios.
By contrast, modern derailleur systems often have two shifters, and require some
forethought to avoid problematic gear combinations.
The mechanism is sealed within the hub and bathed in a lubricant. This protects it
from water and grit.
The single chainline allows for a full chain enclosure chain guard, so the chain is
also protected from water and grit.
The single chainline does not require the chain to bend or twist. As a result, the
chain can be constructed differently, with parallel pins instead of barrel-shaped
ones. Line-contact between the bearing surfaces, instead the point-contact of a
derailleur chain, greatly extends the working life of all components.
The single external sprocket means that the wheel can be built with less dish
making it stronger than a similar wheel dished to accommodate multiple
Hub gears completely avoid the danger of collision with the spokes and wheelcollapse that derailleur systems can suffer.
Hub gears provide a means for shifting gear ratios on drivetrains incompatible
with external deraileurs such as belt drives and shaft drives.
Hub-gears are typically more expensive than derailleur systems.
Gear-hubs with a large number of speeds will tend to be less efficient than a
properly lubricated and adjusted derailleur system in new condition. However,
less sophisticated gear-hubs such as the 3-speed hub (with only a single epicyclic
stage per high/low gear, and direct drive in second gear), when run-in and
properly lubricated, can match the efficiency of similar quality derailleur systems,
because the hub-gear chain runs in a straight line and does not run through the
jockey wheels of a chain tensioner.
Gear-hubs will tend to be heavier than equivalent derailleur systems, and the
additional weight is concentrated at the back wheel. On rear-suspension bicycles
in sporting use this unsprung weight will adversely affect traction and braking.
Gear-hubs are complex and virtually impossible for the ordinary rider to repair most certainly not as a side-of-the-road procedure. However, failures generally
give plenty of warning and repair may be an option.
Gear-hubs systems are generally incompatible with quick release mechanisms/skewer axles.
The gear-hub is an integral part of the wheel and it is not possible to change the
wheel without also changing the hub.
Hub-gears in everyday use
Traditional lever change, 3-speed.
A modern twist-style seven-speed indexed shifter uses the same bowden cable as the
older lever.
Traditional hub gears are indexed at the shifter making operation dependent on
correct cable tension (and lubrication thereof). In practice, gear-jumping and
consequent internal damage are unusual except in high-mileage units. Modern
hub gear-units incorporate the indexing in the unit itself and are therefore
unaffected by shifting malfunctions caused in this way.
The Sturmey Archer and Fichtel & Sachs 'Torpedo' systems defaulted to top gear
at slack-cable, which could make the bicycle usable for long distance travel in flat
terrain even if a fault developed in the change mechanism (rather like a derailleur
system, which can be manually set to a high gear in case of a similar fault). Some
modern hub gear systems (eg 7-speed Shimano) default to bottom gear and are
thus more dependent on the (generally) very reliable cable-pull.
Hybrid gearing with derailleurs
Some systems have combined internally-geared hubs with derailleurs. A freewheeling
hub with a sprocket suitable for narrow chain can be used with a double or triple crankset
and front derailleur, in order to give a wider range and closer gear spacing. A chain
tensioner (or a rear derailleur fixed in one position) is needed to take up the slack, and
care is needed not to over-torque the hub by using too small a chain ring/sprocket ratio.
Alternatively, two drive sprockets can be selected with a rear derailleur and careful
sprocket selection means the gears of one sprocket fall half-way between those of the
other, giving half-step gearing, as on the Brompton 6-speed folding bicycle. This concept
is used and extended in SRAM's 'dualdrive' system. When both front and rear derailleurs
are used with a geared hub, the result is a very wide-ranging drivetrain, at the expense of
increased weight and complexity.
Latest developments
14-speed hub cutaway diagram
Rohloff 14 speed internally-geared rear hub
Hubs with higher numbers of gears use multiple epicyclic gears driven by each other,
their ratios chosen to give evenly spaced gears. The operating principle is the same. An
exception is the older style of Sturmey-Archer 5-speed, which used a second shift lever to
change between close and wide-range sun gears, effectively giving two 3-speed hubs in
one unit. The middle gear in both ranges was direct drive, so there were 5 distinct gears.
The latest 14-ratio hub-gear systems have a 5 to 1 range and are now directly comparable
to "27-speed" derailleur systems, since the latter have 3 overlapping ranges with no more
than about 15 distinct gears. The hub-gear system is much easier and more intuitive to
operate while suffering little from loss of mechanical efficiency.
List of multispeed hub gears
Rohloff Speedhub 500/14
Shimano Alfine SG-700
Shimano Alfine SG-500
Shimano Nexus Inter-8
Shimano Nexus Inter-7
Sachs Elan
SRAM i-Motion 9
SRAM Spectro S7
Sturmey Archer XRF-8 (XRF,XRD,XRR,XRK)
Chapter 10
Manual Transmission
A floor-mounted gear shift lever in a modern passenger car with a manual transmission
A manual transmission, also known as a manual gearbox or standard transmission
(informally, a "manual", "straight shift", "stick (shift)" (US), or "straight drive") is a type
of transmission used in motor vehicle applications. It generally uses a driver-operated
clutch, typically operated by a pedal or lever, for regulating torque transfer from the
internal combustion engine to the transmission, and a gear stick, either operated by hand
(as in a car) or by foot (as on a motorcycle).
A conventional manual transmission is frequently the base equipment in a car; other
options include automated transmissions such as an automatic transmission (often a
manumatic), a semi-automatic transmission, or a continuously variable transmission
Manual transmissions often feature a driver-operated clutch and a movable gear stick.
Most automobile manual transmissions allow the driver to select any forward gear ratio
("gear") at any time, but some, such as those commonly mounted on motorcycles and
some types of racing cars, only allow the driver to select the next-higher or next-lower
gear. This type of transmission is sometimes called a sequential manual transmission.
Sequential transmissions are commonly used in auto racing for their ability to make quick
Manual transmissions are characterized by gear ratios that are selectable by locking
selected gear pairs to the output shaft inside the transmission. Conversely, most automatic
transmissions feature epicyclic (planetary) gearing controlled by brake bands and/or
clutch packs to select gear ratio. Automatic transmissions that allow the driver to
manually select the current gear are called Manumatics. A manual-style transmission
operated by computer is often called an automated transmission rather than an automatic.
Contemporary automobile manual transmissions typically use four to six forward gears
and one reverse gear, although automobile manual transmissions have been built with as
few as two and as many as eight gears. Transmission for heavy trucks and other heavy
equipment usually have at least 9 gears so the transmission can offer both a wide range of
gears and close gear ratios to keep the engine running in the power band. Some heavy
vehicle transmissions have dozens of gears, but many are duplicates, introduced as an
accident of combining gear sets, or introduced to simplify shifting. Some manuals are
referred to by the number of forward gears they offer (e.g., 5-speed) as a way of
distinguishing between automatic or other available manual transmissions. Similarly, a 5speed automatic transmission is referred to as a "5-speed automatic."
Unsynchronized transmission
The earliest form of a manual transmission is thought to have been invented by LouisRené Panhard and Emile Levassor in the late 19th century. This type of transmission
offered multiple gear ratios and, in most cases, reverse. The gears were typically engaged
by sliding them on their shafts (hence the phrase shifting gears), which required a lot of
careful timing and throttle manipulation when shifting, so that the gears would be
spinning at roughly the same speed when engaged; otherwise, the teeth would refuse to
mesh. These transmissions are called sliding mesh transmissions and sometimes called a
crash box, because of the difficulty in changing gears and the loud grinding sound that
often accompanied. Newer manual transmissions on cars, instead have all gears mesh at
all times; these are referred to as constant-mesh transmissions, with "synchro-mesh"
being a further refinement of the constant mesh principle.
In both types, a particular gear combination can only be engaged when the two parts to
engage (either gears or clutches) are at the same speed. To shift to a higher gear, the
transmission is put in neutral and the engine allowed to slow down until the transmission
parts for the next gear are at a proper speed to engage. The vehicle also slows while in
neutral and that slows other transmission parts, so the time in neutral depends on the
grade, wind, and other such factors. To shift to a lower gear, the transmission is put in
neutral and the throttle is used to speed up the engine and thus the relevant transmission
parts, to match speeds for engaging the next lower gear. For both upshifts and
downshifts, the clutch is released (engaged) while in neutral. Some drivers use the clutch
only for starting from a stop, and shifts are done without the clutch. Other drivers will
depress (disengage) the clutch, shift to neutral, then engage the clutch momentarily to
force transmission parts to match the engine speed, then depress the clutch again to shift
to the next gear, a process called double clutching. Double clutching is easier to get
smooth, as speeds that are close but not quite matched need to speed up or slow down
only transmission parts, whereas with the clutch engaged to the engine, mismatched
speeds are fighting the rotational inertia and power of the engine.
Even though automobile and light truck transmissions are now almost universally
synchronised, transmissions for heavy trucks and machinery, motorcycles, and for
dedicated racing are usually not. Non-synchronized transmission designs are used for
several reasons. The friction material, such as brass, in synchronizers is more prone to
wear and breakage than gears, which are forged steel, and the simplicity of the
mechanism improves reliability and reduces cost. In addition, the process of shifting a
synchromesh transmission is slower than that of shifting a non-synchromesh
transmission. For racing of production-based transmissions, sometimes half the teeth (or
dogs) on the synchros are removed to speed the shifting process, at the expense of greater
Heavy duty trucks often use unsynchronized transmissions. Military trucks usually have
synchronized transmissions, allowing untrained personnel to operate them in
emergencies. In the United States, traffic safety rules refer to non-synchronous
transmissions in classes of larger commercial motor vehicles. In Europe, heavy duty
trucks use synchronized gearboxes as standard.
Similarly, most modern motorcycles use unsynchronized transmissions as synchronizers
are generally not necessary or desirable. Their low gear inertias and higher strengths
mean that forcing the gears to alter speed is not damaging, and the pedal operated selector
on modern motorcycles is not conducive to having the long shift time of a synchronized
gearbox. Because of this, it is necessary to synchronize gear speeds by blipping the
throttle when shifting into a lower gear on a motorcycle.
Synchronised transmission
Top and side view of a typical manual transmission, in this case a Ford Toploader, used
in cars with external floor shifters.
Most modern cars are fitted with a synchronised gear box. Transmission gears are always
in mesh and rotating, but gears on one shaft can freely rotate or be locked to the shaft.
The locking mechanism for a gear consists of a collar (or dog collar) on the shaft which
is able to slide sideways so that teeth (or dogs) on its inner surface bridge two circular
rings with teeth on their outer circumference: one attached to the gear, one to the shaft.
When the rings are bridged by the collar, that particular gear is rotationally locked to the
shaft and determines the output speed of the transmission. The gearshift lever
manipulates the collars using a set of linkages, so arranged so that one collar may be
permitted to lock only one gear at any one time; when "shifting gears," the locking collar
from one gear is disengaged before that of another engaged. One collar often serves for
two gears; sliding in one direction selects one transmission speed, in the other direction
selects another.
In a synchromesh gearbox, to correctly match the speed of the gear to that of the shaft as
the gear is engaged, the collar initially applies a force to a cone-shaped brass clutch
attached to the gear, which brings the speeds to match prior to the collar locking into
place. The collar is prevented from bridging the locking rings when the speeds are
mismatched by synchro rings (also called blocker rings or baulk rings, with the latter
being spelt balk in the U.S.). The synchro ring rotates slightly due to the frictional torque
from the cone clutch. In this position, the dog clutch is prevented from engaging. The
brass clutch ring gradually causes parts to spin at the same speed. When they do spin the
same speed, there is no more torque from the cone clutch, and the dog clutch is allowed
to fall in to engagement. In a modern gearbox, the action of all of these components is so
smooth and fast it is hardly noticed.
The modern cone system was developed by Porsche and introduced in the 1952 Porsche
356; cone synchronisers were called Porsche-type for many years after this. In the early
1950s, only the second-third shift was synchromesh in most cars, requiring only a single
synchro and a simple linkage; drivers' manuals in cars suggested that if the driver needed
to shift from second to first, it was best to come to a complete stop then shift into first and
start up again. With continuing sophistication of mechanical development, however, fully
synchromesh transmissions with three speeds, then four speeds, and then five speeds,
became universal by the 1980s. Many modern manual transmission cars, especially sports
cars, now offer six speeds.
Reverse gear, however, is usually not synchromesh, as there is only one reverse gear in
the normal automotive transmission and changing gears into reverse while moving is not
required. Among the cars that have synchromesh in reverse are the 1995-2000 Ford
Contour and Mercury Mystique, '00-'05 Chevrolet Cavalier, Mercedes 190 2.3-16, the V6
equipped Alfa Romeo GTV/Spider (916), certain Chrysler, Jeep, and GM products which
use the New Venture NV3500 and NV3550 units, the European Ford Sierra and
Granada/Scorpio equipped with the MT75 gearbox, the Volvo 850, and almost all
Lamborghinis and BMWs.
Like other transmissions, a manual transmission has several shafts with various gears and
other components attached to them. Typically, a rear-wheel-drive transmission has three
shafts: an input shaft, a countershaft and an output shaft. The countershaft is sometimes
called a layshaft.
In a rear-wheel-drive transmission, the input and output shaft lie along the same line, and
may in fact be combined into a single shaft within the transmission. This single shaft is
called a mainshaft. The input and output ends of this combined shaft rotate
independently, at different speeds, which is possible because one piece slides into a
hollow bore in the other piece, where it is supported by a bearing. Sometimes the term
mainshaft refers to just the input shaft or just the output shaft, rather than the entire
In some transmissions, it's possible for the input and output components of the mainshaft
to be locked together to create a 1:1 gear ratio, causing the power flow to bypass the
countershaft. The mainshaft then behaves like a single, solid shaft, a situation referred to
as direct drive.
Even in transmissions that do not feature direct drive, it's an advantage for the input and
output to lie along the same line, because this reduces the amount of torsion that the
transmission case has to bear.
Under one possible design, the transmission's input shaft has just one pinion gear, which
drives the countershaft. Along the countershaft are mounted gears of various sizes, which
rotate when the input shaft rotates. These gears correspond to the forward speeds and
reverse. Each of the forward gears on the countershaft is permanently meshed with a
corresponding gear on the output shaft. However, these driven gears are not rigidly
attached to the output shaft: although the shaft runs through them, they spin
independently of it, which is made possible by bearings in their hubs.
Most front-wheel-drive transmissions for transverse engine mounting are designed
differently. For one thing, they have an integral final drive and differential. For another,
they usually have only two shafts; input and countershaft, sometimes called input and
output. The input shaft runs the whole length of the gearbox, and there is no separate
input pinion. At the end of the second (counter/output) shaft is a pinion gear that mates
with the ring gear on the differential.
Front-wheel and rear-wheel-drive transmissions operate similarly. When the transmission
is in neutral, and the clutch is disengaged, the input shaft, clutch disk and countershaft
can continue to rotate under their own inertia. In this state, the engine, the input shaft and
clutch, and the output shaft all rotate independently.
Dog clutch
Dog clutches. The gear-like teeth ("dogs", right-side images) engage and disengage with
each other.
Among many different types of clutches, a dog clutch provides non-slip coupling of two
rotating members. It is not at all suited to intentional slipping, in contrast with the footoperated friction clutch of a manual-transmission car.
The gear selector does not engage or disengage the actual gear teeth which are
permanently meshed. Rather, the action of the gear selector is to lock one of the freely
spinning gears to the shaft that runs through its hub. The shaft then spins together with
that gear. The output shaft's speed relative to the countershaft is determined by the ratio
of the two gears: the one permanently attached to the countershaft, and that gear's mate
which is now locked to the output shaft.
Locking the output shaft with a gear is achieved by means of a dog clutch selector. The
dog clutch is a sliding selector mechanism which is splined to the output shaft, meaning
that its hub has teeth that fit into slots (splines) on the shaft, forcing that shaft to rotate
with it. However, the splines allow the selector to move back and forth on the shaft,
which happens when it is pushed by a selector fork that is linked to the gear lever. The
fork does not rotate, so it is attached to a collar bearing on the selector. The selector is
typically symmetric: it slides between two gears and has a synchromesh and teeth on each
side in order to lock either gear to the shaft.
Synchronizer rings
If the teeth, the so-called dog teeth, make contact with the gear, but the two parts are
spinning at different speeds, the teeth will fail to engage and a loud grinding sound will
be heard as they clatter together. For this reason, a modern dog clutch in an automobile
has a synchronizer mechanism or synchromesh, which consists of a cone clutch and
blocking ring. Before the teeth can engage, the cone clutch engages first which brings the
selector and gear to the same speed using friction. Moreover, until synchronization
occurs, the teeth are prevented from making contact, because further motion of the
selector is prevented by a blocker (or baulk) ring. When synchronization occurs, friction
on the blocker ring is relieved and it twists slightly, bringing into alignment certain
grooves and notches that allow further passage of the selector which brings the teeth
together. Of course, the exact design of the synchronizer varies from manufacturer to
The synchronizer has to change the momentum of the entire input shaft and clutch disk.
Additionally, it can be abused by exposure to the momentum and power of the engine
itself, which is what happens when attempts are made to select a gear without fully
disengaging the clutch. This causes extra wear on the rings and sleeves, reducing their
service life. When an experimenting driver tries to "match the revs" on a synchronized
transmission and force it into gear without using the clutch, the synchronizer will make
up for any discrepancy in RPM. The success in engaging the gear without clutching can
deceive the driver into thinking that the RPM of the layshaft and transmission were
actually exactly matched. Nevertheless, approximate rev. matching with clutching can
decrease the general delta between layshaft and transmission and decrease synchro wear.
The previous discussion normally applies only to the forward gears. The implementation
of the reverse gear is usually different, implemented in the following way to reduce the
cost of the transmission. Reverse is also a pair of gears: one gear on the countershaft and
one on the output shaft. However, whereas all the forward gears are always meshed
together, there is a gap between the reverse gears. Moreover, they are both attached to
their shafts: neither one rotates freely about the shaft. What happens when reverse is
selected is that a small gear, called an idler gear or reverse idler, is slid between them.
The idler has teeth which mesh with both gears, and thus it couples these gears together
and reverses the direction of rotation without changing the gear ratio.
In other words, when reverse gear is selected, it is in fact actual gear teeth that are being
meshed, with no aid from a synchronization mechanism. For this reason, the output shaft
must not be rotating when reverse is selected: the car must be stopped. In order that
reverse can be selected without grinding even if the input shaft is spinning inertially,
there may be a mechanism to stop the input shaft from spinning. The driver brings the
vehicle to a stop, and selects reverse. As that selection is made, some mechanism in the
transmission stops the input shaft. Both gears are stopped and the idler can be inserted
between them. There is a clear description of such a mechanism in the Honda Civic 19961998 Service Manual, which refers to it as a "noise reduction system":
Whenever the clutch pedal is depressed to shift into reverse, the mainshaft continues to
rotate because of its inertia. The resulting speed difference between mainshaft and
reverse idler gear produces gear noise [grinding]. The reverse gear noise reduction
system employs a cam plate which was added to the reverse shift holder. When shifting
into reverse, the 5th/reverse shift piece, connected to the shift lever, rotates the cam plate.
This causes the 5th synchro set to stop the rotating mainshaft.
A reverse gear implemented this way makes a loud whining sound, which is not normally
heard in the forward gears. The teeth on the forward gears of most consumer automobiles
are helically cut. When helical gears rotate, there is constant contact between gears,
which results in quiet operation. In spite of all forward gears being always meshed, they
do not make a sound that can be easily heard above the engine noise. By contrast, most
reverse gears are spur gears, meaning that they have straight teeth, in order to allow for
the sliding engagement of the idler, which is difficult with helical gears. The teeth of spur
gears clatter together when the gears spin, generating a characteristic whine.
It is clear that the spur gear design of reverse gear represents some compromises (less
robust, unsynchronized engagement and loud noise) which are acceptable due to the
relatively small amount of driving that takes place in reverse. The gearbox of the classic
SAAB 900 is a notable example of a gearbox with a helical reverse gear engaged in the
same unsynchronized manner as the spur gears described above. Its strange design allows
reverse to share cogs with first gear, and is exceptionally quiet, but results in difficult
engagement and unreliable operation. However, many modern transmissions now include
a reverse gear synchronizer and helical gearing.
Design variations
Gear variety
Manual transmissions in passenger vehicles are often equipped with 4, 5, or more
recently 6 forward gears in conventional manual transmissions with a gear stick, and up
to 8 forward gears in semi-automatic transmissions. Nearly all have one reverse gear. In
three or four speed transmissions, in most cases, the topmost gear is direct (i.e., a 1:1
ratio). For five speed or higher transmissions, the highest gear is usually an overdrive
gear, with a ratio of less than 1:1. Older cars were generally equipped with 3-speed
transmissions, or 4-speed transmissions for high performance models and 5-speeds for
the most sophisticated of automobiles; in the 1970s, 5-speed transmissions began to
appear in low priced mass market automobiles and even compact pickup trucks,
pioneered by Toyota (who advertised the fact by giving each model the suffix SR5 as it
acquired the fifth speed). Today, mass market automotive manual transmissions are
essentially all 5-speeds, with 6-speed transmissions beginning to emerge in high
performance vehicles in the early 1990s, and recently beginning to be offered on some
high-efficiency and conventional passenger cars. Some 7-speed manual-derived
transmissions are offered on high-end performance cars, such as the Bugatti Veyron 16.4,
or the BMW M5. Both of these cars feature a paddle shifter. Recently, even 8-speed
transmissions were being offered, such as in the Lexus IS F, and in 2012 Mercedes-Benz
plan to introduce a 9-speed gearbox.
External overdrive
On earlier models with three or four forward speeds, the lack of an overdrive ratio for
relaxed and fuel-efficient highway cruising was often filled by incorporating a separate
overdrive unit in the rear housing of the transmission. This unit was separately actuated
by a knob or button, often incorporated into the gearshift knob.
Shaft and gear configuration
On a conventional rear-drive transmission, there are three basic shafts; the input, the
output, and the countershaft. The input and output together are called the mainshaft, since
they are joined inside the transmission so they appear to be a single shaft, although they
rotate totally independently of each other. The input length of this shaft is much shorter
than the output shaft. Parallel to the mainshaft is the countershaft. There are a number of
gears fixed along the countershaft, and matching gears along the output shaft, although
these are not fixed, and rotate independently of the output shaft. There are sliding dog
collars, or dog clutches, between the gears on the output shaft, and to engage a gear to the
shaft, the collar slides into the space between the shaft and the inside space of the gear,
thus rotating the shaft as well. One collar is usually mounted between two gears, and
slides both ways to engage one or the other gears, so on a four speed there would be two
collars. A front-drive transmission is basically the same, but may be simplified. There
often are two shafts, the input and the output, but depending on the direction of rotation
of the engine, three may be required. Rather than the input shaft driving the countershaft
with a pinion gear, the input shaft takes over the countershaft's job, and the output shaft
runs parallel to it. The gears are positioned and engaged just as they are on the
countershaft and output shaft of a rear-drive. This merely eliminates one major
component, the pinion gear. Part of the reason that the input and output are in-line on a
rear drive unit is to relieve torsional stress on the transmission and mountings, but this
isn't an issue in a front-drive as the gearbox is integrated into the transaxle.
The basic process is not universal. The fixed and free gears can be mounted on either the
input or output shaft, or both.
The distribution of the shifters is also a matter of design; it need not be the case that all of
the free-rotating gears with selectors are on one shaft, and the permanently splined gears
on the other. For instance a five speed transmission might have the first-to-second
selectors on the countershaft, but the third-to-fourth selector and the fifth selector on the
mainshaft, which is the configuration in the 1998 Honda Civic. This means that when the
car is stopped and idling in neutral with the clutch engaged and the input shaft spinning,
the third, fourth and fifth gear pairs do not rotate.
In some transmission designs (Volvo 850 and V/S70 series, for example) there are
actually two countershafts, both driving an output pinion meshing with the front-wheeldrive transaxle's ring gear. This allows the transmission designer to make the
transmission narrower, since each countershaft need only be half as long as a traditional
countershaft with four gears and two shifters.
In all vehicles using a transmission (virtually all modern vehicles), a coupling device is
used to separate the engine and transmission when necessary. The clutch accomplishes
this in manual transmissions. Without it, the engine and tires would at all times be
inextricably linked, and any time the vehicle stopped the engine would stall. Without the
clutch, changing gears would be very difficult, even with the vehicle moving already:
deselecting a gear while the transmission is under load requires considerable force, and
selecting a gear requires the revolution speed of the engine to be held at a very precise
value which depends on the vehicle speed and desired gear. In a car the clutch is usually
operated by a pedal; on a motorcycle, a lever on the left handlebar serves the purpose.
When the clutch pedal is fully depressed, the clutch is fully disengaged, and no
torque is transferred from the engine to the transmission (and by extension to the
drive wheels). In this uncoupled state it is possible to select gears or to stop the
car without stopping the engine.
When the clutch pedal is fully released, the clutch is fully engaged, and
practically all of the engine's torque is transferred. In this coupled state, the clutch
does not slip, but rather acts as rigid coupling, and power is transmitted to the
wheels with minimal practical waste heat.
Between these extremes of engagement and disengagement the clutch slips to
varying degrees. When the clutch slips it still transmits torque despite the
difference in speeds between the engine crankshaft and the transmission input.
Because this torque is transmitted by means of friction rather than direct
mechanical contact, considerable power is wasted as heat (which is dissipated by
the clutch). Properly applied, slip allows the vehicle to be started from a standstill,
and when it is already moving, allows the engine rotation to gradually adjust to a
newly selected gear ratio.
Learning to use the clutch efficiently requires the development of muscle memory
and a level of coordination analogous to that required to learn a musical
instrument or to play a sport.
A rider of a highly-tuned motocross or off-road motorcycle may "hit" or "fan" the
clutch when exiting corners to assist the engine in revving to the point where it
delivers the most power.
Gear shift types
Floor-mounted shifter
A 5 speed gear lever
In many modern passenger cars, gears are selected by manipulating a lever connected to
the transmission via linkage or cables and mounted on the floor of the automobile. This is
called a gear stick, shift stick, gearshift, gear lever, gear selector, or shifter. Moving
the lever forward, backward, left, and right into specific positions selects particular gears.
A sample layout of a four-speed transmission is shown below. N marks neutral, the
position wherein no gears are engaged and the engine is decoupled from the vehicle's
drive wheels. In reality, the entire horizontal line is a neutral position, although the shifter
is usually equipped with springs so that it will return to the N position if not moved to
another gear. The R marks reverse, the gear position used for moving the vehicle
This layout is called the shift pattern. Because of the shift quadrants, the basic
arrangement is often called an H-pattern. The shift pattern is usually molded or printed
on or near the gear knob. While the layout for gears one through four is nearly universal,
the location of reverse is not. Depending on the particular transmission design, reverse
may be located at the upper left extent of the shift pattern, at the lower left, at the lower
right, or at the upper right. There is usually a mechanism that only allows selection of
reverse from the neutral position, or a reverse blockout that must be released by
depressing the spring-loaded gear knob or lifting a spring-loaded collar on the shift stick,
to reduce the likelihood that reverse will be inadvertently selected by the driver.
This is the most common five-speed shift pattern:
This layout is reasonably intuitive because it starts at the upper left and works left to
right, top to bottom, with reverse at the end of the sequence and toward the rear of the
This is another five-speed shift pattern, which can be found in Saabs, BMWs, some
Audis, Eagle, Volvos, Volkswagens, Škodas, Opels, Hyundais, most Renaults, some
diesel Fords, and more:
Dog-leg first shift patterns are used on many race cars and on older road vehicles with
three-speed transmissions:
The name derives from the up-and-over path between first and second gears. Its use is
common in race cars and sports cars, but is diminishing as six speed and sequential
gearboxes are becoming more common. Having first gear across the dog leg is beneficial
as first gear is traditionally only used for getting the car moving and hence it allows
second and third gears to be aligned fore and aft of each other, which facilitates shifting
between the two. As most racing gearboxes are non-synchromesh there is no appreciable
delay when upshifting from first through the dog leg into second.
This gear pattern can also be found on some heavy vehicles in which first gear is an
extra-low ratio for use in extreme standing-start conditions, and would see little use in
normal driving.
This is a typical shift pattern for a six-speed transmission:
Six speeds is the maximum usually seen in single range transmissions, however many
semi trucks and other large commercial vehicles have manual transmissions with 8, 16 or
even 20 speeds, which is made possible due to multi-range gearboxes. In such a case,
Reverse is placed outside of the "H," with a canted shift path, to prevent the shift lever
from intruding too far into the driver's space (in left-hand drive cars) when reverse is
selected. This is the most common layout for a six-speed manual transmission.
Most front-engined, rear-wheel drive cars have a transmission that sits between the driver
and the front passenger seat. Floor-mounted shifters are often connected directly to the
transmission. Front-wheel drive and rear-engined cars often require a mechanical linkage
to connect the shifter to the transmission.
Historically, four-speed floor shifters were sometimes referred to as "four on the floor,"
during the period when steering column mounted shifters were more common. The latter,
often being the standard non-performance transmission, usually had only three forward
speeds and were referred to as "three on the tree."
Column-mounted shifter
Column mounted gear shift lever in a Saab 96
Some cars have a gear lever mounted on the steering column of the car. It was common
in some countries in the past but is no longer common today. However, many automatic
transmissions still use this placement.
Column shifters are mechanically similar to floor shifters, although shifting occurs in a
vertical plane instead of a horizontal one. Column shifters also generally involve
additional linkages to connect the shifter with the transmission. Also, the pattern is not
"intuitive," as the shifter has to be moved backward and upward into R to make the car go
backward. The major advantage of a column shifter is that the driver can switch between
the two most commonly used gears without letting go of the steering wheel, by reaching
the lever using the index and middle fingers.
A 3-speed column shifter, nicknamed "Three on the Tree" began appearing in America in
the late 1930s and became common during the 1940s and '50s. Its layout is as shown
First gear in a 3-speed is often called "low," while third is usually called "high." There is,
of course, no overdrive. Later, European and Japanese models began to have 4-speed
column shifters and some of these made their way to the USA. Its layout is shown here:
However, the column manual shifter disappeared in North America by the mid 1980s,
last appearing in the 1987 Chevrolet c10. But in the rest of the world, the column
mounted shifter remained in production, and was in fact common in some places. For
example, all Toyota Crown and Nissan Cedric taxis in Hong Kong had the 4-speed
column shift until 1999 when automatic began to be offered. Since the late 1980s or early
1990s, a 5-speed column shifter has been made in some vans sold in Asia and Europe,
such as Toyota Hiace and Mitsubishi L400.
Console-mounted shifter
Newer small cars and MPV's, like the Suzuki MR Wagon, the Fiat Multipla, the Toyota
Matrix, the Pontiac Vibe, the Chrysler RT platform cars and the Honda Civic Si EP3 may
feature a manual or automatic transmission gear shifter located on the vehicle's
instrument panel. Console-mounted shifters are similar to floor-mounted gear shifters in
that most of the ones used in modern cars operate on a horizontal plane and can be
mounted to the vehicle's transmission in much the same way a floor-mounted shifter can.
However, because of the location of the gear shifter in comparison to the locations of the
column shifter and the floor shifter, as well as the positioning of the shifter to the rest of
the controls on the panel often require that the gearshift be mounted in a space that does
not feature a lot of controls integral to the vehicle's operation or frequently used controls,
such as those for the car stereo or car air conditioning, to help prevent accidental
activation or driver confusion, especially in right-hand drive cars.
More and more small cars and vans from manufacturers such as Suzuki, Honda, and
Volkswagen are featuring console shifters in that they free up space on the floor for other
car features such as storage compartments without requiring that the gear shift be
mounted on the steering column. Also, the basic location of the gear shift in comparison
to the column shifter makes console shifters easier to operate than column shifters.
Sequential manual
Some transmissions do not allow the driver to arbitrarily select any gear. Instead, the
driver may only ever select the next-lowest or next-highest gear ratio. Sequential
transmissions often incorporate a synchro-less dog-clutch engagement mechanism
(instead of the synchromesh dog clutch common on H-pattern automotive transmissions),
in which case the clutch is only necessary when selecting first or reverse gear from
neutral, and most gear changes can be performed without the clutch. However, sequential
shifting and synchro-less engagement are not inherently linked, though they often occur
together due to the environment(s) in which these transmissions are used, such as racing
cars and motorcycles.
Sequential transmissions are generally controlled by a forward-backward lever, foot
pedal, or set of paddles mounted behind the steering wheel. In some cases, these are
connected mechanically to the transmission. In many modern examples, these controls
are attached to sensors which instruct a transmission computer to perform a shift—many
of these systems can be switched into an automatic mode, where the computer controls
the timing of shifts, much like an automatic transmission.
Motorcycles typically employ sequential transmissions, although the shift pattern is
modified slightly for safety reasons. In a motorcycle the gears are usually shifted with the
left foot pedal, the layout being this:
The gear shift lever on a 2003 Suzuki SV650S motorcycle.
3┘ 2┘N1
The pedal goes one step–both up and down–from the center, before it reaches its limit
and has to be allowed to move back to the center position. Thus, changing multiple gears
in one direction is accomplished by repeatedly pumping the pedal, either up or down.
Although neutral is listed as being between first and second gears for this type of
transmission, it "feels" more like first and second gear are just "further away" from each
other than any other two sequential gears. Because this can lead to difficulty in finding
neutral for inexperienced riders most motorcycles have a neutral indicator light on the
instrument panel to help find neutral. The reason neutral does not actually have its own
spot in the sequence is to make it quicker to shift from first to second when moving.
Depending on the age of your motorcycle, gearbox, or skill, you can accidentally shift
into neutral, although most high end, newer model motorcycles have found ways around
this. The reason for having neutral between the first and second gears instead of at the
bottom is that when stopped, the rider can just click down repeatedly and know that they
will end up in first and not neutral. This allows a rider to quickly move his bike from a
standstill in an emergency situation. This may also help on a steep hill on which high
torque is required. It could be disadvantageous or even dangerous to attempt to be in first
without realizing it, then try for a lower gear, only to get neutral.
On motorcycles used on race tracks, the shifting pattern is often reversed, that is, the rider
clicks down to upshift. This usage pattern increases the ground clearance by placing the
riders foot above the shift lever when the rider is most likely to need it, namely when
leaning over and exiting a tight turn.
The shift pattern for most underbone motorcycles with an automatic centrifugal clutch is
also modified for two key reasons - to enable the less-experienced riders to shift the gears
without problems of "finding" neutral, and also due to the greater force needed to "lift"
the gearshift lever (because the gearshift pedal of an underbone motorcycle also operates
the clutch). The gearshift lever of an underbone motorcycle has two ends. The rider clicks
down the front end with the left toe all the way to the top gear and clicks down the rear
end with the heel all the way down to neutral. Some underbone models such as the Honda
Wave and Kawasaki Fury series have a "rotary" shift pattern, which means that the rider
can shift directly to neutral from the top gear, but for safety reasons this is only possible
when the motorcycle is stationary. Some models also have gear position indicators for all
gear positions at the instrument panel.
Some new transmissions (Alfa Romeo's Selespeed gearbox and BMW's Sequential
Manual Gearbox (SMG) for example) are conventional manual transmissions with a
computerized control mechanism. These transmissions feature independently selectable
gears but do not have a clutch pedal. Instead, the transmission computer controls a servo
which disengages the clutch when necessary.
These transmissions vary from sequential transmissions in that they still allow
nonsequential shifts: BMWs SMG system, for example, can shift from 6th gear directly to
4th gear.
In the case of the early second generation Saab 900, a 'Seletronic' option was available
where gears were shifted with a conventional shifter, but the clutch is controlled by a
Benefits and drawbacks
Manual transmissions generally offer better fuel economy than automatic torque
converter transmissions; however the disparity has been somewhat offset with the
introduction of locking torque converters on automatic transmissions. Increased fuel
economy with a properly operated manual transmission vehicle versus an equivalent
automatic transmission vehicle can range from 5% to about 15% depending on driving
conditions and style of driving. Manual transmissions do not require active cooling and
generally weigh less than comparable automatics. The manual transmission couples the
engine to the transmission with a rigid clutch instead of a torque converter which slips by
nature. Manual transmissions also lack the parasitic power consumption of the automatic
transmission's hydraulic pump. Additionally, they require less maintenance and are easier
to repair because they have fewer moving parts and are, mechanically, much simpler than
automatic transmissions. When properly operated by an experienced driver, manual
transmissions also tend to last longer than automatic transmissions.
Manual transmissions also generally offer a higher selection of gear ratios. Many vehicles
offer a 5-speed or 6-speed manual, whereas the automatic option would typically be a 4speed. The higher selection of gears allowed for more uses of the engine's power band,
allowing for higher fuel economy and power output. This is generally due to the space
available inside of a manual transmission versus an automatic since the latter requires
extra components for self-shifting, such as torque converters and pumps. Automatic
transmissions are now adding more speeds as the technology matures. ZF currently
makes an 8-Speed automatic transmission, which is used on the Rolls Royce Ghost and
the Bentley Mulsanne. The automatic transmission in the Nissan 370Z also has 7 speeds.
Manual transmissions are more efficient than conventional automatics and belt-driven
continuously-variable transmissions. The driver has more direct control over the car with
a manual than with an automatic, which can be employed by an experienced,
knowledgeable driver who knows the correct procedure for executing a driving
maneuver, and wants the vehicle to realize his or her intentions exactly and instantly.
When starting forward, for example, the driver can control how much torque goes to the
tires, which is useful on slippery surfaces such as ice, snow or mud. This can be done
with clutch finesse, or by starting in second gear instead of first. An engine coupled with
a manual transmission can often be started by the method of push starting. This is
particularly useful if the starter is inoperable or defunct or the battery has drained below
operable voltage. Likewise, a vehicle with a manual transmission and no clutch/starter
interlock switch can be moved, if necessary, by cranking the starter while in gear. This is
useful when the vehicle will not start, but must be immediately moved e.g. off the road in
the event of a breakdown, if the vehicle has stalled on a railway crossing, or in extreme
off-roading cases such as an engine that has stalled in deep water.
Currently only fully manual transmissions allow the driver to fully exploit the engine
power at low to medium engine speeds. This is because even automatic transmissions
which provide some manual mode (e.g. tiptronic), use a throttle kickdown switch, which
forces a downshift on full throttle and causes the gearbox to ignore a user command to
upshift on full throttle. This is especially notable on uphill roads, where cars with
automatic transmission need to slow down to avoid downshifts, whereas cars with
manual transmission and identical or lower engine power are still able to maintain their
In contrast to most manual gearboxes, most automatic transmissions have a free-wheelclutch. This means that the engine does not slow down the car when the driver steps off
the throttle, also known as engine braking. This leads to more usage of the brakes in cars
with automatic transmissions. However, the automatic gearboxes in commodity Nissans
and Hondas disable the free wheel operation completely if the driver has selected a gear
position other than "D" - either "1", "2", or "D with overdrive off". This works by
blocking the free-wheel sprag using a multi-disk clutch called the "overrun clutch".
The smoothness and correct timing of gear shifts are wholly dependent on the driver's
experience and skill. If an inexperienced driver selects the wrong gear by mistake, she/he
can do damage to the engine and/or transmission.
Attempting to select reverse while the vehicle is moving forward causes severe gear wear
(except in transmissions with synchromesh on the reverse gear). Most manual
transmissions have a gate that locks out reverse directly from 5th gear however, to help
prevent this. In order to engage reverse from 5th, the shift lever has to be moved to the
center position between 2nd and 3rd, then back over and into reverse. Many newer sixspeed manual transmissions have a collar under the shift knob which must be lifted to
engage reverse to also help prevent this.
Choosing too low a gear with the car moving at speed can over-rev and damage the
engine. There is a learning curve with a manual transmission; the driver must develop a
feel for properly engaging the clutch, especially when starting forward on a steep road or
when parking on an incline.
Some automatic transmissions can shift ratios faster than a manual gear change can be
accomplished, due to the time required for the average driver to push the clutch pedal to
the floor and move the gearstick from one position to another. This is especially true in
regards to dual clutch transmissions, which are specialized computer-controlled manual
transmissions. Even though some automatic transmissions and semi-automatic
transmissions can shift faster, many purists still prefer a regular manual transmission.
Manual transmissions place a slightly greater workload on the driver in heavy traffic
situations, when the driver must often operate the clutch pedal. In comparison, automatic
transmissions merely require moving the foot from the accelerator pedal to the brake
pedal, and vice versa. Manual transmissions require the driver to remove one hand
periodically from the steering wheel while the vehicle is in motion.
Applications and popularity
Many types of automobiles are equipped with manual transmissions. Small economy cars
predominantly feature manual transmissions because they are cheap and efficient,
although many are optionally equipped with automatics. Economy cars are also often
powered by very small engines, and manual transmissions make more efficient use of the
power produced.
Sports cars are also often equipped with manual transmissions because they offer more
direct driver involvement and better performance. Off-road vehicles and trucks often
feature manual transmissions because they allow direct gear selection and are often more
rugged than their automatic counterparts.
Conversely, manual transmissions are no longer popular in many classes of cars sold in
North America, Australia and Asia, although they remain dominant in Europe and
developing countries. Nearly all cars are available with an automatic transmission option,
and family cars and large trucks sold in the US are predominantly fitted with automatics,
however in some cases if a buyer wishes he/she can have the car fitted with a manual
transmission at the factory. In Europe most cars are sold with manual transmissions. Most
luxury cars are only available with an automatic transmission. In most cases where both
transmissions are available for a given car, automatics are an at cost option, but in some
cases the reverse is true. Some cars, such as rental cars and taxis, are nearly universally
equipped with automatic transmissions in countries such as the US, but the opposite is
true in Europe. As of 2008, 75.2% of vehicles made in Western Europe were equipped
with manual transmission, versus 16.1% with automatic and 8.7% with other.
In some places (for example Australia, New Zealand (for the second-phase Restricted
licence, but not the final Full licence), Belgium, China, Estonia, Dominican Republic,
Finland, France, Germany, Ireland, Israel, Netherlands, Norway, Poland, Singapore,
Slovenia, South Africa, South Korea, Spain, Sri Lanka, Sweden, Turkey, U.A.E and the
UK), when a driver takes the licensing road test using an automatic transmission, the
resulting license is restricted to the use of automatic transmissions. This treatment of the
manual transmission skill seems to maintain the widespread use of the manual
transmission. As many new drivers worry that their restricted license will become an
obstacle for them where most cars have manual transmissions, they make the effort to
learn with manual transmissions and obtain full licenses. Some other countries (such as
India, Pakistan, Malaysia, Serbia, Brazil, and Denmark) go even further, whereby the
license is granted only when a test is passed on a manual transmission. In Denmark and
Brazil you are allowed to take the test on an automatic if you are handicapped, with such
license you will not be able to drive a manual transmission.
Truck transmissions
Some trucks have transmissions that look and behave like ordinary car transmissions these transmissions are used on lighter trucks, typically have up to 6 gears, and usually
have synchromesh.
For trucks needing more gears, the standard "H" pattern can get very complicated, so
additional controls are used to select additional gears. The "H" pattern is retained, then an
additional control selects among alternatives. In older trucks, the control is often a
separate lever mounted on the floor or more recently a pneumatic switch mounted on the
"H" lever; in newer trucks the control is often an electrical switch mounted on the "H"
lever. Multi-control transmissions are built in much higher power ratings, but rarely use
There are several common alternatives for the shifting pattern. Usual types are:
Range transmissions use an "H" pattern through a narrow range of gears, then a
"range" control shifts the "H" pattern between high and low ranges. For example,
an 8-speed range transmission has an H shift pattern with four gears. The first
through fourth gears are accessed when low range is selected. To access the fifth
through eighth gears, the range selector is moved to high range, and the gear lever
again shifted through the first through fourth gear positions. In high range, the
first gear position becomes fifth, the second gear position becomes sixth, and so
Splitter transmissions use an "H" pattern with a wide range of gears, and the
other selector splits each sequential gear position in two: First gear is in first
position/low split, second gear is in first position/high split, third gear is in second
position/low split, fourth gear is in second position/high split, and so on.
Range-Splitter transmissions combine range-splitting and gear-splitting. This
allows even more gear ratios. Both a range selector and a splitter selector are
Although there are many gear positions, shifting through gears usually follows a regular
pattern. For example, a series of upshifts might use "move to splitter direct; move to
splitter overdrive; move shift lever to #2 and move splitter to underdrive; move splitter to
direct; move splitter to overdrive; move shift lever to #3 and move splitter to underdrive";
and so on. In older trucks using floor-mounted levers, a bigger problem is common gear
shifts require the drivers to move their hands between shift levers in a single shift, and
without synchromesh, shifts must be carefully timed or the transmission will not engage.
For this reason, some splitter transmissions have an additional "under under" range, so
when the splitter is already in "under" it can be quickly downshifted again, without the
delay of a double shift.
Today's truck transmissions are most commonly "range-splitter". The most common 13
speed has a standard H pattern, and the pattern from left upper corner is as follows: R,
down to L, over and up to 1, down to 2, up and over to 3, down to 4. The "butterfly"
range lever in the center front of the knob is flipped up to high range while in 4th, then
shifted back to 1. The 1 through 4 positions of the knob are repeated. Also, each can be
split using the thumb-actuated under-overdrive lever on the left side of the knob while in
high range. The "thumb" lever is not available in low range, except in 18 speeds; 1
through 4 in low range can be split using the thumb lever and L can be split with the
"Butterfly" lever. L cannot be split using the thumb lever in either the 13 or 18 speed.
The 9 speed transmission is basically a 13 speed without the under-overdrive thumb
Truck transmissions use many physical layouts. For example, the output of an N-speed
transmission may drive an M-speed secondary transmission, giving a total of N*M gear
combinations; for example a 4-speed main box and 3-speed splitter gives 12 ratios.
Transmissions may be in separate cases with a shaft in between; in separate cases bolted
together; or all in one case, using the same lubricating oil. The second transmission is
often called a "Brownie" or "Brownie box" after a popular brand. With a third
transmission, gears are multiplied yet again, giving greater range or closer spacing. Some
trucks thus have dozens of gear positions, although most are duplicates. Sometimes a
secondary transmission is integrated with the differential in the rear axle, called a "twospeed rear end." Two-speed differentials are always splitters. In newer transmissions,
there may be two countershafts, so each main shaft gear can be driven from one or the
other countershaft; this allows construction with short and robust countershafts, while
still allowing many gear combinations inside a single gear case.
Heavy-duty transmissions are almost always non-synchromesh. One argument is
synchromesh adds weight that could be payload, is one more thing to fail, and drivers
spend thousands of hours driving so can take the time to learn to drive efficiently with a
non-synchromesh transmission. Heavy-duty trucks driven frequently in city traffic, such
as cement mixers, need to be shifted very often and in stop-and-go traffic. Since few
heavy-duty transmissions have synchromesh, automatic transmissions are commonly
used instead, despite their increased weight, cost, and loss of efficiency.
Heavy trucks are usually powered with diesel engines. Diesel truck engines from the
1970s and earlier tend to have a narrow power band, so need many close-spaced gears.
Starting with the 1968 Maxidyne, diesel truck engines have increasingly used
turbochargers and electronic controls that widen the power band, allowing fewer and
fewer gear ratios. A transmission with fewer ratios is lighter and may be more efficient
due to fewer transmissions in series. Fewer shifts also makes the truck more drivable. As
of 2005, fleet operators often use 9,10,13 or 18-speed transmissions, but automated
manual and semi-automatic transmissions are becoming more common on heavy
vehicles, as they can improve efficiency and drivability, reduce the barrier to entry for
new drivers, and may improve safety by allowing the driver to concentrate on road
Because clutches use changes in friction to modulate the transfer of torque between
engine and transmission, they are subject to wear in everyday use. A very good clutch,
when used by an expert driver, can last hundreds of thousands of kilometres (or miles).
Weak clutches, abrupt downshifting, inexperienced drivers, and aggressive driving can
lead to more frequent repair or replacement.
Manual transmissions are lubricated with gear oil or engine oil in some cars, which must
be changed periodically in some cars, although not as frequently as the automatic
transmission fluid in a vehicle so equipped. (Some manufacturers specify that changing
the gear oil is never necessary except after transmission work or to rectify a leak.)
Gear oil has a characteristic aroma due to the addition of sulfur-bearing anti-wear
compounds. These compounds are used to reduce the high sliding friction by the helical
gear cut of the teeth (this cut eliminates the characteristic whine of straight cut spur
gears). On motorcycles with "wet" clutches (clutch is bathed in engine oil), there is
usually nothing separating the lower part of the engine from the transmission, so the same
oil lubricates both the engine and transmission. The original Mini placed the gearbox in
the oil sump below the engine, thus using the same oil for both.
First gear
Second gear
Third gear
Fourth gear
Chapter 11
Automatic Transmission
An 8-gear automatic transmission
An automatic gearbox is one type of motor vehicle transmission that can automatically
change gear ratios as the vehicle moves, freeing the driver from having to shift gears
manually. Most automatic transmissions have a defined set of gear ranges, often with a
parking pawl feature that locks the output shaft of the transmission.
Similar but larger devices are also used for heavy-duty commercial and industrial
vehicles and equipment. Some machines with limited speed ranges or fixed engine
speeds, such as some forklifts and lawn mowers, only use a torque converter to provide a
variable gearing of the engine to the wheels.
Besides automatics, there are also other types of automated transmissions such as
continuous variable transmissions (CVTs) and semi-automatic transmissions, that free the
driver from having to shift gears manually, by using the transmission's computer to
change gear, if for example the driver were redlining the engine. Despite superficial
similarity to other automated transmissions, automatic transmissions differ significantly
in internal operation and driver's "feel" from semi-automatics and CVTs. An automatic
uses a torque converter instead of clutch to manage the connection between the
transmission gearing and the engine. In contrast, a CVT uses a belt or other torque
transmission schema to allow an "infinite" number of gear ratios instead of a fixed
number of gear ratios. A semi-automatic retains a clutch like a manual transmission, but
controls the clutch through electrohydraulic means.
A conventional manual transmission is frequently the base equipment in a car, with the
option being an automated transmission such as a conventional automatic, semiautomatic, or CVT. The ability to shift gears manually, often via paddle shifters, can also
be found on certain automated transmissions (manumatics such as Tiptronic), semiautomatics (BMW SMG), and continuous variable transmissions (CVTs) (such as
Comparison with manual transmission
Most cars sold in North America since the 1950s have been available with an automatic
transmission. Conversely, automatic transmission is less popular in Europe, with 80% of
drivers opting for manual transmission.. In most Asian markets and in Australia,
automatic transmissions have become very popular since the 1990s.
Vehicles equipped with automatic transmissions are less complex to drive. Consequently,
in some jurisdictions, drivers who have passed their driving test in a vehicle with an
automatic transmission will not be licensed to drive a manual transmission vehicle.
Examples of driving license restrictions are Croatia, Dominican Republic, Israel, United
Kingdom, some states in Australia, France, Portugal, Latvia, Lebanon, Lithuania, Ireland,
Belgium, Germany, Pakistan, the Netherlands, Sweden, Austria, Norway, Poland,
Hungary, South Africa, Trinidad and Tobago, China, Hong Kong, Macau, Mauritius,
South Korea, Romania, Singapore, Philippines, United Arab Emirates, India, Estonia,
Finland, Switzerland, Slovenia, Republic of Ireland and New Zealand (Restricted licence
Automatic transmission modes
Conventionally, in order to select the transmission operating 'mode', the driver moves a
selection lever located either on the steering column or on the floor (as with a manual). In
order to select modes, or to manually select specific gear ratios, the driver must push a
button in (called the shift lock button) or pull the handle (only on column mounted
shifters) out. Some vehicles position selector buttons for each mode on the cockpit
instead, freeing up space on the central console. Vehicles conforming to US Government
standards must have the modes ordered P-R-N-D-L (left to right, top to bottom, or
clockwise). Prior to this, quadrant-selected automatic transmissions often used a P-N-DL-R layout, or similar. Such a pattern led to a number of deaths and injuries owing to
unintentional gear selection, as well as the danger of having a selector (when worn) jump
into Reverse from Low gear during engine braking maneuvers.
Automatic transmissions have various modes depending on the model and make of the
transmission. Some of the common modes include
Park (P)
This selection mechanically locks the output shaft of transmission, restricting the
vehicle from moving in any direction. A parking pawl prevents the transmission
from rotating, and therefore the vehicle from moving, although the vehicle's nondriven roadwheels may still rotate freely. For this reason, it is recommended to
use the hand brake (or parking brake) because this actually locks (in most cases)
the rear wheels and prevents them from moving. This also increases the life of the
transmission and the park pin mechanism, because parking on an incline with the
transmission in park without the parking brake engaged will cause undue stress on
the parking pin. An efficiently-adjusted hand brake should also prevent the car
from moving if a worn selector accidentally drops into reverse gear during early
morning fast-idle engine warm-ups. It should be noted that locking the
transmission output shaft does not positively lock the driving wheels. If one
driving wheel slips while the transmission is in "park," the other will roll freely as
the slipping wheel rotates in the opposite direction. Only a (properly adjusted)
parking brake can be relied upon to positively lock both of the parking-braked
wheels. (This is not the case with certain 1950's Chrysler products that carried
their parking brake on the transmission tailshaft, a defect compounded by the
provision of a bumper jack). It is typical of front-wheel-drive vehicles for the
parking brake to be on the rear (non-driving) wheels, so use of both the parking
brake and the transmission park lock provides the greatest security against
unintended movement on slopes. Unfortunately, the rear of most front-wheeldrive vehicles has only about half the weight on the rear wheel as is on the front
wheels, greatly reducing the security provided by the parking brake as compared
to either rear-wheel-drive vehicles with parking brake on the rear wheels (which
generally have near half of the total vehicle weight on the rear wheels, except for
empty pickup and open-bed trucks) or to front-wheel-drive vehicles with the
parking brake on the front wheels, which generally have about two-thirds of the
vehicle's weight (unloaded) on the front wheels.
A car should be allowed to come to a complete stop before setting the
transmission into park to prevent damage. Usually, Park (P) is one of only two
selections in which the car's engine can be started, the other being Neutral (N). In
many modern cars and trucks, the driver must have the foot brake applied before
the transmission can be taken out of park. The Park position is omitted on
buses/coaches with automatic transmission (on which a parking pawl is not
practical), which must be placed in neutral with the parking brakes set. Advice is
given in some owner's manuals [example: 1997 Oldsmobile Cutlass Supreme
owner's manual] that if the vehicle is parked on a steep slope using the park lock
only, it may not be possible to release the park lock (move the selector lever out
of "P"). Another vehicle may be required to push the stuck vehicle uphill slightly
to remove the loading on the park lock pawl.
Most automobiles require P or N to be set on the selector lever before the internal
combustion engine can be started. This is typically achieved via a normally open
'inhibitor' switch, which is wired in series with the starter motor engagement
circuit, and is only closed when P or N is selected, thus completing the circuit
(when the key is turned to the start position)
Reverse (R)
This engages reverse gear within the transmission, giving the ability for the
vehicle to drive backwards. In order for the driver to select reverse in modern
transmissions, they must come to a complete stop, push the shift lock button in (or
pull the shift lever forward in the case of a column shifter) and select reverse. Not
coming to a complete stop can cause severe damage to the transmission. Many
modern automatic transmissions have a safety mechanism in place, which does to
some extent prevent (but does not completely avoid) inadvertently putting the car
in reverse when the vehicle is moving forwards. This mechanism usually consists
of a solenoid-controlled physical barrier on either side of the Reverse position,
which is electronically engaged by a switch on the brake pedal. Therefore, the
brake pedal needs to be depressed in order to allow the selection of reverse. Some
electronic transmissions prevent or delay engagement of reverse gear altogether
while the car is moving.
Some shifters with a shift button allow the driver to freely move the shifter from
R to N or D, or simply moving the shifter to N or D without actually depressing
the button. However, the driver cannot put back the shifter to R without
depressing the shift button to prevent accidental shifting, especially at high
speeds, which could damage the transmission.
Neutral/No gear (N)
This disengages all gear trains within the transmission, effectively disconnecting
the transmission from the driven roadwheels, so the vehicle is able to move freely
under its own weight and gain momentum without the motive force from the
engine (engine braking). This is the only other selection in which the vehicle's
engine can be started.
Drive (D)
This position allows the transmission to engage the full range of available forward
gear trains, and therefore allows the vehicle to move forward and accelerate
through its range of gears. The number of gear 'ratios' a transmission has depends
on the model, but they initially ranged from three (predominant before the 1990s),
to four and five speeds (losing popularity to six-speed autos, though still favored
by Chrysler and Honda/Acura). Six-speed automatic transmissions are now
probably the most common offering Toyota Camry V6 models, the Chevrolet
Malibu LTZ, Corvette, GM trucks, Pontiac G8, Ford Falcon BF 2005-2007 and
Falcon FG 2008 - current in Australia with 6 speed ZF, and most newer model
Ford/Lincoln/Mercury vehicles). However, seven-speed autos are becoming
available (found in Mercedes 7G gearbox), as are eight-speed autos in the newer
models of Lexus and BMW cars.
OverDrive (D, OD, or a boxed [D])
This mode is used in some transmissions to allow early computer-controlled
transmissions to engage the Automatic Overdrive. In these transmissions, Drive
(D) locks the Automatic Overdrive off, but is identical otherwise. OD (Overdrive)
in these cars is engaged under steady speeds or low acceleration at approximately
35–45 mph (56–72 km/h). Under hard acceleration or below 35–45 mph (56–72
km/h), the transmission will automatically downshift. Vehicles with this option
should be driven in this mode unless circumstances require a lower gear.
Third (3)
This mode limits the transmission to the first three gear ratios, or sometimes locks
the transmission in third gear. This can be used to climb or going down hill. Some
vehicles will automatically shift up out of third gear in this mode if a certain RPM
range is reached in order to prevent engine damage. This gear is also
recommended while towing a caravan.
Second (2 or S)
This mode limits the transmission to the first two gear ratios, or locks the
transmission in second gear on Ford, Kia, and Honda models. This can be used to
drive in adverse conditions such as snow and ice, as well as climbing or going
down hills in the winter time. Some vehicles will automatically shift up out of
second gear in this mode if a certain RPM range is reached in order to prevent
engine damage.
Although traditionally considered second gear, there are other names used.
Chrysler models with a three-speed automatic since the late 1980s have called this
gear 3 while using the traditional names for Drive and Low.
First (1 or L [Low])
This mode locks the transmission in first gear only. It will not change to any other
gear range. This, like second, can be used during the winter season, or for towing.
As well as the above modes there are also other modes, dependent on the manufacturer
and model. Some examples include
In Hondas and Acuras equipped with five-speed automatic transmissions, this
mode is used commonly for highway use (as stated in the manual), and uses all
five forward gears.
This mode is also found in Honda and Acura four- or five-speed automatics, and
only uses the first four gear ratios. According to the manual, it is used for "stop
and go traffic", such as city driving.
D3 or 3
This mode is found in Honda, Acura, Volkswagen and Pontiac four-speed
automatics and only uses the first three gear ratios. According to the manual, it is
used for "stop & go traffic", such as city driving.
S or Sport
This is commonly described as 'Sport mode'. It operates in an identical manner as
'D' mode, except that the upshifts change much higher up the engine's rev range.
This has the effect on maximising all the available engine output, and therefore
enhances the performance of the vehicle, particularly during acceleration. This
mode will also downchange much higher up the rev range compared to 'D' mode,
maximising the effects of engine braking. This mode will have a detrimental
effect on fuel economy. Hyundai has a Norm/Power switch next to the gearshift
for this purpose on the Tiburon.
Some early GM's equipped with Tourqueflite transmsissons used (S) to indicate Second
gear, being the same as the 2 position on a Chrysler, shifting between only first and
second gears. This would have been recommended for use on steep grades, or slippery
roads like dirt, or ice, and limited to speeds under 40 mph. (L) was used in some early
GM's to indicate (L)ow gear, being the same as the 2 position on a Chrysler, locking the
transmission into first gear. This would have been recommended for use on steep grades,
or slippery roads like dirt, or ice, and limited to speeds under 15 mph.
+ −, and M
This is for the 'manual mode' selection of gears in certain automatics, such as
Porsche's Tiptronic. The M feature can also be found in Chrysler and General
Motors products such as the Dodge Magnum and Pontiac G6, as well as Toyota's
Camry, Corolla, Fortuner, Previa and Innova. Mitsubishi and some Audi models
(TT), meanwhile do not have the M, and instead have the + and -, which is
separated from the rest of the shift modes; the same is true for some Peugeot
products like Peugeot 206. Meanwhile, the driver can shift up and down at will by
toggling the (console mounted) shift lever like a semi-automatic transmission.
This mode may be engaged either through a selector/position or by actually
changing the gears (e.g., tipping the gear-down paddles mounted near the driver's
fingers on the steering wheel).
Winter (W)
In some Mercedes-Benz, BMW and General Motors Europe models, a 'Winter
mode' can be engaged so that second gear is selected instead of first when pulling
away from stationary, to reduce the likelihood of loss of traction due to wheelspin
on snow or ice. On GM cars, this was D2 in the 1950s, and is Second Gear Start
after 1990. On Ford, Kia, and Honda automatics, this feature can be accessed by
moving the gear selector to 2 to start, then taking your foot off the accelerator
while selecting D once the car is moving.
Brake (B)
A mode selectable on some Toyota models. In non-hybrid cars, this mode lets the
engine do compression braking, also known as engine braking, typically when
encountering a steep downhill. Instead of engaging the brakes, the engine in a
non-hybrid car switches to a lower gear and slows down the spinning tires. The
engine holds the car back, instead of the brakes slowing it down. For hybrid cars,
this mode converts the electric motor into a generator for the battery. It is not the
same as downshifting in a non-hybrid car, but it has the same effect in slowing the
car without using the brakes. GM called this HR (hill retarder) and GR (grade
retarder) in the 1950s.
Hydraulic automatic transmissions
The predominant form of automatic transmission is hydraulically operated; using a fluid
coupling or torque converter, and a set of planetary gearsets to provide a range of gear
Parts and operation
A cut-away model of a torque converter
A hydraulic automatic transmission consists of the following parts:
Torque converter: A type of fluid coupling, hydraulically connecting the engine to
the transmission. It takes the place of a mechanical clutch, allowing the
transmission to stay 'in gear' and the engine to remain running while the vehicle is
stationary, without stalling. A torque converter differs from a fluid coupling, in
that it provides a variable amount of torque multiplication at low engine speeds,
increasing "breakaway" acceleration. This is accomplished with a third member in
the "coupling assembly" known as the stator, and by altering the shapes of the
vanes inside the coupling in such a way as to curve the fluid's path into the stator.
The stator captures the kinetic energy of the transmission fluid, in effect using the
leftover force of it to enhance torque multiplication.
Pump, not to be confused with the impeller inside the torque converter, is
typically a gear pump mounted between the torque converter and the planetary
gearset. It draws transmission fluid from a sump and pressurizes it, which is
needed for transmission components to operate. The input for the pump is
connected to the torque converter housing, which in turn is bolted to the engine's
flywheel, so the pump provides pressure whenever the engine is running and there
is enough transmission fluid.
Planetary gearset: A compound epicyclic planetary gearset, whose bands and
clutches are actuated by hydraulic servos controlled by the valve body, providing
two or more gear ratios.
Clutches and bands: to effect gear changes, one of two types of clutches or bands
are used to hold a particular member of the planetary gearset motionless, while
allowing another member to rotate, thereby transmitting torque and producing
gear reductions or overdrive ratios. These clutches are actuated by the valve body
(see below), their sequence controlled by the transmission's internal
programming. Principally, a type of device known as a sprag or roller clutch is
used for routine upshifts/downshifts. Operating much as a ratchet, it transmits
torque only in one direction, free-wheeling or "overrunning" in the other. The
advantage of this type of clutch is that it eliminates the sensitivity of timing a
simultaneous clutch release/apply on two planetaries, simply "taking up" the
drivetrain load when actuated, and releasing automatically when the next gear's
sprag clutch assumes the torque transfer. The bands come into play for manually
selected gears, such as low range or reverse, and operate on the planetary drum's
circumference. Bands are not applied when drive/overdrive range is selected, the
torque being transmitted by the sprag clutches instead. Bands are used for
braking; the GM Turbo-Hydramatics incorporated this..
Valve body: hydraulic control center that receives pressurized fluid from the main
pump operated by the fluid coupling/torque converter. The pressure coming from
this pump is regulated and used to run a network of spring-loaded valves, check
balls and servo pistons. The valves use the pump pressure and the pressure from a
centrifugal governor on the output side (as well as hydraulic signals from the
range selector valves and the throttle valve or modulator) to control which ratio is
selected on the gearset; as the vehicle and engine change speed, the difference
between the pressures changes, causing different sets of valves to open and close.
The hydraulic pressure controlled by these valves drives the various clutch and
brake band actuators, thereby controlling the operation of the planetary gearset to
select the optimum gear ratio for the current operating conditions. However, in
many modern automatic transmissions, the valves are controlled by electromechanical servos which are controlled by the electronic engine control unit
(ECU) or a separate transmission control unit (TCU).
Hydraulic & lubricating oil: called automatic transmission fluid (ATF), this
component of the transmission provides lubrication, corrosion prevention, and a
hydraulic medium to convey mechanical power (for the operation of the
transmission). Primarily made from refined petroleum, and processed to provide
properties that promote smooth power transmission and increase service life, the
ATF is one of the few parts of the automatic transmission that needs routine
service as the vehicle ages.
The multitude of parts, along with the complex design of the valve body, originally made
hydraulic automatic transmissions much more complicated (and expensive) to build and
repair than manual transmissions. In most cars (except US family, luxury, sport-utility
vehicle, and minivan models) they have usually been extra-cost options for this reason.
Mass manufacturing and decades of improvement have reduced this cost gap.
Energy efficiency
Hydraulic automatic transmissions are almost always less energy efficient than manual
transmissions due mainly to viscous and pumping losses; both in the torque converter and
the hydraulic actuators. A relatively small amount of energy is required to pressurize the
hydraulic control system, which uses fluid pressure to determine the correct shifting
patterns and operate the various automatic clutch mechanisms.
Manual transmissions use a mechanical clutch to transmit torque, rather than a torque
converter, thus avoiding the primary source of loss in an automatic transmission. Manual
transmissions also avoid the power requirement of the hydraulic control system, by
relying on the human muscle power of the vehicle operator to disengage the clutch and
actuate the gear levers, and the mental power of the operator to make appropriate gear
ratio selections. Thus the manual transmission requires very little engine power to
function, with the main power consumption due to drag from the gear train being
immersed in the lubricating oil of the gearbox.
The energy efficiency of automatic transmission has increased with the introduction of
the torque converter lock-up clutch, which practically eliminates fluid losses when
engaged. Modern automatic transmission also minimize energy usage and complexity, by
minimizing the amount of shifting logic that is done hydraulically. Typically, control of
the transmission has been transferred to computerized control systems which do not use
fluid pressure for shift logic or actuation of clutching mechanisms.
The on road acceleration of an automatic transmission can occasionally exceed that of an
otherwise identical vehicle equipped with a manual transmission in turbocharged diesel
applications. Turbo-boost is normally lost between gear changes in a manual whereas in
an automatic the accelerator pedal can remain fully depressed. This however is still
largely dependent upon the number and optimal spacing of gear ratios for each unit, and
whether or not the elimination of spooldown/accelerator lift off represent a significant
enough gain to counter the slightly higher power consumption of the automatic
transmission itself.
History and improvements
Modern automatic transmissions can trace their origins to an early "horseless carriage"
gearbox that was developed in 1904 by the Sturtevant brothers of Boston, Massachusetts.
This unit had two forward speeds, the ratio change being brought about by flyweights
that were driven by the engine. At higher engine speeds, high gear was engaged. As the
vehicle slowed down and engine RPM decreased, the gearbox would shift back to low.
Unfortunately, the metallurgy of the time wasn't up to the task, and owing to the
abruptness of the gear change, the transmission would often fail without warning.
The next significant phase in the automatic transmission's development occurred in 1908
with the introduction of Henry Ford's remarkable Model T. The Model T, in addition to
being cheap and reliable by the standards of the day, featured a simple, two speed plus
reverse planetary transmission whose operation was manually controlled by the driver
using pedals. The pedals actuated the transmission's friction elements (bands and
clutches) to select the desired gear. In some respects, this type of transmission was less
demanding of the driver's skills than the contemporary, unsynchronized manual
transmission, but still required that the driver know when to make a shift, as well as how
to get the car off to a smooth start.
In 1934, both REO and General Motors developed semi-automatic transmissions that
were less difficult to operate than a fully manual unit. These designs, however, continued
to use a clutch to engage the engine with the transmission. The General Motors unit,
dubbed the "Automatic Safety Transmission," was notable in that it employed a powershifting planetary gearbox that was hydraulically controlled and was sensitive to road
speed, anticipating future development.
Parallel to the development in the 1930s of an automatically-shifting gearbox was
Chrysler's work on adapting the fluid coupling to automotive use. Invented early in the
20th century, the fluid coupling was the answer to the question of how to avoid stalling
the engine when the vehicle was stopped with the transmission in gear. Chrysler itself
never used the fluid coupling with any of its automatic transmissions, but did use it in
conjunction with a hybrid manual transmission called "Fluid Drive" (the similar HyDrive used a torque converter). These developments in automatic gearbox and fluid
coupling technology eventually culminated in the introduction in 1939 of the General
Motors Hydra-Matic, the world's first mass-produced automatic transmission.
Available as an option on 1940 Oldsmobiles and later Cadillacs, the Hydra-Matic
combined a fluid coupling with three hydraulically-controlled planetary gearsets to
produce four forward speeds plus reverse. The transmission was sensitive to engine
throttle position and road speed, producing fully automatic up- and down-shifting that
varied according to operating conditions.
The Hydra-Matic was subsequently adopted by Cadillac and Pontiac, and was sold to
various other automakers, including Bentley, Hudson, Kaiser, Nash, and Rolls-Royce. It
also found use during World War II in some military vehicles. From 1950-1954, Lincoln
cars were also available with the Hydra-Matic. Mercedes-Benz subsequently devised a
four-speed fluid coupling transmission that was similar in principle to the Hydra-Matic,
but of a different design.
Interestingly, the original Hydra-Matic incorporated two features which are widely
emulated in today's transmissions. The Hydra-Matic's ratio spread through the four gears
produced excellent "step off" and acceleration in first, good spacing of intermediate
gears, and the effect of an overdrive in fourth, by virtue of the low numerical rear axle
ratio used in the vehicles of the time. In addition, in third and fourth gear, the fluid
coupling only handled a portion of the engine's torque, resulting in a high degree of
efficiency. In this respect, the transmission's behavior was similar to modern units
incorporating a lock-up torque converter.
In 1956, GM introduced the "Jetaway" Hydra-Matic, which was different in design than
the older model. Addressing the issue of shift quality, which was an ongoing problem
with the original Hydra-Matic, the new transmission utilized two fluid couplings, the
primary one that linked the transmission to the engine, and a secondary one that replaced
the clutch assembly that controlled the forward gearset in the original. The result was
much smoother shifting, especially from first to second gear, but with a loss in efficiency
and an increase in complexity. Another "innovation" for this new style Hydra-Matic was
the appearance of a "Park" position on the selector. The original Hydra-Matic, which
continued in production until the mid-1960s, still used the "Reverse" position for parking
pawl engagement.
The first torque converter automatic, Buick's Dynaflow, was introduced for the 1948
model year. It was followed by Packard's Ultramatic in mid-1949 and Chevrolet's
Powerglide for the 1950 model year. Each of these transmissions had only two forward
speeds, relying on the converter for additional torque multiplication. In the early 1950s,
BorgWarner developed a series of three-speed torque converter automatics for American
Motors, Ford Motor Company, Studebaker, and several other manufacturers in the US
and other countries. Chrysler was late in developing its own true automatic, introducing
the two-speed torque converter PowerFlite in 1953, and the three-speed TorqueFlite in
1956. The latter was the first to utilize the Simpson compound planetary gearset.
General Motors produced multiple-turbine torque converters from 1954 to 1961. These
included the Twin-Turbine Dynaflow and the triple-turbine Turboglide transmissions.
The shifting took place in the torque converter, rather than through pressure valves and
changes in planetary gear connections. Each turbine was connected to the drive shaft
through a different gear train. These phased from one ratio to another according to
demand, rather than shifting. The Turboglide actually had two speed ratios in reverse,
with one of the turbines rotating backwards.
By the late 1960s, most of the fluid-coupling four-speed and two-speed transmissions had
disappeared in favor of three-speed units with torque converters. Also around this time,
whale oil was removed from automatic transmission fluid. By the early 1980s, these were
being supplemented and eventually replaced by overdrive-equipped transmissions
providing four or more forward speeds. Many transmissions also adopted the lock-up
torque converter (a mechanical clutch locking the torque converter pump and turbine
together to eliminate slip at cruising speed) to improve fuel economy.
As computerised engine control units (ECUs) became more capable, much of the logic
built into the transmission's valve body was offloaded to the ECU. (Some manufacturers
use a separate computer dedicated to the transmission, but sharing information with the
engine management computer.) In this case, solenoids turned on and off by the computer
control shift patterns and gear ratios, rather than the spring-loaded valves in the valve
body. This allows for more precise control of shift points, shift quality, lower shift times,
and (on some newer cars) semi-automatic control, where the driver tells the computer
when to shift. The result is an impressive combination of efficiency and smoothness.
Some computers even identify the driver's style and adapt to best suit it.
ZF Friedrichshafen and BMW were responsible for introducing the first six-speed (the ZF
6HP26 in the 2002 BMW E65 7-Series). Mercedes-Benz's 7G-Tronic was the first sevenspeed in 2003, with Toyota introducing an eight-speed in 2007 on the Lexus LS 460.
Derived from the 7G-Tronic, Mercedes-Benz unveiled a semi-automatic transmission
with the torque converter replaced with a wet multi clutch called the AMG SPEEDSHIFT
Automatic transmission models
Some of the best known automatic transmission families include:
General Motors — Powerglide, "Turbo-Hydramatic" TH350, TH400 and 700R4,
4L60-E, 4L80-E, Holden Trimatic
Ford: Cruise-O-Matic, C4, C6, AOD/AODE, E4OD, ATX, AXOD/AX4S/AX4N
Chrysler: TorqueFlite 727 and 904, A500, A518, 45RFE, 545RFE
BorgWarner (later Aisin AW)
ZF Friedrichshafen automatic transmissions
Allison Transmission
Voith Turbo
Aisin AW; Aisin AW is a Japanese automotive parts supplier, known for its
automatic transmissions and navigation systems
Volkswagen Group - 01M
Drivetrain Systems International (DSI) - M93, M97 and M74 4-speeds, M78 and
M79 6-speeds
Automatic transmission families are usually based on Ravigneaux, Lepelletier, or
Simpson planetary gearsets. Each uses some arrangement of one or two central sun gears,
and a ring gear, with differing arrangements of planet gears that surround the sun and
mesh with the ring. An exception to this is the Hondamatic line from Honda, which uses
sliding gears on parallel axes like a manual transmission without any planetary gearsets.
Although the Honda is quite different from all other automatics, it is also quite different
from an automated manual transmission (AMT).
Many of the above AMTs exist in modified states, which were created by racing
enthusiasts and their mechanics by systematically re-engineering the transmission to
achieve higher levels of performance. These are known as "performance transmissions".
An example of a manufacturer of high performance transmissions of General Motors and
Ford transmissions is PerformaBuilt.
Continuously variable transmissions
A fundamentally different type of automatic transmission is the continuously variable
transmission or CVT, which can smoothly and steplessly alter its gear ratio by varying the
diameter of a pair of belt or chain-linked pulleys, wheels or cones. Some continuously
variable transmissions use a hydrostatic drive — consisting of a variable displacement
pump and a hydraulic motor — to transmit power without gears. CVT designs are usually
as fuel efficient as manual transmissions in city driving, but early designs lose efficiency
as engine speed increases.
A slightly different approach to CVT is the concept of toroidal CVT or infinitely variable
transmission (IVT). These concepts provide zero and reverse gear ratios.
Some current hybrid vehicles, notably those of Toyota, Lexus and Ford Motor Company,
have an "electronically-controlled CVT" (E-CVT). In this system, the transmission has
fixed gears, but the ratio of wheel-speed to engine-speed can be continuously varied by
controlling the speed of the third input to a differential using an electric motor-generator.
Manually controlled automatic transmissions
Most automatic transmissions offer the driver a certain amount of manual control over
the transmission's shifts (beyond the obvious selection of forward, reverse, or neutral).
Those controls take several forms:
Throttle kickdown
Most automatic transmissions include some means of forcing a downshift into the
lowest possible gear ratio if the throttle pedal is fully depressed. In many older
designs, kickdown is accomplished by mechanically actuating a valve inside the
transmission. Most modern designs use a solenoid-operated valve that is triggered
by a switch on the throttle linkage or by the engine control unit (ECM) in
response to an abrupt increase in engine power.
Mode selection
Allows the driver to choose between preset shifting programs. For example,
'Economy mode' saves fuel by upshifting at lower engine speeds, while 'Sport
mode' (aka Power or Performance) delays shifting for maximum acceleration. The
modes also change how the computer responds to throttle input.
Low gear ranges
Conventionally, automatic transmissions have selector positions that allow the
driver to limit the maximum ratio that the transmission may engage. On older
transmissions, this was accomplished by a mechanical lockout in the transmission
valve body preventing an upshift until the lockout was disengaged; on computercontrolled transmissions, the same effect is accomplished by firmware. The
transmission can still upshift and downshift automatically between the remaining
ratios: for example, in the 3 range, a transmission could shift from first to second
to third, but not into fourth or higher ratios. Some transmissions will still upshift
automatically into the higher ratio if the engine reaches its maximum permissible
speed in the selected range.
Manual controls
Some transmissions have a mode in which the driver has full control of ratio
changes (either by moving the selector, or through the use of buttons or paddles),
completely overriding the automated function of the hydraulic controller. Such
control is particularly useful in cornering, to avoid unwanted upshifts or
downshifts that could compromise the vehicle's balance or traction. "Manumatic"
shifters, first popularized by Porsche in the 1990s under the trade name Tiptronic,
have become a popular option on sports cars and other performance vehicles.
With the near-universal prevalence of electronically controlled transmissions,
they are comparatively simple and inexpensive, requiring only software changes,
and the provision of the actual manual controls for the driver. The amount of true
manual control provided is highly variable: some systems will override the
driver's selections under certain conditions, generally in the interest of preventing
engine damage. Since these gearboxes also have a throttle kickdown switch, it is
impossible to fully exploit the engine power at low to medium engine speeds.
Second gear takeoff
Some automatics, particularly those fitted to larger capacity or high torque
engines, either when '2' is manually selected, or by engaging a "winter mode",
will start off in second gear instead of first, and then not shift into a higher gear
until returned to D. Also note that as with most American automatic
transmissions, selecting "2" using the selection lever will not tell the transmission
to be in only 2nd gear, rather, it will simply limit the transmission to 2nd gear
after prolonging the duration of 1st gear through higher speeds than normal
operation. The 2000-2002 Lincoln LS V8 (the five-speed automatic without
manumatic capabilities (as opposed to the optional sport package w/ manu-matic
5sp) started in 2nd gear during most starts both in winter and summer by selecting
the "D5" transmission selection notch in the shiftgate (For fuel savings), whereas
"D4" would always start in 1st gear. This is done to reduce torque multiplication
when proceeding forward from a standstill in conditions where traction was
limited — on snow- or ice-covered roads, for example.
Some automatic transmissions modified or designed specifically for drag racing may also
incorporate a transmission brake, or "trans-brake," as part of a manual valve body.
Activated by electrical solenoid control, a trans-brake simultaneously engages the first
and reverse gears, locking the transmission and preventing the input shaft from turning.
This allows the driver of the car to raise the engine RPM against the resistance of the
torque converter, then launch the car by simply releasing the trans-brake switch.
Chapter 12
List of Gear Nomenclature
Gears have a wide range of unique terminology known as gear nomenclature. Many of
the terms defined cite the same reference work.
Principal dimensions
The addendum is the height by which a tooth of a gear projects beyond (outside for
external, or inside for internal) the standard pitch circle or pitch line; also, the radial
distance between the pitch circle and the addendum circle.
Addendum angle
Addendum angle in a bevel gear, is the angle between elements of the face cone and
pitch cone.
Addendum circle
Internal gear diameters
Root circle
The addendum circle coincides with the tops of the teeth of a gear and is concentric with
the standard (reference) pitch circle and radially distant from it by the amount of the
addendum. For external gears, the addendum circle lies on the outside cylinder while on
internal gears the addendum circle lies on the internal cylinder.
Angle of pressure
Apex to back
Apex to back
Mounting distance
Apex to back, in a bevel gear or hypoid gear, is the distance in the direction of the axis
from the apex of the pitch cone to a locating surface at the back of the blank.
Back angle
The back angle of a bevel gear is the angle between an element of the back cone and a
plane of rotation, and usually is equal to the pitch angle.
Back cone
Principal dimensions
The back cone of a bevel or hypoid gear is an imaginary cone tangent to the outer ends
of the teeth, with its elements perpendicular to those of the pitch cone. The surface of the
gear blank at the outer ends of the teeth is customarily formed to such a back cone.
Back cone distance
Back cone distance in a bevel gear is the distance along an element of the back cone
from its apex to the pitch cone.
Base circle
Involute teeth
The base circle of an involute gear is the circle from which involute tooth profiles are
Base cylinder
Base cylinder
The base cylinder corresponds to the base circle, and is the cylinder from which involute
tooth surfaces are developed.
Base diameter
Base diameter
The base diameter of an involute gear is the diameter of the base circle.
Bull gear
The term bull gear is used to refer to the larger of two spur gears that are in engagement
in any machine. The smaller gear is usually referred to as a pinion.
Center distance
Center distance
Center distance (operating) is the shortest distance between non-intersecting axes. It is
measured along the mutual perpendicular to the axes, called the line of centers. It applies
to spur gears, parallel axis or crossed axis helical gears, and worm gearing.
Central plane
Central plane
The central plane of a worm gear is perpendicular to the gear axis and contains the
common perpendicular of the gear and worm axes. In the usual case with axes at right
angles, it contains the worm axis.
Composite action test
Schematic of the composite action test
The composite action test (double flank) is a method of inspection in which the work
gear is rolled in tight double flank contact with a master gear or a specified gear, in order
to determine (radial) composite variations (deviations). The composite action test must be
made on a variable center distance composite action test device.
Cone distance
Cone distance
Cone distance in a bevel gear is the general term for the distance along an element of the
pitch cone from the apex to any given position in the teeth.
Outer cone distance in bevel gears is the distance from the apex of the pitch cone to the
outer ends of the teeth. When not otherwise specified, the short term cone distance is
understood to be outer cone distance.
Mean cone distance in bevel gears is the distance from the apex of the pitch cone to the
middle of the face width.
Inner cone distance in bevel gears is the distance from the apex of the pitch cone to the
inner ends of the teeth.
Conjugate gears
Conjugate gears transmit uniform rotary motion from one shaft to another by means of
gear teeth. The normals to the profiles of these teeth, at all points of contact, must pass
through a fixed point in the common centerline of the two shafts.
Crossed helical gear
A crossed helical gear is a gear that operate on non-intersecting, non-parallel axes.
The term crossed helical gears has superseded the term spiral gears. There is
theoretically point contact between the teeth at any instant. They have teeth of the same
or different helix angles, of the same or opposite hand. A combination of spur and helical
or other types can operate on crossed axes.
Crossing point
The crossing point is the point of intersection of bevel gear axes; also the apparent point
of intersection of the axes in hypoid gears, crossed helical gears, worm gears, and offset
face gears, when projected to a plane parallel to both axes.
Crown circle
The crown circle in a bevel or hypoid gear is the circle of intersection of the back cone
and face cone.
Crowned teeth
Crowned gear
Crowned teeth have surfaces modified in the lengthwise direction to produce localized
contact or to prevent contact at their ends.
Dedendum angle
Dedendum angle in a bevel gear, is the angle between elements of the root cone and
pitch cone.
Equivalent pitch radius
Back cone equivalent
Equivalent pitch radius is the radius of the pitch circle in a cross section of gear teeth in
any plane other than a plane of rotation. It is properly the radius of curvature of the pitch
surface in the given cross section. Examples of such sections are the transverse section of
bevel gear teeth and the normal section of helical teeth.
Face (tip) angle
Face (tip) angle in a bevel or hypoid gear, is the angle between an element of the face
cone and its axis.
Face cone
The face cone, also known as the tip cone is the imaginary surface that coincides with
the tops of the teeth of a bevel or hypoid gear.
Face gear
Face worm gear
A face gear set typically consists of a disk-shaped gear, grooved on at least one face, in
combination with a spur, helical, or conical pinion. A face gear has a planar pitch surface
and a planar root surface, both of which are perpendicular to the axis of rotation. It can
also be referred to as a face wheel, crown gear, crown wheel, contrate gear or contrate
Face width
Face width
The face width of a gear is the length of teeth in an axial plane. For double helical, it
does not include the gap.
Total face width is the actual dimension of a gear blank including the portion that
exceeds the effective face width, or as in double helical gears where the total face width
includes any distance or gap separating right hand and left hand helices.
For a cylindrical gear, effective face width is the portion that contacts the mating teeth.
One member of a pair of gears may engage only a portion of its mate.
For a bevel gear, different definitions for effective face width are applicable.
Form diameter
Form diameter
Form diameter is the diameter of a circle at which the trochoid (fillet curve) produced
by the tooling intersects, or joins, the involute or specified profile. Although these terms
are not preferred, it is also known as the true involute form diameter (TIF), start of
involute diameter (SOI), or when undercut exists, as the undercut diameter. This diameter
cannot be less than the base circle diameter.
Front angle
The front angle, in a bevel gear, denotes the angle between an element of the front cone
and a plane of rotation, and usually equals the pitch angle.
Front cone
The front cone of a hypoid or bevel gear is an imaginary cone tangent to the inner ends
of the teeth, with its elements perpendicular to those of the pitch cone. The surface of the
gear blank at the inner ends of the teeth is customarily formed to such a front cone, but
sometimes may be a plane on a pinion or a cylinder in a nearly flat gear.
Gear center
A gear center is the center of the pitch circle.
Heel and toe
The heel of a tooth on a bevel gear or pinion is the portion of the tooth surface near its
outer end.
The toe of a tooth on a bevel gear or pinion is the portion of the tooth surface near its
inner end.
Helical rack
A helical rack has a planar pitch surface and teeth that are oblique to the direction of
Index deviation
The displacement of any tooth flank from its theoretical position, relative to a datum
tooth flank.
Distinction is made as to the direction and algebraic sign of this reading. A condition
wherein the actual tooth flank position was nearer to the datum tooth flank, in the
specified measuring path direction (clockwise or counterclockwise), than the theoretical
position would be considered a minus (-) deviation. A condition wherein the actual tooth
flank position was farther from the datum tooth flank, in the specified measuring path
direction, than the theoretical position would be considered a plus (+) deviation.
The direction of tolerancing for index deviation along the arc of the tolerance diameter
circle within the transverse plane.
Inside cylinder
Diameters, Internal Gear
The inside cylinder is the surface that coincides with the tops of the teeth of an internal
cylindrical gear.
Inside diameter
Internal gear diameters
Inside diameter is the diameter of the addendum circle of an internal gear.
Involute polar angle
Involute polar angle
Expressed as θ, the involute polar angle is the angle between a radius vector to a point,
P, on an involute curve and a radial line to the intersection, A, of the curve with the base
Involute roll angle
Involute roll angle
Expressed as ε, the involute roll angle is the angle whose arc on the base circle of radius
unity equals the tangent of the pressure angle at a selected point on the involute.
Involute teeth
Involute teeth
Involute teeth of spur gears, helical gears, and worms are those in which the profile in a
transverse plane (exclusive of the fillet curve) is the involute of a circle.
Top and bottom lands
Bottom land
The bottom land is the surface at the bottom of a gear tooth space adjoining the fillet.
Top land
Top land is the (sometimes flat) surface of the top of a gear tooth.
Line of centers
The line of centers connects the centers of the pitch circles of two engaging gears; it is
also the common perpendicular of the axes in crossed helical gears and wormgears. When
one of the gears is a rack, the line of centers is perpendicular to its pitch line.
Mounting distance
Mounting distance
Mounting distance, for assembling bevel gears or hypoid gears, is the distance from the
crossing point of the axes to a locating surface of a gear, which may be at either back or
Normal module
Normal module is the value of the module in a normal plane of a helical gear or worm.
mn = mtcosβ
Normal plane
Planes at a pitch point on a helical tooth
A normal plane is normal to a tooth surface at a pitch point, and perpendicular to the
pitch plane. In a helical rack, a normal plane is normal to all the teeth it intersects. In a
helical gear, however, a plane can be normal to only one tooth at a point lying in the
plane surface. At such a point, the normal plane contains the line normal to the tooth
Important positions of a normal plane in tooth measurement and tool design of helical
teeth and worm threads are:
1. the plane normal to the pitch helix at side of tooth;
2. the plane normal to the pitch helix at center of tooth;
3. the plane normal to the pitch helix at center of space between two teeth
In a spiral bevel gear, one of the positions of a normal plane is at a mean point and the
plane is normal to the tooth trace.
Offset is the perpendicular distance between the axes of hypoid gears or offset face gears.
In the diagram to the right, (a) and (b) are referred to as having an offset below center,
while those in (c) and (d) have an offset above center. In determining the direction of
offset, it is customary to look at the gear with the pinion at the right. For below center
offset the pinion has a left hand spiral, and for above center offset the pinion has a right
hand spiral.
Outside cylinder
Cylindrical surfaces
The outside (tip or addendum) cylinder is the surface that coincides with the tops of the
teeth of an external cylindrical gear.
Outside diameter
Wormgear diameters
The outside diameter of a gear is the diameter of the addendum (tip) circle. In a bevel
gear it is the diameter of the crown circle. In a throated wormgear it is the maximum
diameter of the blank. The term applies to external gears.
Conical surfaces
Pitch angle
Angle relationships
Pitch angle in bevel gears, is the angle between an element of a pitch cone and its axis.
In external and internal bevel gears, the pitch angles are respectively less than and greater
than 90 degrees.
Pitch circle
A pitch circle (operating) is the curve of intersection of a pitch surface of revolution and
a plane of rotation. It is the imaginary circle that rolls without slipping with a pitch circle
of a mating gear.
Pitch cone
Pitch cones
A pitch cone is the imaginary cone in a bevel gear that rolls without slipping on a pitch
surface of another gear.
Pitch cylinder
Pitch cylinder
A pitch cylinder is the imaginary cylinder in a spur or helical gear that rolls without
slipping on a pitch plane or pitch cylinder of another gear.
Pitch helix
Tooth helix
The pitch helix is the intersection of the tooth surface and the pitch cylinder of a helical
gear or cylindrical worm.
Base helix
The base helix of a helical, involute gear or involute worm lies on its base cylinder.
Base helix angle
Base helix angle is the helix angle on the base cylinder of involute helical teeth or
Base lead angle
Base lead angle is the lead angle on the base cylinder. It is the complement of the base
helix angle.
Outside helix
The outside (tip or addendum) helix is the intersection of the tooth surface and the
outside cylinder of a helical gear or cylindrical worm.
Outside helix angle
Normal helix
Outside helix angle is the helix angle on the outside cylinder.
Outside lead angle
Outside lead angle is the lead angle on the outside cylinder. It is the complement of the
outside helix angle.
Normal helix
A normal helix is a helix on the pitch cylinder, normal to the pitch helix.
Pitch line
The pitch line corresponds, in the cross section of a rack, to the pitch circle (operating) in
the cross section of a gear.
Pitch point
The pitch point is the point of tangency of two pitch circles (or of a pitch circle and pitch
line) and is on the line of centers.
Pitch surfaces
Pitch surfaces
Pitch surfaces are the imaginary planes, cylinders, or cones that roll together without
slipping. For a constant velocity ratio, the pitch cylinders and pitch cones are circular.
Pitch cones
Pitch plane
Pitch planes
The pitch plane of a pair of gears is the plane perpendicular to the axial plane and
tangent to the pitch surfaces. A pitch plane in an individual gear may be any plane
tangent to its pitch surface.
The pitch plane of a rack or in a crown gear is the imaginary planar surface that rolls
without slipping with a pitch cylinder or pitch cone of another gear. The pitch plane of a
rack or crown gear is also the pitch surface.
Transverse plane
The transverse plane is perpendicular to the axial plane and to the pitch plane. In gears
with parallel axes, the transverse and the plane of rotation coincide.
Principal directions
Principal directions
Principal directions are directions in the pitch plane, and correspond to the principal cross
sections of a tooth.
The axial direction is a direction parallel to an axis.
The transverse direction is a direction within a transverse plane.
The normal direction is a direction within a normal plane.
Profile radius of curvature
Fillet radius
Profile radius of curvature is the radius of curvature of a tooth profile, usually at the
pitch point or a point of contact. It varies continuously along the involute profile.
Radial composite deviation
Total composite variation trace
Tooth-to-tooth radial composite deviation (double flank) is the greatest change in center
distance while the gear being tested is rotated through any angle of 360 degree/z during
double flank composite action test.
Tooth-to-tooth radial composite tolerance (double flank) is the permissible amount of
tooth-to-tooth radial composite deviation.
Total radial composite deviation (double flank) is the total change in center distance
while the gear being tested is rotated one complete revolution during a double flank
composite action test.
Total radial composite tolerance (double flank) is the permissible amount of total radial
composite deviation.
Root angle
Root angle in a bevel or hypoid gear, is the angle between an element of the root cone
and its axis.
Root circle
Internal gear diameters
The root circle coincides with the bottoms of the tooth spaces.
Root cone
Principal dimensions
The root cone is the imaginary surface that coincides with the bottoms of the tooth
spaces in a bevel or hypoid gear.
Root cylinder
The root cylinder is the imaginary surface that coincides with the bottoms of the tooth
spaces in a cylindrical gear.
Shaft angle
Shaft angle
A shaft angle is the angle between the axes of two non-parallel gear shafts. In a pair of
crossed helical gears, the shaft angle lies between the oppositely rotating portions of two
shafts. This applies also in the case of worm gearing. In bevel gears, the shaft angle is the
sum of the two pitch angles. In hypoid gears, the shaft angle is given when starting a
design, and it does not have a fixed relation to the pitch angles and spiral angles.
Spur gear
Spur gear
A spur gear has a cylindrical pitch surface and teeth that are parallel to the axis.
Spur rack
A spur rack has a planar pitch surface and straight teeth that are at right angles to the
direction of motion.
Standard pitch circle
The standard pitch circle is the circle which intersects the involute at the point where
the pressure angle is equal to the profile angle of the basic rack.
Standard pitch diameter
The standard reference pitch diameter is the diameter of the standard pitch circle. In
spur and helical gears, unless otherwise specified, the standard pitch diameter is related to
the number of teeth and the standard transverse pitch. The diameter can be roughly
estimated by taking the average of the diameter measuring the tips of the gear teeth and
the base of the gear teeth.
The pitch diameter is useful in determining the spacing between gear centers because
proper spacing of gears implies tangent pitch circles. The pitch diameters of two gears
may be used to calculate the gear ratio in the same way the number of teeth is used.
Where N is the total number of teeth, p is the circular pitch, Pd is the diametrical pitch,
and ψ is the helix angle for helical gears.
Standard reference pitch diameter
The standard reference pitch diameter is the diameter of the standard pitch circle. In
spur and helical gears, unless otherwise specified, the standard pitch diameter is related to
the number of teeth and the standard transverse pitch. It is obtained as:
Test radius
The test radius (Rr) is a number used as an arithmetic convention established to simplify
the determination of the proper test distance between a master and a work gear for a
composite action test. It is used as a measure of the effective size of a gear. The test
radius of the master, plus the test radius of the work gear is the set up center distance on a
composite action test device. Test radius is not the same as the operating pitch radii of
two tightly meshing gears unless both are perfect and to basic or standard tooth thickness.
Throat diameter
Wormgear diameters
The throat diameter is the diameter of the addendum circle at the central plane of a
wormgear or of a double-enveloping wormgear.
Throat form radius
Throat form radius is the radius of the throat of an enveloping wormgear or of a doubleenveloping worm, in an axial plane.
Tip radius
Tip radius
Tip radius is the radius of the circular arc used to join a side-cutting edge and an endcutting edge in gear cutting tools. Edge radius is an alternate term.
Tip relief
Tip relief
Tip relief is a modification of a tooth profile whereby a small amount of material is
removed near the tip of the gear tooth.
Tooth surface
Profile of a spur gear
Notation and numbering for an external gear
Notation and numbering for an internal gear
The tooth surface (flank) forms the side of a gear tooth.
It is convenient to choose one face of the gear as the reference face and to mark it with
the letter “I”. The other non-reference face might be termed face “II”.
For an observer looking at the reference face, so that the tooth is seen with its tip
uppermost, the right flank is on the right and the left flank is on the left. Right and left
flanks are denoted by the letters “R” and “L” respectively.
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