ASMALL, INSECT-INSPIRED ROBOT THAT RUNS AND JUMPS

A SMALL, INSECT-INSPIRED ROBOT
THAT RUNS AND JUMPS
by
Bram G. A. Lambrecht
Submitted in partial fulfillment of the requirements
For the degree of Master of Science in Engineering
Thesis Adviser: Dr. Roger Quinn
Department of Mechanical and Aerospace Engineering
Case Western Reserve University
January 2005
Copyright © 2005 by Bram G. A. Lambrecht
All rights reserved.
Table of Contents
Table of Contents................................................................................................................ 1
List of Figures ..................................................................................................................... 3
Acknowledgements............................................................................................................. 5
Abstract ............................................................................................................................... 6
Chapter 1 – Introduction ..................................................................................................... 7
1.1 Whegs ..................................................................................................................... 8
1.2 Mini-Whegs .......................................................................................................... 10
1.3 Structure of the Thesis .......................................................................................... 13
Chapter 2 – Background and Inspiration .......................................................................... 16
2.1 Biological Inspiration............................................................................................ 16
2.2 Other Jumping Robots .......................................................................................... 22
2.3 Jumping Concepts for Mini-Whegs ...................................................................... 27
2.4 Discussion ............................................................................................................. 30
Chapter 3 – A Jumping Prototype..................................................................................... 31
3.1 Design ................................................................................................................... 31
3.2 Implementing the four-bar jumping mechanism................................................... 34
3.3 Spring selection..................................................................................................... 39
3.4 Discussion ............................................................................................................. 41
Chapter 4 – Development of Reliable Components ......................................................... 44
4.1 Steering mechanisms ............................................................................................ 45
4.2 Leg and Foot Design............................................................................................. 51
4.3 Quantification of improved Mini-Whegs performance ........................................ 56
Chapter 5 – First Attempt at Independent Running and Jumping .................................... 60
5.1 Motor Selection..................................................................................................... 60
5.2 Design ................................................................................................................... 61
5.3 Spring Selection .................................................................................................... 67
5.4 Results................................................................................................................... 67
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Chapter 6 – Weight, Size, and Cost Reduction................................................................. 69
6.1 Design Goals and Specifications .......................................................................... 69
6.2 Component Selection ............................................................................................ 71
6.3 Part Design and Material Selection....................................................................... 73
6.4 Manufacture and Assembly .................................................................................. 76
6.5 Testing................................................................................................................... 79
6.6 Mini-Whegs 8 ....................................................................................................... 82
6.7 Discussion ............................................................................................................. 83
Chapter 7 – A Fully Controllable Jumping Robot ............................................................ 84
7.1 Design Goals and Specifications .......................................................................... 84
7.2 Component Selection ............................................................................................ 85
7.3 Design ................................................................................................................... 86
7.4 Testing................................................................................................................... 92
7.5 Discussion ............................................................................................................. 94
Chapter 8 – Summary and Future Work ........................................................................... 96
8.1 Summary ............................................................................................................... 96
8.2 Future Work .......................................................................................................... 97
Appendix A – Mini-Whegs Evolution.............................................................................. 99
Appendix B – Calculations for the design of Mini-Whegs 6J ........................................ 108
B.1 Chain Length Measurement ............................................................................... 108
B.2 Slip Gear Contact Ratio...................................................................................... 108
Appendix C – Data for Mini-Whegs 7............................................................................ 109
C.1 Approximate cost of components....................................................................... 109
C.2 Comparison of Maxon motor to MPI servo ....................................................... 111
C.3 Current draw for various operating conditions .................................................. 112
C.4 Top speed calculations ....................................................................................... 112
Appendix D – Torque Considerations in Mini-Whegs 9J .............................................. 113
Bibliography ................................................................................................................... 114
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List of Figures
Figure 1.1 – PROLERO...................................................................................................... 8
Figure 1.2 – Whegs are more mobile than wheels.............................................................. 9
Figure 1.3 – Whegs I........................................................................................................... 9
Figure 1.4 – Overview of Mini-Whegs robots.................................................................. 11
Figure 1.5 – Evolution of jumping Mini-Whegs .............................................................. 13
Figure 2.1 – Alternating tripod gait .................................................................................. 17
Figure 2.2 – Stanford’s iSprawl ........................................................................................ 18
Figure 2.3 – The cockroach uses pairs of legs in unison to overcome obstacles.............. 19
Figure 2.4 – Torsionally compliant elements in Whegs ................................................... 19
Figure 2.5 – Whegs II incorporates a body joint .............................................................. 20
Figure 2.6 – Froghopper insect ......................................................................................... 21
Figure 2.7 – University of Minnesota’s Scout .................................................................. 23
Figure 2.8 – Sandia National Laboratory’s Hopper.......................................................... 24
Figure 2.9 – Jet Propulsion Laboratory’s Froghopper ...................................................... 25
Figure 2.10 – Carnegie Mellon’s 3D Bow Leg Hopper.................................................... 26
Figure 2.11 – Flip'n Fido toy ............................................................................................ 27
Figure 2.12 – Scorpion jumping concept.......................................................................... 28
Figure 2.13 – Mousetrap jumping concept ....................................................................... 29
Figure 2.14 – Four-bar jumping concept .......................................................................... 30
Figure 3.1 – Layout of Mini-Whegs 4J............................................................................. 32
Figure 3.2 – Side view of Mini-Whegs 4J ........................................................................ 33
Figure 3.3 – Slip-gear mechanism .................................................................................... 35
Figure 3.4 – Custom components for Mini-Whegs 4J...................................................... 36
Figure 3.5 – Motion of the four-bar mechanism during a jump. ...................................... 38
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Figure 3.6 – Preloaded springs store more energy............................................................ 40
Figure 3.7 –Mini-Whegs 4J jumping up a 15cm stair ...................................................... 42
Figure 4.1 – Layout of Mini-Whegs 5 .............................................................................. 46
Figure 4.2 – Ball and cup steering joint............................................................................ 49
Figure 4.3 – Mini-Whegs 5............................................................................................... 53
Figure 4.4 – Wheg appendage evolution .......................................................................... 54
Figure 4.5 – A rounded heel smooths the transition between spoke impacts. .................. 55
Figure 4.6 –Mini-Whegs 5 traversing obstacles ............................................................... 58
Figure 5.1 – Layout of Mini-Whegs 6J............................................................................. 62
Figure 5.2 – Chain length approximation ......................................................................... 63
Figure 5.3 – Rendering of Mini-Whegs 6J ....................................................................... 66
Figure 6.1 – Interior of Mini-Whegs 7.............................................................................. 72
Figure 6.2 – Exploded view of Mini-Whegs 7 ................................................................. 74
Figure 6.3 – Chain geometry for Mini-Whegs 7............................................................... 76
Figure 6.4 – Bottom view of Mini-Whegs 7..................................................................... 79
Figure 6.5 – Mini-Whegs 7 with a 3.8 cm obstacle .......................................................... 81
Figure 6.6 – The robot is able to surmount the obstacle................................................... 81
Figure 7.1 – Layout of Mini-Whegs 9J............................................................................. 87
Figure 7.2 – Rendering of Mini-Whegs 9J ....................................................................... 88
Figure 7.3 – Jumping mechanism of Mini-Whegs 9J ....................................................... 90
Figure 7.4 – Plot of spring stiffness .................................................................................. 92
Figure 7.5 –Mini-Whegs 9J jumps over a 9cm barrier. .................................................... 93
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Acknowledgements
I would like to thank everyone at the Center for Biologically Inspired Robotics
Research at Case for making this thesis possible. Thanks especially to Andy Horchler,
Bill Lewinger, and Jeremy Morrey for your previous research, ideas, and assistance.
Thanks to everyone else in the lab for urging me to get my work finished…when you
weren’t helping me procrastinate. Thanks to my advisor, Roger Quinn for giving in to
my incessant queries about research opportunities in the lab while I was a sophomore.
Thanks also to Roger Quinn and Joe Prahl for encouraging me to finish my Bachelor’s
and Master’s degrees in the same summer. It is possible, and not entirely insane.
5
A Small, Insect-Inspired Robot that Runs and Jumps
Abstract
by
Bram G. A. Lambrecht
Studies of insect locomotion, such as walking in cockroaches and jumping in
froghoppers, provide inspiration for highly mobile small robots. This thesis describes
several small vehicles called Mini-Whegs which incorporate abstracted insect locomotion
principles to improve mobility over rough terrain and relatively large obstacles. The
development of a robust, reliable, inexpensive, and lightweight Mini-Whegs platform
paves the way for the most recent robot, Mini-Whegs 9J, which includes independent
running and jumping capabilities. Mini-Whegs 9J can run at more than three body
lengths per second and jump over or onto obstacles almost two body lengths tall.
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Chapter 1 – Introduction
Small mobile robots are useful in a variety of applications. They can perform in
hostile environments and outmaneuver larger vehicles in confined spaces. Small robots
can be useful for covert or search and rescue operations. Large groups of small robots
provide redundancy in exploration missions. Small mobile robots are also appropriate for
insect inspired research.
Currently existing small robots are often limited in mobility due to external power
supplies, excessive weight, or small wheels.
The Center for Biologically Inspired
Robotics Research (Biorobotics Lab) at Case Western Reserve University has already
developed several small robots called Mini-Whegs which overcome some of these
obstacles. The radio controlled robots can steer and run at speeds of more than eight
body lengths per second. A prototype has also been built which incorporates a jumping
mechanism into the robot at the expense of steering and control.
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The purpose of this thesis is to describe the design process for creating a small
robot that combines steering, control, and jumping elements into the same vehicle while
incorporating inspiration from biological models for locomotion from the cockroach and
froghopper.
Figure 1.1 – Six motors drive the six L-shaped legs of
PROLERO.
1.1 Whegs
Legs offer greater mobility than wheels over uneven surfaces.
However,
traditional legged robots require many actuators and are difficult to control.
Some
previous attempts have been made by research groups to create a simpler leg mechanism.
For example, the European Space Agency’s PROLERO (PROtotype of LEgged ROver)
consists of six spokes driven in a circular arc by six individual motors (Figure 1.1)
(Martin-Alvarez et al. 1996). RHex improves upon the basic PROLERO design (Saranli
et al. 2000, 2001). It has passively compliant legs and a software control system that
permits the operator to change its gaits. Roger Quinn of the Biorobotics Lab at Case took
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the combination of wheels and legs one step further, to create whegs (Quinn et al. 2001).
In this paper, wheg will refer to the appendage, while Whegs and Mini-Whegs will refer
to the robots which employ wheg appendages for locomotion. A wheg is a three-spoke
appendage driven like a wheel at a central hub. The bare spokes allow a wheg to reach
over larger obstacles than a wheel (Figure 1.2). The first robot to use whegs, Whegs I,
used six whegs driven by a single motor (Figure 1.3). Neighboring pairs of whegs were
offset by 60º to give the robot an alternating tripod gait, making it statically stable at any
point in its stride.
Figure 1.2 – Whegs can reach much higher than wheels to
overcome obstacles.
Figure 1.3 – Whegs I
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1.2 Mini-Whegs
Mini-Whegs demonstrates the scalability of the whegs concept. To reduce length
and complexity, Mini-Whegs robots employ four whegs in an alternating diagonal gait.
The four whegs are driven by a single central motor. Steering is accomplished with a
servo driven rack and pinion design, similar to automotive steering. Mini-Whegs robots
have been through several iterations (Figure 1.4).
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Mini-Whegs 1 (2001)
Mini-Whegs 2 (2001)
Mini-Whegs 3 (2002)
Mini-Whegs 5 (2002)
Mini-Whegs 7 (2003)
Mini-Whegs 8 (2004)
Figure 1.4 – Overview of Mini-Whegs robots which do not
include a jumping mechanism (not to scale).
Mini-Whegs 1 was a prototype to prove the scalability of the whegs concept.
Mini-Whegs 2 was an early attempt at an even smaller robot. However, the small
batteries used to power the central motor could not provide the electric current necessary
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to drive the motor. The tiny custom made components also made the robot difficult to
assemble. Mini-Whegs 3 returned to the scale of Mini-Whegs 1. It was used as a
platform for testing several steering joint mechanisms. Mini-Whegs 4J was a prototype
to prove that a jumping mechanism could be added to a whegs platform to overcome
larger obstacles. However, it did not include steering or radio control. Mini-Whegs 5
was built to test different foot designs and to create a more robust and reliable steering
design. After Mini-Whegs 5, Mini-Whegs 6J was built to attempt to create a fully
controllable jumping robot, combining the features of Mini-Whegs 4J and Mini-Whegs 5.
However, this robot proved to be too heavy to operate effectively. The Mini-Whegs
platform was reexamined to find a way to reduce weight and size, leading to the
development and construction of Mini-Whegs 7. Concepts used in Mini-Whegs 7 were
then incorporated in a more complete design called Mini-Whegs 8, and finally in a fully
controlled jumping robot called Mini-Whegs 9J. An overview of all generations of MiniWhegs can be seen in Figure 1.4 and Figure 1.5. See Appendix A for more detailed
information about each robot.
Mini-Whegs 4J (2002)
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Mini-Whegs 6J (2003)
Mini-Whegs 9J (2004)
Figure 1.5 – Evolution of jumping Mini-Whegs (not to scale).
1.3 Structure of the Thesis
The purpose of the work described in this thesis was to develop a fully
controllable, small, jumping Whegs robot. Several intermediate robots were constructed
to test concepts and to increase mobility or reduce size and weight.
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The first three chapters of the thesis describe the inspiration and previous work on
this project. First, this chapter discusses the need for small robots and explains the
concept of whegs as developed by Quinn et al.
Chapter 2 gives a more in-depth
background of existing solutions for running and jumping in nature and in previous work
on other robots. Insect research on cockroaches and jumping insects, like the froghopper,
provides biological inspiration for the jumping whegs robot.
In addition, existing
jumping solutions in other robots are discussed. Chapter 3 describes the development of
a prototype jumping Whegs platform. This prototype jumping Whegs robot, called MiniWhegs 4J, cannot be steered and jumping is not independent of walking. However, it
does work as a proof of concept for the incorporation of a jumping mechanism in a MiniWhegs robot.
The next four chapters describe the design, construction, and testing of several
small robots which lead to the final design.
Chapter 4 discusses the design and
improvements in several of the components of Mini-Whegs 5, focusing on a reliable
steering design and on an effective design for the wheg appendages. The next chapter
describes the first attempt at combining steering and radio control into a Mini-Whegs
robot with independent running and jumping. The resulting robot, Mini-Whegs 6J, was
too heavy and large to function properly, so further steps were necessary to create a
successful design. Chapter 6 discusses the lighter, smaller, and cheaper robots, MiniWhegs 7 and Mini-Whegs 8, designed to overcome the flaws of the first controllable
jumping effort. In Chapter 7, the methods used to create the lighter, smaller robots are
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combined with successful components of the first jumping attempt to create the final
robot, Mini-Whegs 9J.
Chapter 2 – Background and Inspiration
Small robots are excellent for fitting into tight spaces, moving about undetected or
facing environments too dangerous for humans. However, most environments in which
robots are expected to perform contain many obstacles to mobility. Obstacles as small as
a stair or a rock, which would be quite easy for a human to step over, can stop a small
wheeled or tracked robot. Therefore, it is useful to examine other modes of locomotion
to improve robot mobility.
2.1 Biological Inspiration
Insects are extremely mobile creatures. They exist in almost every environment
known to man. They can run, climb, jump, swim, and even fly. The success with which
insects move about their environments forms an excellent source of inspiration for the
development of small mobile robots.
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2.1.1 Cockroach walking
Cockroaches make an excellent subject for biological research because they are
large enough to observe and experiment with easily. The products of millions of years of
evolutionary fine tuning, cockroaches run quickly and easily surmount obstacles in their
paths. By examining the mechanisms these insects use for locomotion, effective robotic
vehicles can be designed.
Figure 2.1 – The cockroach walks in an alternating tripod gait.
The highlighted legs move together.
The death head cockroach nominally walks in a tripod gait (Wilson, 1966). The
animal’s front and rear legs on one side move in unison with the middle leg on the
opposite side of its body. At least three legs remain in contact with the ground at all
times, forming a statically stable tripod (Figure 2.1).
One of the primary problems encountered when designing a legged vehicle that is
propelled by electric motors is that the power to weight ratio of motors is poor relative to
muscles. Furthermore, this ratio decreases with the size of the motors. Whegs solves this
problem by using only one motor to propel all six legs. Using this strategy its actuator
system has a 50% greater power to weight ratio than RHex (Quinn et al. 2003). iSprawl,
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developed at Stanford University, is a new hexapod robot that uses this same strategy
(Kim et al, 2004). A motor drives a dual crank slider mechanism to convert rotary to
linear motion. The linear motion of the slider is transmitted to the legs of the robot via
cables sliding inside flexible tubes (Figure 2.2). Each cable pulls or pushes the feet of the
robot up or down. By fastening the front and rear cables of one side with the middle
cable from the other side of the robot to the same crank slider mechanism, a tripod is
formed. The second crank slider turns 180º out of phase from the first, completing the
alternating tripod gait. The 15.5cm long robot can move over 15 body lengths per second
(2.3m/s).
Figure 2.2 – iSprawl has six legs, each driven by a flexible
cable, to create an alternating tripod gait.
When running in a tripod gait, the front legs of the cockroach swing as high as its
head, allowing the insect to climb over irregular terrain without changing its gait. This
allows the cockroach to traverse irregular terrain without significant gait changes (Full
and Tu, 1991). However, when larger obstacles are encountered, the animal changes its
gait. The front legs move together to reach onto an obstacle before climbing it (Figure
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2.3). The middle legs are also used to push the front of the body upwards to allow the
insect to climb over the barrier (Watson, et al. 2002).
Figure 2.3 – The cockroach uses each pair of legs in unison to
overcome an obstacle.
The mobility principles which allow the cockroach to navigate difficult terrain are
incorporated in Whegs II (Allen, 2004). A single motor drives six wheg appendages via
a chain and sprocket drive train in this 47cm long robot. As mentioned in Chapter 1, the
three-spoke design of the whegs creates a high reach, even higher relative to the body
than a cockroach’s reach. As in other Whegs robots, the whegs are initially offset to
create a nominal alternating tripod gait.
Figure 2.4 – Torsionally compliant elements allow pairs of
whegs to operate in phase to overcome large obstacles. The
black wheg is on the left side of the robot, while the gray wheg is
on the right. As the robot approaches the step (A), the whegs are
offset by 60º to create the normal tripod gait. The obstacle
forces the whegs into phase (B-C) so they can work together to
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climb onto the obstacle (D-E). After the obstacle is cleared, the
torsion springs pull the whegs back to the normal offset (F-H).
When an obstacle is encountered, torsionally compliant mechanisms between the
axle and each wheg allow the wheg to rotate up to 60º. Thus, the offset between
neighboring whegs is eliminated so that the appendages can move in unison to overcome
an obstacle (Figure 2.4). In addition to the torsionally compliant devices, a body joint
along the same axis as the middle wheg axle of the robot allows the front of the robot to
be tilted upwards to increase the reach of the front whegs even further (Figure 2.5).
Using both the abstracted biological principals of gait change and body flexion, Whegs II
is able to overcome obstacles 23cm high with whegs measuring only 20cm in diameter.
Figure 2.5 – Whegs II incorporates a body joint for increased
mobility.
2.1.2 Froghopper jumping
Many insects jump to escape from predators, to increase their speed across land,
or to launch into flight. Some insects, like bush crickets, have long rear legs which
provide leverage which enable them to jump longer distances than insects of comparable
mass with shorter legs (Burrows and Morris, 2002).
The froghopper, Philaenus
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spumarius, on the other hand, has relatively short legs, but can outperform any other
jumping insect relative to its body length. This unique insect has highly specialized rear
legs which the animal simply drags behind it while walking.
Before a jump, the
froghopper rotates its rear legs forward until they are parallel with the body, with the
femora tucked between the middle legs and the body. The tibiae fold back until they are
also parallel with the body. A ridge on each femur engages with a protrusion on the
coxa, locking the femur in place. The muscle which powers the jump can then slowly
contract while the leg remains immobile. When enough energy is stored in the muscle,
the femur disengages from the coxa, snapping quickly outward with a force 414 times the
body weight of the insect. The release of the leg during jumping occurs within 1ms
(Figure 2.6) (Burrows, 2003).
Figure 2.6 – The froghopper contracts its jumping muscles and
then leaps within 1ms.
Like the froghopper, the jumping Mini-Whegs robots discussed in this thesis use
four legs for locomotion with an additional set of legs specialized for jumping. The
jumping legs retract slowly until enough energy for a jump has been stored, at which
point the legs can extend suddenly to complete the jump.
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2.2 Other Jumping Robots
Besides examining biological methods for jumping, several methods have been
developed in other robots to overcome large obstacles. Some of these robots use jumping
or hopping as a primary mode of locomotion, while others use jumping as an option when
the primary mobility method is not sufficient to surmount an obstacle.
2.2.1 Scout
Scout, a small robot developed at the University of Minnesota, is a good example
of a small robot that can jump to overcome obstacles in its path (Stoeter et al. 2002).
Scout is a cylindrical robot 4.0cm in diameter and 11.0cm long. Wheels at either end of
the cylinder provide the primary method of locomotion. A triangular spring-steel foot
between the wheels stabilizes the robot during normal rolling. When an obstacle is
encountered, a winch inside the cylindrical body draws the foot against the side of the
robot. When the winch releases suddenly, the spring steel foot straightens and impacts
the ground, causing the robot to jump up to 20 cm high. The combination of rolling and
jumping locomotion makes Scout well suited for environments with flat surfaces
interrupted by stairs, such as the inside of a building (Figure 2.7). However, the low
ground clearance while rolling makes navigation over rough terrain difficult for the robot.
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Figure 2.7 – Scout includes a triangular spring steel jumping
foot which allows it to jump up stairs.
2.2.2 Hopper
Sandia National Laboratory’s Intelligent Systems and Robotics Center (ISRC) has
developed a robot called Hopper, which uses jumping as its only mode of locomotion
(Sandia 2000). The robot, about the size of a coffee can, has a weighted, rounded bottom
so that it rights itself after each jump (Figure 2.8). A gimbaled system inside the robot
slightly offsets the weighting to direct the robot’s next jump in a desired direction. A
gasoline powered piston fires and strikes the ground to make the robot jump 3m to 6m
high. The Hopper can jump again in as little as 5 seconds.
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Figure 2.8 – The Hopper can leap up to 6 meters high using a
gasoline combustion powered piston.
2.2.3 Frogbot
Like Hopper, Frogbot, developed by NASA’s Jet Propulsion Laboratory and the
California Institute of Technology, uses a single foot to jump from location to location
(NASA 2000). The 40cm tall Frogbot consists of an aluminum frame which acts as a leg.
The leg bends at a spring-loaded knee (Figure 2.9). A single motor stores energy in the
spring as it causes the knee to bend. When the motor releases the spring, the robot jumps
up to 1.8m high. Since the robot falls over when it lands, plastic levers are deployed to
right the Frogbot after every hop.
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Figure 2.9 – Stiff springs contract quickly to extend the bent leg
of Froghopper.
2.2.4 Bow Leg
Carnegie Mellon’s 3D Bow Leg Hopper, is a third vehicle which uses a single leg
to move (Zeglin and Brown, 2002). A string pulls on the end of the fiberglass leg,
causing it to bend like an archer’s bow. The angle of the leg relative to the body is
adjusted by servos via two other control strings to direct the jump (Figure 2.10).
Releasing the main string straightens the bow leg, and allows the robot to jump up to
50cm.
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Figure 2.10 – A single flexible fiberglass leg adjusted by control
strings forms the propulsion method for the 3D Bow Leg
Hopper.
2.2.5 Flip’n Fido
Toys can provide an inexpensive example of jumping vehicles as well. The
Gemmy Industries Corporation’s Flip’n Fido is a 10cm long dog-shaped vehicle which
walks and does back-flips several centimeters high. An inexpensive motor drives an
extensive gear reduction ending in a cam. The cam is part of a mechanical linkage which
moves the legs of the robot and stretches a stiff spring (Figure 2.11). The front legs of
the vehicle move in unison, as do the rear legs. After several shuffling steps, the rear legs
retract against the bottom of the body, stretching the spring. When the legs are fully
retracted, the legs spring back, sending the toy into a flip.
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Figure 2.11 – A stiff spring stores energy created through an
extensive gear train in the Flip'n Fido toy.
2.3 Jumping Concepts for Mini-Whegs
Several solutions for creating a jumping mechanism in a robot have been
developed, some better suited towards integration in a Mini-Whegs platform than others
were. The mechanism must release enough energy to provide a 15cm to 20cm vertical
leap. The mechanism should be compact so that it does not interfere with the normal
wheg locomotion.
A mechanical energy storage method is desired for repeatable
jumping, as a spring does not require refueling to operate a second time. Ultimately,
three different spring types were considered: a flat bending spring, a torsion spring, and a
linear spring (Morrey 2003).
2.3.1 Scorpion
Operation of Mini-Whegs 3 showed that the high torque Maxon motor was easily
capable of flipping the robot upside down. Since Mini-Whegs is equally mobile upright
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or upside down, a jumping mechanism design was considered which would be stored on
the top of the robot. When a jump was desired, the robot would flip over by driving into
the obstacle. This would bring the jumping mechanism to the bottom of the robot, where
it could be released to complete a jump.
Figure 2.12 – The Scorpion jumping concept retracted on top of
the robot before a jump (left), and then released from the bottom
of the robot (right).
The Scorpion jumping mechanism consists of a long piece of spring steel bent
over the top of the robot in a configuration similar to the tail of a scorpion, held in place
by a cable on a winch. When flipped over, the cable is released, allowing the steel to
straighten and impact the ground (Figure 2.12), similar to the operation of the spring steel
foot on the Scout robots. While the design was successful in creating high, predictable
leaps on a Mini-Whegs mockup, the Scorpion design was ultimately eliminated for its
large size relative to the robot. The large piece of spring steel dramatically increases the
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height of the robot and eliminates room for the addition of other components, such as
electronics.
2.3.2 Mousetrap
Experimentation showed that the torsion springs which cause a mousetrap to snap
closed stored more than enough energy to create a jumping motion. A torsion spring was
fixed to the bottom of a Mini-Whegs mockup, with the free arm of the spring attached to
a lever arm which impacts the ground to make the robot jump (Figure 2.13).
Unfortunately, the design caused the mockup to flip excessively in the air. The simple
wire lever arm was difficult to control, making jumps inconsistent.
Figure 2.13 – The Mousetrap jumping concept in action.
2.3.3 Four-bar
The Four-bar mechanism which was finally adopted in the first jumping MiniWhegs prototype is a progression of the Mousetrap design. The mechanism consists of a
parallel four-bar linkage which fits between the wheg axles of the robot. The four-bar
design makes the motion of the jumping legs during a jump much more predictable than
the slender legs of the Mousetrap concept. A physical stop in the rotation is easily
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achieved to reduce rewinding time after a jump. Energy is stored in a linear extension
spring which stretches from extensions of the jumping legs across the top of the robot
(Figure 2.14). As the four-bar mechanism is retracted against the bottom of the body of
the robot, the spring stretches. When the mechanism is released, the spring contracts
quickly, pulling the extension of the jumping legs with it. As the leg pivots about an
axle, it pushes a small foot toward the ground, which impacts and sends the mockup into
the air.
Figure 2.14 – The Four-bar jumping mechanism is powered by a
linear extension spring on top of the robot.
2.4 Discussion
The success of the Four-bar design led to its integration in a complete MiniWhegs prototype, discussed in the next chapter.
The resulting design, especially
including the manner in which the mechanism is slowly retracted and suddenly released,
imitates the manner in which a froghopper insect jumps. The resulting robot incorporates
a functional jumping mechanism without eliminating any of the cockroach-inspired
mobility of whegs.
Chapter 3 – A Jumping Prototype
To prove that a jumping ability could be successfully added to a Mini-Whegs
platform, Mini-Whegs 4J was designed and built by Jeremy Morrey (Morrey 2003). This
working prototype has jumped to heights exceeding 20cm, so it can easily jump onto a
standard stair. The robot uses a single motor to drive both running and jumping. The
jumping mechanism is loaded and released automatically while the robot runs. As the
robot runs forward, the mechanism slowly retracts, then releases, and repeats.
3.1 Design
Mini-Whegs 4J is similar in design to other Mini-Whegs designs. Steering and
control were unnecessary to prove the jumping concept, so components related to these
functions were eliminated to save space and weight. The chassis of the robot is similar to
the chassis of Mini-Whegs 3, with the addition of several mounting holes for the jumping
mechanism.
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power
switch
batteries
jump spring (H)
front axle (B)
drive motor (A)
drive
chains
jump mechanism
transmission (D)
drive-to-jumping
mechanism
connection chain (E)
slip-gear (F)
jump mechanism
retraction gear
rear axle (C)
parallel four-bar
jumping mechanism
(retracted) (G)
Figure 3.1 – Top view of Mini-Whegs 4J showing the location of
important components. The front of the robot is at the top of the
figure.
Figure 3.1 shows the layout of the jumping prototype with several key
components labeled. The 1.2W RE-13 Maxon motor (A) used in Mini-Whegs 3 is again
used to drive the whegs at the front (B) and rear (C) axles. A secondary transmission (D)
is driven by a chain (E) between the wheg axle and the custom-built input to the
transmission. A “slip-gear” (F) transmits power from the jumping transmission to an axle
rigidly connected to the parallel four-bar jumping mechanism (G). Energy for each jump
is stored in a linear spring (H), which stretches across the top of the vehicle. Figure 3.2
more clearly shows the four-bar jumping mechanism and spring attachment.
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titanium jump
legs.
aluminum foot
Figure 3.2 – Side view of Mini-Whegs 4J with elements of the
jumping mechanism labeled.
3.1.1 Chassis Modifications
The chassis of Mini-Whegs 4J is based on the chassis of Mini-Whegs 3. Extra
carefully spaced mounting holes for the jump axles were added, taking into consideration
the finite increments allowed between chain sprockets without requiring additional
tensioners. Components were placed as close together as possible without interference to
minimize the weight of the robot. The resulting chassis measures 9.4cm long by 7.6cm
wide, about 1cm longer and 1.3cm wider than Mini-Whegs 3.
3.1.2 Control System
Since Mini-Whegs 4J was a prototype to demonstrate the successful integration of
a jumping mechanism with a Mini-Whegs platform, radio control was eliminated. Two 3
Volt CR2 batteries in series are directly connected to the drive motor with a small switch.
When the switch is turned on, the motor drives both wheg axles, while the rear wheg axle
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drives the secondary transmission for the jumping mechanism. Thus, the robot runs as
the mechanism retracts, jumps, and repeats until it is turned off.
3.2 Implementing the four-bar jumping mechanism
Realizing the jumping mechanism selected for the robot required selecting a
repeatable energy storage device to make multiple jumps possible. The desired jump
trajectory is upwards and forwards so that the robot can jump onto a standard stair step.
Keeping in line with the other Mini-Whegs robots, the design must be simple and robust,
small and light. The jumping mechanism should integrate well with the regular MiniWhegs chassis, requiring as few design changes as possible.
3.2.1 Mechanism activation
The selected four-bar jumping mechanism has only one degree of freedom, so
theoretically, only one actuator is necessary to retract and release the linkage. In order to
allow the stored energy for each jump to be stored in a repeatable device and in order for
that energy to be released very quickly, a spring was selected as the means for energy
storage. Several electromechanical methods for stretching or contracting a spring were
examined, including use of a servo, solenoid, winch, or cam. Criteria for selection of the
final method used included a good power to weight ratio, large range of motion, small
size, and good repeatability.
mechanical “slip-gear”.
The design which proved to be most feasible was a
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A
35
B
(p)
C
(g)
D
Figure 3.3 – The slip-gear consists of a pinion (p) with several
teeth removed, and an unmodified gear (g). While the teeth are
engaged (A-B), the jumping mechanism retracts, “winding up’
the spring. When the teeth become disengaged, energy stored in
a spring causes the gear to rotate quickly (C-D) in the opposite
direction of winding.
The slip-gear consists of a pinion with several teeth removed driving a second
unmodified gear attached to one joint on the four-bar mechanism. In Mini-Whegs 4J, the
pinion and full gear are both 32 pitch, 14 teeth gears. The pinion has 8 teeth removed,
leaving two sections of 3 teeth on opposite sides of the pinion. Figure 3.3 demonstrates
how the slip-gear works. As the pinion rotates, its teeth engage with the gear (A) rigidly
attached to the four-bar. This rotates the mechanism up towards the body of the robot
just long enough to stretch the spring to its fully extended position, or about 100° of
rotation. The pinion continues to rotate (B) until none of the teeth are engaged with the
gear (C). At this point, the gear is free to rotate independently of the pinion (D), so the
spring retracts suddenly, opening the jumping mechanism to its unloaded position and
causes the robot to jump.
As the pinion rotates even further, the teeth reengage,
rewinding the mechanism for the next jump (A). Since the pinion has two separate sets
of teeth, the jumping mechanism retracts and releases twice per revolution of the pinion.
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This system requires no active input for control; it can simply wind and jump repeatedly.
This is sufficient for Mini-Whegs 4J, since it is simply a demonstration vehicle for
jumping integration.
Figure 3.4 – Custom components for the jumping transmission in
Mini-Whegs 4J: (clockwise from nickel shown for scale) Maxon
275:1 planetary transmission, custom shaft housing, custom
input shaft, clip to hold shaft in place, input gear for
transmission.
Stretching a spring stiff enough to cause the robot to jump requires more torque at
the slip-gear pinion than can be provided by the Maxon motor and transmission used for
driving the whegs appendages, so an additional gear reduction was necessary.
A
secondary 275:1 metal gear planetary transmission was selected to achieve a total gear
reduction of 18,545:1. The slip-gear pinion is directly mounted on the output shaft of the
transmission. Since the transmission is normally mounted directly onto the motor, a
custom housing had to be fabricated to allow an input shaft to be added (Figure 3.4).
This input shaft is driven by the rear wheg axle of the robot via a chain and sprocket
connection.
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3.2.2 Geometry and materials
Bending in the long aluminum legs of the mockup jumping mechanism was
noticed after extensive testing. Keeping clearance between the sides of the robot and the
whegs to a minimum eliminated the option to add more material to the legs to strengthen
them. Instead, titanium was chosen for the legs of the linkage for its strength to weight
properties. The feet and other components can still be made from aluminum since they
are experience lower bending loads.
To synchronize the motion between left and right legs and to strengthen the
mechanism laterally, three shafts connect the sides of the robot at the joints of the
mechanism. No cross-brace shaft can be mounted at the front of the jump feet since these
joints must slide along the side of the robot in order for the mechanism to retract close to
the body. Instead, an additional shaft at the top of the mechanism braces the sides while
doubling as a mount for the spring. The shafts at the top two joints double as axles
rotating in precision ball-bearings. The front-most axle is larger in diameter and is driven
by the slip-gear transmission. Flats on the ends of the axle allow it to drive the legs of the
four-bar linkage without slipping.
The legs of the mechanism are designed to be as long as possible without
interfering with the front wheg axle of the robot. This creates the longest lever arm for
jumping and allows the jumping feet to impact the ground below the center of gravity of
the robot (Figure 3.5). The feet are oriented 20° below horizontal to make the robot jump
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upward and forward. Sharp points on the end of the feet ensure good traction during
jumping.
Figure 3.5 – Photographs illustrating the motion of the four-bar
mechanism during a jump.
In the original four bar design, the rearmost axle was driven, which avoids
transmitting force through the un-braced joints at the front of the jump feet. However,
space considerations in the robot do not allow the rear jumping axle to be driven. So, a
strong joint is needed at the front of the jump feet. There is no room for a ball bearing, so
a small brass bushing was used. A small hub protrudes from the feet. The bushing fits
around this protrusion, which then fits into an appropriately sized hole in the jump leg.
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The leg is held in place by a short screw, with a Teflon washer separating the screw head
from the leg.
3.3 Spring selection
The more energy stored in the spring for a given input force, the higher the robot
will be able to jump. Thus, an important consideration in the selection of a spring to
store energy for jumping is that the spring be preloaded, that is, it should always be
partially stretched. The energy stored in the spring which can be released during jumping
is equal to the work done in stretching the spring, that is, the area under the forcedisplacement curve between the minimum and maximum stretch positions. For the same
maximum force available to wind the spring, a softer, preloaded spring will be able to
store more energy than a stiffer spring with no preload. Theoretically, a spring of
infinitesimal stiffness with infinite preload would have a completely flat forcedisplacement curve, allowing it to store twice the energy of a stiff spring with no preload.
However, the limited length of the robot does not allow for infinite springs, so a
compromise must be made between spring length and stiffness.
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Fmax
Fp
k1
k2
E1
E2
xp
x1
x2
x1
Figure 3.6 – A softer (k2) spring with a preload (xp) stores (2 –
k2/k1) times more energy than a stiff spring (k1) for the same
displacement (x1) and maximum force (Fmax).
Figure 3.6 shows the relationship between preload of soft springs and energy
storage. Consider two linear springs, one of high stiffness k1, and a softer spring of
stiffness k2. Suppose the motor available can stretch spring 1 from its free length to a
displacement x by exerting a force Fmax=k1x1. The same force can stretch spring 2 to a
displacement x2 where Fmax=k2x2. However, when the force from the motor is removed,
the spring can only move a maximum distance x because of the geometry of the system.
Thus, after the mechanism is released, spring 1 will return to its free length, but spring 2
will return to a displacement xp = x2–x1. The “preload” for the displacement xp is
Fp = k2xp. With all the forces known, the energy released during a jump can be measured.
The energy will be equal to the difference of the energy required to stretch the spring to
its maximum displacement and the energy left in the spring after the jump. For the first
spring, the energy released is E1 = ½Fmaxx1 = ½k1x1². For the second spring, the energy is
E2 = ½Fmaxx2 – ½Fpxp = ½k2(2x2x1 – x1²).
Since Fmax is the same for both springs,
k1x1 = k2x2, so x2 = k1/k2 x1. Thus, E2 = ½(2k1–k2) x1². The ratio, R = E2/E1, of the energy
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released in the second spring to the energy released in the first spring is R = (2 – k2/k1).
Clearly, the smaller k2, i.e. the softer the preloaded spring, the more energy it can store.
For an infinitesimally stiff spring (k2→0), R→2, so twice as much energy can be stored in
the spring.
Unfortunately, a very soft spring must also have a very long preload
displacement (xp = x2 – x1 = Fmax/k2 – x1), so a compromise must be made between length
and stiffness.
The final spring was chosen experimentally from a selection of springs of
different lengths and stiffness with the previously described considerations in mind. The
spring cannot be too small, or the forces encountered will cause it to deform permanently.
It must also be stiff enough to cause the robot to jump to the desired height. After testing
several springs at different positions on the robot, a spring with a stiffness of about
0.5 N/mm was selected. This spring resulted in the highest jumping of all the springs
tested.
3.4 Discussion
Mini-Whegs 4J successfully proves that a jumping capability can be added to a
small robot to improve mobility and conquer obstacles of relatively large size. The robot
can leap over 20cm high, easily jumping onto a standard stair (Figure 3.7). While the
robot runs, energy is slowly stored in a spring. It takes about one minute to fully retract
the jumping mechanism.
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Figure 3.7 – Composite of video frames showing Mini-Whegs 4J
jumping up a 15cm stair.
The four-bar jumping mechanism allows performance with a variety of spring
sizes, varying stiffness, and different preloads to be characterized. Experimenting shows
that a moderately stiff spring with a significant amount of preload works best. Softer
springs with more preload tend to deform plastically, while stiffer springs cannot store as
much energy.
Mini-Whegs 4J can run both upright and upside down, so the orientation after
landing from a jump is unimportant. However, the robot can only jump when upright.
This is not a problem since, with the jumping mechanism retracted, the robot can easily
flip over like other Mini-Whegs robots by running into a large obstacle.
There is
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sufficient torque available to cause the front of the robot to climb an obstacle until the
whole robot flips over.
The lack of a control system makes Mini-Whegs 4J unsuitable as a platform for
other research, such as sensor integration. It is simply a demonstration of running and
jumping powered by the same motor. For independent and controllable operation to be
achieved, jumping and running need to be separated. This separation was first attempted
in Mini-Whegs 6J, discussed in Chapter 5. Before Mini-Whegs 6J was built, several
design changes were made to the steering mechanism and wheg appendages to improve
the mobility of running in the Mini-Whegs platform. These changes, discussed in the
next chapter, were first integrated in Mini-Whegs 5.
Chapter 4 – Development of Reliable Components
Before creating a completely controllable robot with independent running and
jumping modes of locomotion, further development of the steering mechanism and wheg
appendages was needed to create a reliable Mini-Whegs platform. These changers were
made in order to create a robot robust enough to withstand repeated impacts from
jumping, falling, and running. Steering mechanisms in Mini-Whegs 1, 2, and 3 were
subject to failure after relatively few cycles due to the weak springs and flexible materials
used in their construction. The first several Mini-Whegs robots also had pointed feet at
the end of the whegs, making maneuverability difficult on hard surfaces with little
traction. They also caught easily on rough or tangled surfaces, causing the robot to flip or
somersault. Several design changes, described in the following sections, were made to
improve the performance of both the steering and appendage elements.
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4.1 Steering mechanisms
In order to navigate around obstacles to travel from one location to another, MiniWhegs robots need to have some sort of steering mechanism.
The offset between
neighboring appendages must be maintained for smooth walking, so skid steering—
where the legs on one side of the robot simply move faster than the other side—is not an
option. Thus, some mechanical linkage is required to pivot the whegs relative to the
body of the robot, or to change the angle between the axles through a body joint.
All of the whegs on the robot must be powered. Thus, a mechanism is required
which can transfer rotation through a pivot without seriously affecting the offsets
between the whegs. A tight turning radius is desirable for improved maneuverability, so
a large range of motion in the steering mechanism is also required.
4.1.1 Rack and Pinion Steering
Pivoting the whegs themselves instead of using a body joint is a more compact
and easier to control solution. Since only the whegs instead of a whole section of the
body must rotate, less torque, and hence a smaller servo, is necessary to steer the robot.
Also, the drive train does not need to be in the center of the robot, which frees up space
for other components and results in a more efficient layout.
The first Mini-Whegs robot includes a small servo which moves a rod side to side
through the chassis via a small arm. The ends of the rod contain pins which fit into slots
on the steering uprights. Thus, when the rod moves, the pin pulls the upright to one side
or the other. All the robots designed after Mini-Whegs 1 use a rack and pinion system
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instead. A small pinion on the servo drives a gear rack instead of a simple rod. The
connection to the uprights remains the same.
Mini-Whegs 2, Mini-Whegs 3, and Mini-Whegs 5 (Figure 4.1) all use a 64 pitch
brass rack and pinion. This gives precise control over steering mechanism position.
However, the brass components are heavy, and the small teeth easily disengage if the
servo mount bends out of place by even a small amount.
steering upright
steering servo
radio receiver
drive
chains
Maxon motor
batteries
Figure 4.1 – Top view of Mini-Whegs 5 showing the layout of
components.
A nylon rack was chosen for Mini-Whegs 6 and subsequent robots, primarily to
reduce weight. The 48 pitch gear rack and pinions chosen have larger teeth than the brass
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parts, so they are also less likely to disengage. Since nylon is much more flexible than
brass, there was a possibility for the rack to bend out of engagement with the pinion on
the servo. However, by strategically placing support posts underneath the rack and
holding the servo down with a small piece of foam, these problems are entirely avoided.
The combination of larger teeth and an improved mounting system leads to a
much more reliable steering solution than with the brass rack. The weight reduction of
5g (87%) in the rack alone also creates an opportunity to carry a greater payload with the
same robot.
4.1.2 Simplified Universal Joint
In order to transfer power from the driven axle to the whegs on the steering
uprights, a small joint is required. Two intersecting degrees of freedom are required to
allow the axle to rotate while it pivots to steer.
The first solutions for a small joint involve a flexible shaft. The ends of the
driven axle on Mini-Whegs 1 are attached to a short length of spring tubing. The spring
is attached to a small hub which rotates in the steering upright and attaches to the wheg.
The spring has the advantage of adding some torsional compliance to the system. The
compliance allows the front whegs to come into phase when an obstacle is encountered,
so that both whegs can be used to lift the robot onto the obstacle.
However, the
connection is not durable. The spring unwinds easily after repeated use and must be
replaced.
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Mini-Whegs 2 uses a piece of Delrin® polymer for the flexible shaft.
48
The
Delrin® component is relatively long in order to add some torsional compliance. At the
pivot point, two perpendicular slots are cut into the axle. The Delrin® bends about these
slots, creating a sort of solid universal joint. However, the slot also creates a stress
concentration, so after repeated use, the connection breaks.
Mini-Whegs 3 returned to a spring solution, this time with some plastic tubing
added inside the spring to keep it from collapsing. While being somewhat more durable,
many of the problems with Mini-Whegs 1 remain.
Thus, for Mini-Whegs 5, flexible materials were abandoned entirely.
The
required two degrees of motion are achieved through a pinned ball and cup mechanism
(inspired by Althof, 2002). A ball on the end of the driven axle fits into a cup which
forms the rotating hub to which the wheg is attached (Figure 4.2). The cup is held in
place by a bearing in the steering upright. A slot is cut into the cup. A short pin through
the center of the ball slides in this slot, providing the first degree of freedom. The cup
can also rotate around the pin, providing the second perpendicular degree of freedom.
When the pin pushes against the side of the slot, the cup rotates with the driven axle, so
that the wheg can rotate as well. This simplified universal joint completely eliminates
any torsional compliance, but is also durable and reliable.
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3.6cm
Figure 4.2 – Rendering of the ball and cup steering joint first
used in Mini-Whegs 5.
Unlike a flexible spring, the mechanism has an exact center of rotation, so the
uprights must be designed to rotate about the same axis. So, some careful design is
required to ensure that all of the components line up correctly when assembled. In
addition to placement of axes, the dimensions of the ball and cup must be chosen to allow
the whegs to pivot as far as possible before the geometry collides. The cup should be as
long as possible to ensure that the pin stays in contact with the slot, but it can not be so
long that it collides with the axle. To increase the range of motion, the driven axle tapers
to a much smaller diameter before the ball is reached. This allows the cup walls to pivot
further around the ball before hitting. Some compromise is necessary to maintain a large
enough diameter in the axle so that it does not break. The final dimensions used allow
the cup to pivot ±30° without interference.
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In Mini-Whegs 5, the balls on the end of the driven axle are machined into the
steel shaft with a computer controlled lathe. Since the balls are machined into opposite
ends of the same shaft, the exact length is somewhat difficult to control due to the lack of
physical stops in the lathe used to cut the parts. Since the cups are easier to machine and
replace, they are machined from brass, which will wear faster than the harder steel. The
materials used lead to a very durable and reliable mechanism. However, the steel and
brass also make the mechanism very heavy.
Because of the durability and reliability of the ball and cup mechanism, MiniWhegs 3 was modified to use the same design. The driven axle was machined in two
half-pieces to allow the length to be adjusted to fit the robot. Each half axle narrows
down and fits into an aluminum sleeve, where it is held in place by set screws. In
addition to allowing the length to be adjusted, the two half pieces also allow the offset to
be adjusted so that an exact 60° offset can be achieved.
In order to reduce the weight of the steering mechanism, Mini-Whegs 7 does not
use brass or steel parts. The driven axle consists of a hollow aluminum shaft which is
threaded to accept two anodized aluminum ball studs, purchased from a radio control toy
supplier. The ball studs must be drilled to accept a pin and turned down slightly to fit
through bearings, but overall the modifications are much simpler than machining a ball
into a solid shaft. The exact length required is also easy to achieve because the axle is a
simple flat end hollow shaft.
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The cup which mates with the ball on the end of the axle is machined from
aluminum stock. Since the ball stud has been anodized, galling between the cup and the
ball is not an issue. Unfortunately, because the ball stud was not specifically designed for
this application, somewhat less travel of the cup (about ±25°) is possible. However, the
different geometry also allows the cup to be slightly smaller, so it can fit into a smaller
space. This reduces the overall width of the robot. The hollow shaft and aluminum
components reduce the weight of the mechanism by over 7g (74%).
4.2 Leg and Foot Design
Like larger Whegs robots, Mini-Whegs employs several three-spoke appendages
called whegs for locomotion. For the sake of simplicity and reduced size, the MiniWhegs series of robots uses just four whegs, which results in an alternating diagonal gait.
While the full size robots use six whegs to create an alternating tripod gait, Mini-Whegs
is small enough and fast enough that an alternating diagonal gait is sufficiently stable.
The wheg appendages have been redesigned several times to improve the mobility of the
robot.
4.2.1 Early Mini-Whegs Leg Designs
The first Mini-Whegs (Mini-Whegs 1) robot uses whegs which are constructed
very much like the whegs of the much larger Whegs I robot. Each wheg consists of a
Delrin® polymer hub drilled to hold three short lengths of steel wire (Figure 4.4 (A)).
The wire legs are held in place using set screws. A fourth set screw keeps the wheg from
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spinning about the driven axle. Overall, these whegs are heavy for their size, stiff, and
require many steps to machine and assemble.
Later Mini-Whegs robots (Mini-Whegs 2, Mini-Whegs 3, and Mini-Whegs 4)
used a wheg design similar in size and shape to the whegs used in Mini-Whegs 1, but
machined entirely out a single piece of Delrin®. The all-Delrin® design results in whegs
which are somewhat flexible, lighter by 2g per wheg, and require no assembly (Figure
4.4 (B)). Instead of a sets screw to stop rotation, a rectangular slot is milled into the
wheg hub. The slot mates with matching flats on the driven axle to keep the whegs offset
by 60°.
Although straight spokes are excellent for reaching onto large obstacles, the sharp
tips of the legs easily catch in rough surfaces, such as carpet. The flexible legs then bend,
and finally release, causing the robot to somersault, and making it difficult to control. In
addition to catching on rough surfaces, the tiny contact patch of the tip of the leg offers
almost no traction on hard, smooth surfaces.
4.2.2 A curved foot improves performance
The wheg design developed for Mini-Whegs 5 is similar to the previously used
all-Delrin® design, but adds a short foot to the end of each leg spoke (Figure 4.4 (C)).
The foot consists of an arc segment with a radius equal to the length of the leg spoke.
The length of the foot, described by the length of the arc in degrees can vary between 0°
and 120°, from bare leg spokes to a complete wheel. A shorter foot yields better
climbing ability, but is harder to control.
A foot length of 25° provides a good
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compromise between smooth operation and obstacle clearance capacity. When paired
with its lateral neighbor, offset by 60°, the 25° arcs provide almost 50% of a complete
wheel. Nominal body motion is decreased from 13.4% of the leg length to 4.6%. The
foot is also short enough that it does not extend far past the front of the body when in
contact with the ground, so climbing ability is hardly affected. The whegs with short feet
are shown on the robot in Figure 4.3.
Figure 4.3 – Mini-Whegs 5. The front of the robot is on the right
side of the photo.
The addition of the foot completely eliminates somersaults and removes a great
deal of body motion, making the robot much easier to control. However, the exposed toe
of the foot can still catch on tangled objects such as string, cable, or vegetation. Also, the
heel of the foot where it attaches to the spoke is squared off. This extends the reach for
climbing as long as possible, but it also creates a jarring impact every time the leg hits.
Traction on smooth hard surfaces is improved greatly by dipping the feet in Plasti
Dip®, a rubbery plastic coating usually used for tool handle grips. Unfortunately, dirt
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and dust stick easily to the coating, making it less tacky and less effective at gripping the
smooth surface. The coating also wears down quickly during repeated operation of the
robot, so some secondary method for improving traction is desirable.
Figure 4.4 – Wheg appendage evolution of Mini-Whegs robots.
A quarter is shown for scale.
4.2.3 Further wheg design development
In order to solve traction and tangling issues, and to further improve walking
smoothness, the wheg shape for Mini-Whegs 7 was completely redesigned. It has since
been adapted at a number of different sizes for three Mini-Whegs robots. Elements of the
leg shape and construction have also been adapted for mid-size and full size Whegs
robots as well.
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The heel of the foot is designed to be parallel to the ground when it first makes
contact. The radius of the foot arc then increases toward the full length (Figure 4.5).
Thus, the impacts onto a sharp corner are eliminated. The contact patch of the foot is
wider to add traction. Small ridges are also cut into the foot and back of the leg to add
gripping surfaces. These ridged surfaces are then coated with Plasti Dip® to improve
traction on hard, smooth surfaces.
Figure 4.5 – A rounded heel smooths the transition between
spoke impacts.
A thin web of material connects the toe of the foot back to the hub of the wheg,
eliminating some of the tangling in foreign objects, especially while moving backwards.
However, during machining of the first set of whegs of this improved design, it became
apparent that the web was too thin and flexible by itself. It broke easily. In addition the
stress concentrations at the roots of the ridges along the leg and foot caused part failures.
These problems were remedied by adding some extra thickness to the foot and leg, while
also adding another thin web of material filling in the space between the leg and toe-hub
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connection. Thus, there are no openings or extrusions in the final wheg design, so
problems with tangling are virtually eliminated (Figure 4.4 (D)).
The final design uses significantly more material than earlier designs and the final
Delrin® legs weighed 4.1g apiece, so some research into lighter materials was justified.
Some prototype whegs were created using stereolithography (SLA). However, these
legs, while weighing 3.3g were far too brittle for extended use and soon fractured near
the hub during normal operation.
Whegs formed from ABS plastic using fused
deposition modeling (FDM) weighed 3.0g. Unfortunately, while lightweight, ABS does
not have high tensile stress, and is stiff and somewhat brittle. Whegs milled from ABS
sheet have very similar properties to those modeled using FDM. Milled Delrin® appears
to be the best available solution. While Delrin® is a relatively dense polymer, it has the
advantage of tensile strength 150% greater than ABS while retaining some flexibility,
even with the stiff design resulting from the reinforcement webbing. The extra traction,
smoother ride, and easier control resulting from the more complex wheg shape justify the
extra weight.
4.3 Quantification of improved Mini-Whegs performance
After making the several design changes as described in this chapter, the new
designs were tested to measure the improved performance and to provide a baseline for
comparison to future robots.
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4.3.1 Methods
Testing of Mini-Whegs 5 was primarily concerned with comparing the
performance of whegs versus the performance of the same robot with wheels of the same
diameter replacing the whegs. All experiments were recorded on digital video tape at 30
frames per second.
In order to determine the top speed of the robot, the carpeted floor was marked
with tape at intervals of 91cm. The robot was then controlled to run at full speed across
the tape strips while being video taped. After three trials, the wheg appendages were
removed and replaced with wheels. The wheels were of a similar width as the wheg feet
and had the same radius as the spoke length of the whegs. Three trials were also run with
wheels.
Steering radius was also quantified in a similar manner. The robot was driven in a
semi-circle across a ruler with the steering servo in its extreme position. Strips of tape
were also placed on the floor at intervals of 15cm to assist in examining the video later.
Several trials were run using whegs and wheels.
In addition to comparing whegs to wheels on flat surfaces and across obstacles,
Mini-Whegs 5 was steered up an incline of varying angle using different wheg shapes,
including the simple feet originally designed, and a larger version of the whegs designed
for Mini-Whegs 7. Several angles and several trials were used for each shape.
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4.3.2 Results
From the video recordings, it was relatively easy to determine in which frame the
robot crossed each strip of tape. By counting frames between tape crossings, six sets of
times for the 91cm distance were found for each case. From these times, the average top
speed of the Mini-Whegs 5 using whegs was determined to be 10 body lengths per
second. Using wheels on the same drive train results in an average speed of 15 body
lengths per second, 50% faster.
The turning radius using whegs depends upon the orientation of the whegs at the
beginning of the turn, but can be as tight as 2 body lengths or as large as 3 body lengths.
The turning radius of the robot when using wheels is consistently 2.5 body lengths—
equal to the average turning radius using whegs.
Mini-Whegs 5 was able to crawl over a 3.8 cm obstacle almost without fail when
driven directly toward it (Figure 4.6). With wheels instead of whegs, the robot cannot
climb across the obstacle at all.
Figure 4.6 – Composite of video frames showing Mini-Whegs 5
traversing two 3.8cm by 8.9cm obstacles while running at three
body lengths per second.
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After running several trials with Mini-Whegs 5 using the whegs with short arc
feet, it was determined that the robot can climb on smooth surfaces up to 13° before
sliding backwards, and up to 30° on a carpeted surface before flipping upside down. The
extra traction from the improved, wider wheg design with small ridges allows the robot to
climb smooth inclines up to 20°. Climbing on a carpeted surface is also improved
somewhat to a maximum angle of 32.5° (Bittle and Cullen, 2004).
Chapter 5 – First Attempt at Independent Running and
Jumping
After successful demonstration of the jumping concept in Mini-Whegs 4J, and
after developing other robust components in Mini-Whegs 5, design began on a robot to
combine elements of the jumping prototype and the reliable platform to create a fully
controllable robot with independent running and jumping modes of locomotion.
5.1 Motor Selection
In order to separate jumping from running, another actuator must be added to the
robot. While several methods were considered, including the addition of a solenoid
activated clutch between the drive motor and a secondary transmission, the addition of a
completely new motor for jumping was determined to be the most viable solution. The
torque requirements for extending the spring on Mini-Whegs 4J were measured
experimentally using suspended weights to cancel out the torque created by the spring as
part of senior project by Dave Johnson (Johnson 2002).
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From the torque requirements, it was then possible to select a larger motor and
transmission. The motor and transmission combination must create the required torque
without drawing more than about 1A, the maximum current the batteries can provide.
The Maxon transmission with the highest allowable intermittent torque, while
staying at a size suitable for Mini-Whegs, is a 13mm, 1119:1 planetary metal gear
transmission. This is a much smaller reduction than the 18,545:1 reduction from the two
transmission combination in Mini-Whegs 4J. The larger load on the motor necessitated
the selection of a larger 2.5W motor instead of the 1.2W motor previously used.
However, the reduced gear reduction has benefits as well—the wind time would be about
10 times faster, and eliminating a second transmission also reduces friction, making the
robot more energy efficient.
5.2 Design
Most of the components for Mini-Whegs 6J are similar to the components from
Mini-Whegs 5 and Mini-Whegs 4J. However, placement and dimensions of the parts had
to be modified in order to fit all the elements into the new design. The frame needs to be
long enough for the front wheg axle, rack and pinion steering, steering servo, batteries,
drive motor, jumping mechanism motor, jumping mechanism drive axle, rear wheg axle,
and rear jumping mechanism axle, with adequate clearance for chain sprockets and
bearings (Figure 5.1).
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jump gears
drive motor
batteries
steering servo
jump motor
drive chains
rack and pinion
steering
Figure 5.1 – Top view of Mini-Whegs 6J with labels indicating
components that affect the size of the chassis.
5.2.1 Chain Sprocket Selection and Spacing
All Mini-Whegs robot use sprocket and chain drives to connect the central drive
motor to the front and rear axles. In most previous Mini-Whegs robots, the spacing has
allowed the chain to hang too loosely, necessitating chain tensioners or causing problems
with snagging.
To help alleviate chain snagging, sprocket sizes were chosen to minimize chain
contact with other components. The sprocket on the front axle must be small to allow the
steering rack to come as close as possible to the front axle, resulting in the greatest
steering upright rotation for a given servo travel. The sprocket must also be big enough
to keep the chain from rubbing against the rack. For these reasons, ten tooth sprockets
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were selected for the drive connection between the front axle and motor. In the rear half
of the robot, the chain must travel around the jumping mechanism motor. Fourteen tooth
sprockets were the smallest sprockets which would allow the chain to move unhindered
by the jump motor housing.
To choose the spacing between sprockets, a series of holes were drilled in two
sheets of Delrin® plastic. Each set of holes was slightly further apart than the previous
set. Axles with sprockets were then mounted in the holes. A 34 link chain was then
wrapped around the axles. The slack in the chain was measured using calipers. The
experiment was repeated for three different hole spacings for both 10 and 14 tooth
sprockets. The actual length of the chain was then estimated from the geometry of the
slack chain and compared to the calculated length of the chain (Figure 5.2).
The
complete chain length calculation can be found in Appendix B.1 .
h
d
c
Figure 5.2 – The stretched length of the chain can be
approximated if the pitch diameter (d) of the chain sprockets, the
center distance (c) between the sprockets, and the height (h) at
the center of the chain are known.
From the six trials, the actual length of the chain in its stretched configuration was
found to be about 0.6% to 1.2% longer than the calculated length of the chain. Since the
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chain should be taut, but not stretched, the dimensions used in the Mini-Whegs 6J design
were based on an extra length of 0.3%.
5.2.2 Jump Gear Selection
The jumping mechanism in Mini-Whegs 6J is retracted and released using a slipgear arrangement like Mini-Whegs 4J. The pinion of the slip-gear is a 32 diametrical
pitch spur gear with several teeth removed. It drives a second complete gear to retract the
mechanism. When the section without teeth is reached, the driven gear slips, releasing
the jumping mechanism (Figure 3.3).
Mini-Whegs 4J uses a pair of aluminum 14 tooth gears. However, the center
distance between the 14 tooth gears would cause interference between components in
Mini-Whegs 6J, so a different set of gears is required. Also, since the new motor has a
smaller transmission than Mini-Whegs 4J, an extra gear reduction is desirable. First,
brass was selected for the material of the gears to ensure more even wear than with the
aluminum gears. The smallest brass 32 pitch gear available from McMaster-Carr (12
teeth) was selected for the slip gear. Then, the smallest available gear (18 teeth) which
would still leave a center distance long enough to allow for both the new motor and jump
axle bearings was selected, for a total gear reduction 3:2.
The number of teeth to remove from the 12 tooth slip gear was calculated using
the contact ratio for the gears. For the 14 tooth gears, 3 teeth remained for retracting the
mechanism. The total teeth in contact for the duration of the retraction is twice the
contact ratio (for the outside teeth), plus the sum of the remaining inside teeth. For the 14
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to 14 tooth gear pair, the contact ratio is 1.463 (Appendix B.2 ), so the number of teeth in
contact is 2×1.463 + 1 = 3.926.
Thus, the total rotation of the driven gear is
3.926/14 × 360° = 100.9°. For the 12 to 18 tooth gear pair, the contact ratio is 1.475, so
the total number of teeth in contact if 4 teeth are left intact is 2×1.475 + 2 = 4.950. This
gives a rotation of 4.950/18 × 360° = 99.0°. The 1.9% difference in rotation should be
insignificant in retracting the mechanism.
5.2.3 Other Physical Modifications
The chassis of the robot was lengthened and widened to make room for all the
additional components.
All the components of the robot were modeled in
Pro/ENGINEER and assembled in the CAD program to ensure that everything fit well.
Figure 5.3 shows the assembly of all the computer designed components.
Thicker
material was used for the Delrin® side rails of the robot to add strength at the increased
length. Jumping mechanism legs were lengthened to fit just behind the steering rack of
the robot. The final chassis is 12.4cm long by 8.4cm wide.
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Figure 5.3 – Rendering of the complete Pro/ENGINEER model
of Mini-Whegs 6J.
5.2.4 Control System
A dual speed controller system was selected to operate the running and jumping
mechanisms. A miniature 4 channel radio receiver which incorporates a unidirectional
speed controller on one of the outputs was ordered from Sky Hooks & Rigging, a
Canadian model aircraft supplier. The speed controlled channel would be used to control
the jumping motor. A miniature switch activated by the position of the slip-gear pinion
was considered to aid the operator in controlling the jumping mechanism, but was
ultimately left out for simplicity. Instead, the operator must watch the robot to see when
it is fully retracted, and the stop the jumping motor. When jumping is desired, the
operator simply moves the throttle on again to complete the rotation of the pinion. A
second bi-directional speed controller was selected to control the drive motor for forward
or reverse operation.
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5.3 Spring Selection
After the parts for the robot were machined and assembled using a miniature CNC
(Computer Numerical Control) mill and some hand-machining, spring selection was
attempted using a combination of calculations and experiments. The maximum allowed
force in the spring was determined using the maximum torque figures from the Maxon
specifications for the transmission. Then available springs from McMaster-Carr were
identified and ordered to meet the maximum specifications and greatest possible preload.
The springs were then mounted on the robot and tested individually for the best results.
5.4 Results
Unfortunately, the robot did not perform as well as Mini-Whegs 4J. The stiffest
springs that the jumping motor could wind were insufficiently stiff to cause the robot to
jump. This was primarily caused by the increased weight of the robot and the long lever
arms of the spring attachment and jumping leg lengths. While Mini-Whegs 4J weighed
approximately 200g, Mini-Whegs 6J weighs almost 300g. The excess weight also made
the robot very slow during normal walking. Not only was Mini-Whegs 6J large and
heavy, it was also expensive to construct due to the use of multiple Maxon motors,
titanium jumping legs, and miniature custom radio control components.
The next
Chapter discusses a completely new Mini-Whegs built to reduce the weight, size, and
cost.
The problems with Mini-Whegs 6J led to a clear problem statement for the
development of a new robot. Most importantly, the robot needed to be lighter and
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smaller. Additionally, there were goals to design a robot which would be closer to a
complete product. Thus, other goals included an enclosed, more weather resistant body,
more commonly available parts, and a component and materials cost of less than $250.
Chapter 6 – Weight, Size, and Cost Reduction
The initial combination of steering and controlled jumping in Mini-Whegs 6J led
to a robot that was too heavy. The addition of a second motor and other jumping
components made Mini-Whegs 6J weigh 294g, almost twice as much as Mini-Whegs 5.
The extra weight meant that the drive motor was barely able to move the robot. Also, the
jumping motor was not strong enough to wind a spring stiff enough to make the robot
jump. Since no more powerful motors were available in a comparable size, Mini-Whegs
6J research was set aside until a lighter platform could be developed. This chapter covers
the design of Mini-Whegs 7, including the selection of components and materials, the
manufacture and assembly of the robot, testing of the completed design, and results.
6.1 Design Goals and Specifications
The lightest successful Mini-Whegs robot built before Mini-Whegs 7 weighed
147g. By reducing the size of the robot, and using lighter materials and components, this
weight could be reduced significantly. The combined weight of the jumping motor and
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four-bar linkage on Mini-Whegs 4J is about 80g, so in order to serve as a viable platform
for the addition of a jumping mechanism, Mini-Whegs 7 had to be able to carry a payload
of at least that much. This led to a target weight of 100g for the new robot. By achiving
this target weight, a combined running and jumping robot would be expected to weigh
less than Mini-Whegs 4J.
In addition to the target weight, the robot was to be smaller than Mini-Whegs 3
while still being able to surmount obstacles up to 3.8cm high and run at over 3 body
lengths per second. The open frame design of previous Mini-Whegs robots makes them
unsuitable for extended outdoor use, so all the components of Mini-Whegs 7 were to be
enclosed within a clamshell chassis. The total cost of the parts purchased and the
materials used in machining should not exceed $250, excluding labor.
In order to achieve the design goals, the following specifications for components
were set. The drive train should use a single plastic chain with smaller sprockets to leave
more room in the robot for other components. Axles should be the same diameter as in
previous Mini-Whegs robots, but should be hollow to reduce weight. The drive motor
should weigh less than 20g, but should provide high torque and speed to propel the robot
at over 3 body lengths per second. The steering components, including the front axle,
should use lighter materials than the brass and steel used in Mini-Whegs 5 and 6J. Ball
studs of the same size as the balls machined on the axle of Mini-Whegs 5 were to be
purchased to be screwed into the front axle. This would allow the remainder of the axle
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to be hollow. In order to achieve the cost goal, a cheaper radio receiver, preferably with
standard connectors to ease assembly, was required.
6.2 Component Selection
Previous Mini-Whegs robots all used 13mm Maxon motors to drive the Whegs.
Maxon motors are well suited for Mini-Whegs since they provide a large amount of
torque at a high speeds. However, the metal gears make them heavy. The motor and
transmission combined in Mini-Whegs 5 weighs 32g. Also, Maxon motors draw current
up to 2A, which means that battery selection for powering the motors is limited. To try
to overcome some of these obstacles, some research into alternative motors was
necessary.
William Lewinger, the electrical engineer assisting with the project, suggested
that it would be possible to modify a hobby micro-servo to achieve continuous rotation at
the output shaft, instead of the normal ±45º rotation. By replacing the potentiometer in
the servo circuit with a pair of constant resistors, the circuitry would create a speed
controller instead of a position controller.
Thus, manufacturer specifications for a
number of different micro-servos were compared to find a suitable candidate. The MPI
servo model MX-50HP, which weighs 9.1g, was selected for its high power to weight
ratio, its small size, and it’s relatively high speed. It was estimated that the servo would
be able to provide similar speeds to the Maxon motor at about half the torque. Since
previous Mini-Whegs robots did not lack torque, the lower torque figure was expected to
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be a valid tradeoff for lower mass and cost. Appendix C.2 details the comparison
between the Maxon motor and MPI servo.
Figure 6.1 – Photo of the interior of Mini-Whegs 7, showing the
single drive chain, wheg axles, servos for drive and steering, and
radio receiver.
All Mini-Whegs robots, with the exception of Mini-Whegs 2 used a pair of
stainless steel 0.1475 pitch chains and aluminum sprockets to connect the drive shaft to
the axles. To reduce weight and ease assembly, a 0.1227 pitch acetal chain with acetal
resin sprockets was selected for the new design. To save further room and weight, only a
single chain, wrapped around the drive shaft sprocket in a U shape, was employed.
Previous designs used a custom radio control receiver designed for ultralightweight model aircraft. While very small and light, the receiver was expensive, hard
to get, and had unreliable electrical connectors.
To reduce costs and improve the
availability and reliability, a different receiver was required. The selection for micro
radio receivers is somewhat limited, especially since the receiver had to be compatible
with existing transmitters in the laboratory. Finally, the Hitec “Feather” four-channel
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receiver, which offers standard size connectors, was selected. It is 3.3cm by 1.9cm by
1.0cm in size and weighs 7.4g as compared to 2.4cm by 1.9cm by 0.cm and 3.3g for the
Sky Hooks and Rigging receiver used in Mini-Whegs 5. The receiver and servos used to
control Mini-Whegs 7 are shown inside the robot in Figure 6.1.
Standard radio control parts, such as the servos and receiver being used, require
between 4.8 and 6 Volts to run properly. The high torque, high speed motors driven by
the batteries also require relative high current, on the order of 100mA or more. Most
readily available small batteries cannot meet both the voltage and current delivery
requirements. There are a few cells, primarily designed for camera applications, that do
meet the needs of Mini-Whegs robots. These include the 3 Volt CR2 cells used on
previous Mini-Whegs designs, which weigh 11g each and are 1.6cm in diameter by
2.6cm long. However, since 2 cells are needed to reach 6 Volts, a significant portion of
the size and weight of the robot is taken up by those batteries. Thus, the smaller, 6 Volt
2CR-1/3N cell was selected for testing. It weighs only 9g and measures 1.3cm in
diameter by 2.5cm long. Brief unloaded tests with two servos and a receiver indicated
that the battery was capable of powering the robot. Later tests with the completed MiniWhegs 7 showed that, while the robot was able to move with the smaller battery, the
higher current delivery capacity of the CR2 cells provided greater mobility.
6.3 Part Design and Material Selection
The body of Mini-Whegs 7 was designed to reduce weight and to make the robot
easier to assemble by reducing the number of fasteners. Previous robots used a pair of
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Delrin® rails connected by aluminum cross-members, held together with 16 #0-80
screws, to hold all the components in place. The steering components, radio receiver, and
drive motor were held in place with even more screws. The new design consists of upper
and lower Delrin® shells which hold two side inserts in place. Delrin® was once again
chosen for its good strength and machineability. In this case, all the chassis components
were hollowed out significantly to reduce weight. The two halves are held together by 4
nylon #2-56 screws. Components are trapped vertically beneath the shells, and held in
place horizontally by short walls, so no extra fasteners are required (Figure 6.2).
assembly screws
receiver
drive servo
bearing
steering upright
single drive chain
steering cup
ball stud with pin
steering servo
Figure 6.2 – Exploded view of showing the assembly of MiniWhegs 7 components.
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The steering mechanism design is a modification of the design used for MiniWhegs 5, described in detail in Chapter 4. The front steering axle on previous robots was
machined from steel to increase its life compared to the other steering components.
However, similarly sized ball studs are readily available as steering linkage parts for
radio control cars. By using the anodized aluminum ball studs instead of machining balls
on the ends of the axles, steel was no longer required for the new design. Thus, both
front and rear axles are hollow aluminum shafts. The ball studs are screwed into the
hollow shafts and held in place with Loctite®. In previous robots, the steering joint cup
was machined from brass for its smooth wear characteristics. Brass is 3 times more
dense than aluminum, however. Since the steering joint ball is anodized, there is little
threat of galling between the ball and the cup, so the cup was also machined from
aluminum. If wear turns out to be minimal, the cup could be machined out of plastic,
about half as dense as aluminum, in future robots to reduce weight even further. The rack
and pinion which control the steering were produced from modified 48 pitch nylon gears.
Once again, plastic was selected over brass to reduce weight.
Choosing the dimensions for the drive chain geometry was complicated.
Choosing the distance between the axles based on only the pitch and number of links
leads to a design in which the chain is too tight to move smoothly. Previous attempts to
quantify the amount of slack necessary to allow smooth operation are not well suited for
a complicated chain path because the discrete chain links do not follow the path exactly.
Also, the previous tests only involved the original stainless steel chain, not the plastic
chain to be used in the new robot. Instead of quantifying the slack on a per link basis, an
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iterative trial and error method was used. For each iteration, the distance between the
axles was reduced by 0.13mm. The side inserts were then milled for that length. The
bearings, axles with sprockets, and the chain were inserted into the corresponding holes.
By spinning the axle using ones fingers, a qualitative estimate of the smoothness of
rotation was made. After three iterations, the chain movement was deemed taut enough
to avoid snagging on the side rails while loose enough to eliminate most of the friction.
The final geometry is illustrated in Figure 6.3.
12 tooth sprocket
9 tooth sprocket
0.1227 pitch
(3.117mm)
chain, 58 links
2.722” (69.14mm)
Figure 6.3 – Chain geometry for Mini-Whegs 7.
6.4 Manufacture and Assembly
Once all the components were selected, parts were designed, and materials were
selected, it was possible to manufacture the robot. Some of the steps in creating the robot
involved modifying existing parts, while other components were machined from material
stock.
For the steering servo and drive servo to fit into the chassis, the cases of the
servos had to be modified slightly. As purchased, the cases include mounting tabs which
needed to be removed. This did not affect the performance of the servos; it simply
reduced their size. The output shaft of the drive servo was machined into a cross shape
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using a small computer controlled (CNC) mill. The sprocket which mates with the servo
was similarly modified so that the two parts would fit together.
The steps for modifying the drive servo for continuous rotation were complex.
First, the case was removed and the reduction gears were pulled off of the potentiometer
shaft. Next, the physical stops inside the potentiometer and on the reduction gears were
removed. Finally, the potentiometer leads were disconnected from the servo circuit and
replaced by a pair of equal resistors.
The steering joint balls were drilled to accept a 1.14mm diameter piece of music
wire. This wire was fixed in place with Loctite®, and acts as the pin for the steering
joint. The hexagonal base of each of the ball studs was also turned down to the same
diameter as the 4.8mm diameter axle. The steering rack was cut to length from the
purchased length of 48 pitch nylon rack. Then, all of the teeth except for those near the
center were removed. The ends were then drilled and tapped to accept a #0-80 screw.
The models for the chassis base, top, and inserts, steering uprights, and whegs
were combined into assembly files in Pro/ENGINEER. These assemblies were exported
as STL files and then machined from Delrin® sheets using a small CNC mill. After
milling, the parts were removed from the assembly frames and sanded to remove any
remaining sprues. The last step in constructing the chassis was to drill and tap the four
assembly posts of the chassis base.
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Finally, the aluminum steering cups and the axles were machined by hand from
aluminum rods using a lathe for preliminary shaping, and then a mill to add flats and
slots.
After all the parts were machined, Mini-Whegs 7 was assembled. A hole was
drilled in the chassis base to allow the receiver antenna to pass through (Figure 6.4). The
antenna was then coiled around the base of the robot and held in place with two strips of
double-sided tape. The electrical engineer helping with the project soldered the electrical
components for the battery holder and helped to route the wires from the servo and
receiver. Sprockets were press-fit onto the axles, and bearings were press-fit into the
cavities in the chassis inserts.
Finally, the axles were placed inside the bearings,
connecting the two inserts. The servos and receiver were held in place and then the entire
subassembly was snapped onto the pins of the chassis base. Slight trimming of the
assembly screws was necessary to allow the chassis top to close completely. The feet of
the whegs were coated with Plasti Dip® rubber coating to improve traction, and were
then attached to the axles and steering joint cups with nylon screws.
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switch
antenna
Plasti Dip® rubber
coating on feet
Figure 6.4 – Bottom of the fully assembled Mini-Whegs 7
showing the rubber coating and coiled antenna. The rubber
band holds the larger batteries in place.
6.5 Testing
The first time Mini-Whegs 7 was turned on, whining noises made it evident that
friction was a problem. However, the servo made almost as much noise inside the robot
as outside, so a second servo was modified for continuous rotation. The internal gears of
the new servo were also greased to improve smooth operation. Additionally, the axles
were turned down slightly near the assemble posts to prevent rubbing.
After these modifications were made, the robot was tested with a power supply
with an internal ammeter. The current draw with the first servo in the robot was about
250mA. With the modified servo and other improvements, the current draw dropped
more than 30%. The current draw was the same regardless of whether the servo was
inside the drive train or completely removed from the robot. Thus, no further attempts
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were made to reduce friction in the drive train. See Appendix C.3 for the data from these
tests.
6.5.1 Quantitative Tests
The testing with the external power source showed that the servo was capable of
higher performance than was seen with the single 6 Volt cell. Thus, a makeshift rig was
assembled to attach a pair of 3 Volt CR2 cells to the top of the robot. Top speed tests
were then made to compare the performance with the different power sources.
Top speed tests for previous robots were run on the laboratory carpet past tape
markings at one foot intervals. The good traction of the rubber coating on the feet
probably enabled it to go faster on a hard linoleum surface, but this was not quantified,
since previous Mini-Whegs were all tested on the carpet. The runs were video recorded,
and then analyzed frame by frame to determine the speed of the robot. Results showed
that Mini-Whegs 7 was about 40% faster with the CR2 cells than with the single 6 Volt
cell. The complete results are listed in Appendix C.4 . The 20% weight increase for such
a large increase in performance seemed to justify using the larger batteries, so subsequent
mobility tests were carried out with the large batteries only.
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Figure 6.5 – Photo depicting the relative height of a 3.8 cm
obstacle to the size of the robot.
Mini-Whegs 7 was also controlled to run over obstacles of various heights. The
largest obstacle successfully overcome, without high-centering and toppling of the robot,
measured 3.8cm (Figure 6.5, Figure 6.6). This height is 25% higher than the length of
any leg at its longest point. If some mechanism, such as a flexible tail, existed to prevent
toppling, larger obstacles could almost certainly be surmounted.
Figure 6.6 – The robot is able to surmount the 3.8 cm obstacle.
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A brief examination of testing videos indicated that the turning radius of the robot
was about three to four body lengths. This is a somewhat larger turning radius than
previous Mini-Whegs designs.
However, the geometry of the steering joint ball in
previous robots was optimized for a large angle.
With the current robot, such an
optimization was not possible without considerably more modification of the purchased
ball studs.
The robot was also tested on a carpeted incline at various angles. When the speed
of the robot was sufficiently reduced, it was able to climb inclines up to 25º. At higher
speeds, the front whegs had a tendency to pop off the surface of the incline and cause the
robot to topple backwards.
Payload capacity was also measured to examine whether a servo-powered robot
would be able to support the extra components of a jumping mechanism. Several brass
masses, ranging from 50g to 200g, were attached to the top of Mini-Whegs 7 with double
sided tape, which was then operated. The robot was able to move at over 3 body lengths
per second while carrying a payload up to 100g. With larger payloads, the robot was still
able to move, albeit at less than 3 body lengths per second. A payload of 200g slowed
the robot to 2 body lengths per second.
6.6 Mini-Whegs 8
As a senior project, Andrew Schifle and Elizabeth Steva created a second
lightweight robot, Mini-Whegs 8, which has a slightly larger chassis to accommodate the
CR2 cells used in most of the testing of Mini-Whegs 7 (Schifle and Steva, 2004) (Figure
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1.4). Mini-Whegs 8, at 9.5cm by 6.7cm by 1.8cm, is smaller than Mini-Whegs 5 (9.1cm
by 6.9cm by 2.0cm and 165g), but weighs the same amount as Mini-Whegs 7 (108g).
The increase in size with no increase in weight was accomplished by using ABS, a less
dense plastic than Delrin®, for the clamshell chassis. The larger size, slightly longer
wheg appendages, and lowered center of gravity (since the batteries are not on top of the
robot) allow Mini-Whegs 8 to climb 3.8cm obstacles more reliably than Mini-Whegs 7.
6.7 Discussion
Several objectives were met with the design of Mini-Whegs 7. The weight of the
robot with its single battery beat the target weight by over 10%, but was over the target
by 8% with the two battery configuration. While not as fast as previous Mini-Whegs
robots, the robot was still able to move at almost four body lengths per second. Obstacle
climbing ability was on par with earlier designs. The cost, at just under $180 (see
Appendix C.1 ), of the current robot was much less than previous Mini-Whegs robots.
With a payload of 50g, Mini-Whegs 7 was almost as fast as with no extra mass at
all. Extra mass of up to 100g—the robot’s own mass—caused the robot to slow a little
more. However, the top speed was still over three body lengths per second. Thus,
addition of a jumping mechanism would still allow the robot to beat the target top speed.
The next Chapter discusses how the design changes made in Mini-Whegs 7 and 8
were combined with some of the successful features of Mini-Whegs 4J and 6J to finally
create a fully controllable jumping robot.
Chapter 7 – A Fully Controllable Jumping Robot
Development of Mini-Whegs 7 and 8 successfully reduced the weight of the
Mini-Whegs platform, making it possible to add extra payload, such as a jumping
mechanism, without significantly reducing the mobility of the robot. Elements of the
designs of Mini-Whegs 7 and 8 were combined with the four-bar mechanism design and
spring-winding motor from Mini-Whegs 6J to create the fully controllable running and
jumping Mini-Whegs 9J.
7.1 Design Goals and Specifications
As discussed in Chapter 6, payload testing on Mini-Whegs 7 showed that the
servo used as a drive motor was easily capable of powering a robot weighing 200g.
Since Mini-Whegs 4J weighs 200g with no control system and only one motor, it was
unlikely that a completely controllable jumping Mini-Whegs robot could be built
weighing much less than Mini-Whegs 4J. Thus, a target weight of 200g was set for Mini84
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85
Whegs 9J. Not only was Mini-Whegs 6J heavy, it was also quite large. While designing
Mini-Whegs 9J, a significant effort was made to pack the components closely, keeping
the chassis the same width as Mini-Whegs 4J, 7.6cm, while keeping the distance between
the front and rear wheg axle under 8cm.
Achieving the target weight and size requires some weight reduction in the
jumping mechanism while retaining the weight reduction techniques used for the rest of
the components in Mini-Whegs 7 and 8. The new robot should use the same drive servo,
chain, and sprockets as those used in Mini-Whegs 7 and 8. If lighter or smaller steering
servo or radio control components are readily available, they should be incorporated into
the new design. All axles and jumping mechanism cross braces should be hollow. The
jumping mechanism motor should weigh no more than the one used in Mini-Whegs 6J,
and the four-bar linkage should use aluminum instead of titanium to reduce weight.
In addition to size and weight goals, performance requirements were also set. The
length of the whegs combined with the low weight of the whole robot should result in a
top speed of over 3 body lengths per second. The spring selected for the jumping
mechanism should allow the robot to jump at least 15cm, the height of a standard stair.
7.2 Component Selection
In order to reduce size and weight, several components even smaller than those
used in Mini-Whegs 7 were used. A Cirrus 4.4g servo was chosen to turn the pinion for
steering, while a 3.5g Cirrus Micro-Joule radio receiver and 2g Cirrus Micro-Joule S5A2
speed controller were selected to control the jumping mechanism motor. As in Mini-
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Whegs 7, an MPI MX50-HP servo was modified for continuous rotation to act as a drive
motor for the whegs. The electronics of the servo act as a speed controller, so no
additional speed controller is required for running.
Other components, such as rack and pinion for steering, and the ball studs for the
simplified universal joints in the front wheg axle were the same as those used in MiniWhegs 7.
Aluminum was used instead of titanium for the jumping legs, and the
aluminum braces for the jumping mechanism were hollowed to reduce weight even
further.
7.3 Design
As with previous Mini-Whegs robots, all the parts were modeled in
Pro/ENGINEER before being manufactured or assembled. Using the volume calculating
capabilities of the CAD program, it was possible to monitor the mass of each component.
In addition to providing an estimate for the final mass of the actual robot, the mass
calculations showed which components required the most weight reduction to achieve the
target total mass.
7.3.1 Chassis and component layout
The chassis of Mini-Whegs 9J is similar to that of Mini-Whegs 7 and 8. A pair of
hollowed ABS side rails support bearings for the drive and jump axles. The side rails fit
into a bottom shell, also made from ABS, via several small posts. The bottom shell
contains several short walls and shelves to support the internal components, such as the
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motor and servos (Figure 7.1). A second shell fits over the top of the first and attaches
with six #2-56 screws.
radio receiver, speed
controller, and
antenna
jumping motor and
transmission
jumping mechanism
axle
steering servo
batteries
drive servo
drive chain
Figure 7.1 – Rendering of the internal components of MiniWhegs 9J.
The spring of the jumping mechanism is external to the body, so the ground
clearance is reduced when the robot is upside down. By placing the batteries for the
robot vertically inside the body and protruding through the top, some of the lost space at
the top of the robot was utilized. Placing the batteries vertically also allowed the length
of the robot to be reduced to achieve the target length, and allows the batteries to be
removed more easily when they need to be changed.
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Inside the robot, the steering servo fits between the two batteries. The spring fits
between the batteries on top of the robot, and attaches to a short aluminum protrusion in
front of the battery housing (Figure 7.2). The batteries help to brace against the force of
the spring. A small battery lid fits over the top of the batteries on the outside of the robot.
Thus, the batteries can be changed by opening just the lid, without removing the spring or
upper body shell. The lid is held in place by two #2-56 screws. It also contains a small
switch to turn on the robot.
removable battery lid
jumping spring
aluminum brace for
spring
power switch
Figure 7.2 – Rendering of the complete robot. The jumping
spring attaches to a brace in front of the batteries and fits
underneath the removable battery lid.
7.3.2 Jumping mechanism modifications
In addition to reducing the weight of the components which appear in other MiniWhegs robots, some design modifications were made to reduce the weight and cost of the
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jumping mechanism as well. The four bar mechanisms in Mini-Whegs 4J and MiniWhegs 6J consist of titanium links attached to solid aluminum shafts with steel screws
and washers, and brass bushings to reduce friction at the joints. While titanium is
stronger than aluminum on a per mass basis, it is more expensive and denser. Since the
links cannot conveniently be made any smaller than they already are on Mini-Whegs 4J,
using aluminum would actually reduce the total weight of the links by 7g. In order to add
needed stiffness, a single or double rib was added to the links to create a T or C shaped
cross section. The resulting links are light (8g in total), easy to machine, and much less
expensive than those made of titanium. An additional 5g were removed by using hollow
aluminum shafts for cross braces with larger 8-32 nylon screws. The large diameter of
the assembly screw allows the shafts to be thin-walled (3.0mm internal diameter in a
4.8mm shaft), while the large heads eliminate the need for washers to keep the screws
from pulling through the holes in the links. Thin Teflon washers are used to reduce
friction between the screws and the links. The complete assembly can be seen in Figure
7.3.
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Figure 7.3 – Side view renderings showing the jumping
mechanism of Mini-Whegs 9J retracted (top) and released
(bottom).
The motor and transmission combination used in Mini-Whegs 6J was reused in
Mini-Whegs 9J. Space between the transmission output shaft and the jumping axle
remains the same, so the same size 12 tooth pinion and 18 tooth gear were used.
However, to reduce weight by 5g, aluminum gears were selected instead of brass. The 18
tooth gear only rotates through about 100°, so about half of the teeth on the unused side
of the gear were removed to reduce weight and improve clearance between the gear and
the rear wheg axle.
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7.3.3 Spring selection
After designing and assembling the new jumping mechanism, it was desirable to
choose the spring would be able to store the maximum amount of energy possible when
the mechanism was fully wound. Ideally, this spring would require the same amount of
force to extend at any length. As discussed in Chapter 3, such a spring does not exist, so
a soft spring with a significant amount of preload is desirable. For the same maximum
applicable force, the softer spring will store more energy for a given displacement up to
that force.
However, there are also space considerations, so the spring cannot be
stretched very far to build up preload. The dimensions of Mini-Whegs 9J limit the free
spring length to a maximum of about 4.4cm. The spring must also be strong enough to
avoid plastic deformation at the maximum load, so there is a lower limit of about 2.5cm
in length and 0.8cm in diameter for readily available springs.
Two springs were selected from a random assortment which fit the size
requirements. The first spring allowed the robot to jump into the air, but the second
spring was too stiff for the motor to wind. Since the springs were from an assortment, no
stiffness data were available. To remedy this situation, several weights of known mass
were successively hung from the spring and the displacement was measured. The data
points collected were used to plot the stiffness of the springs (Figure 7.4). From this
information, several alternative springs were selected which fit the dimensional criteria
and whose stiffness fit in between the stiffness of the two original springs. These new
springs were then tested in the robot, and the one which resulted in the highest jump was
selected for the final robot.
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Spring selection for Mini-Whegs 9J
Weight applied to spring (N)
20
F = 2.92x
15
F = 0.91x
10
5
Too soft
Too stiff
Selected spring
0
0
5
10
15
20
Displacement (mm)
Figure 7.4 – Two springs from a random assortment were tested
on the robot and then tested to find their stiffness. The spring
which performed best on the robot has a stiffness of 1.05 N/mm.
7.4 Testing
While testing different springs to select the one which performed best, the ABS
side rail of the robot cracked near the slip-gear mechanism. The high resistance from the
stiff springs being tested caused the pinion and gear of the slip-gear to push away from
each other. To remedy this undesirable situation, modifications were made to the design.
First, the side rail was re-machined from Delrin®, which has much higher tensile strength
than ABS. A few of the weight reducing holes in the side rail were also eliminated to
remove stress concentrations. Secondly, a thin piece of Delrin® was machined which
attaches to the transmission of the jumping motor with two mounting screws. This small
A Small, Insect Inspired Robot that Runs and Jumps
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brace also attaches to the jumping axle via a ball bearing. Thus, the small piece of
Delrin® holds the motor and axle at a fixed distance, keeping the slip-gear engaged.
Figure 7.5 – Composite of video frames showing Mini-Whegs 9J
easily clearing a 9cm barrier.
After reinforcing the frame, the best spring was remounted on the robot. Running
and jumping were then recorded on video for further analysis. By moving different
joysticks on the radio transmitter, the operator can easily control steering, running, and
jumping independently. With the selected spring, the robot can jump as high as 18cm
from the lowest point of the robot to the ground. By adjusting the speed of the robot on
the approach to jumping, the jump trajectory can be controlled. For a more vertical jump,
the robot should start standing still. For a forward and upwards trajectory, the robot
should run while it jumps. Since the modes of locomotion are independent, either
trajectory is easy to accomplish. When jumping over obstacles onto ground at the same
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94
level, the robot lands upright, eliminating the need for the operator to drive the robot into
an obstacle to flip it over (Figure 7.5).
7.5 Discussion
The final Mini-Whegs 9J robot weighs 191g, much less than Mini-Whegs 6J,
which weighed 294g. The lower weight and smaller chassis allow the robot to jump
much more easily than the previous attempt at a fully controllable jumping robot. The
robot has a top speed of 3.3 body lengths per second (26cm/s), which is about a third of
the top speed of Mini-Whegs 5. The highest jump is 4cm lower than the highest jump of
Mini-Whegs 4J. However, the target speed and jumping height set for Mini-Whegs 9J
were met, so the combination of both modes of locomotion in the same robot can be
considered a success. A goal for a future Mini-Whegs robot would be to improve
performance in either mode of locomotion by incorporating different motors or power
supplies to increase the power to weight ratio .
For future development, it would be worthwhile to do further research on
available motors, transmissions, and other methods for winding the spring in the jumping
mechanism. Theoretical calculations with manufacturer data for the chosen spring and
transmission show that the torque on the transmission from the spring at its fully
extended position (about 600mNm) meets or exceeds the maximum allowable torque for
the transmission (Appendix D – ). Winding of the spring is relatively quick, especially
compared to Mini-Whegs 4J, so the reduced speed of a larger transmission would not be
detrimental. However, no higher rated transmission in an appropriate size is available
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95
from Maxon, so a different manufacturer, customized transmission, or custom final
transmission stage will be required for higher jumping.
Chapter 8 – Summary and Future Work
8.1 Summary
Mini-Whegs 4J successfully proves that a jumping capability can be added to a
small robot to improve mobility and overcome obstacles of relatively large size.
However, it does not include active control of the jumping mechanism. The robot jumps
at regular intervals while running, which is not a useful design for actual terrain.
To prepare for the development of a complete running and jumping robot, robust
and reliable components were designed and tested in Mini-Whegs 5.
A simplified
universal joint consisting of a ball and cup is used to create a strong and efficient steering
mechanism. Mini-Whegs 5 can easily crawl over obstacles larger than the radius of its
whegs, run at speeds up to 10 body lengths per second, and turn within a radius of 2.5
body lengths.
96
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97
Mini-Whegs 6J was the first attempt at combining the successful features of MiniWhegs 4J and Mini-Whegs 5 in the same robot. The resulting design is much larger and
heavier than either previous robot individually.
Excess weight makes Mini-Whegs 6J too heavy to jump, so Mini-Whegs 7 was
designed to reduce the weight of the Mini-Whegs platform. Mini-Whegs 7 weighs
approximately a third as much as Mini-Whegs 6J. The use of an inexpensive servo for
driving makes Mini-Whegs 7 very light, but also significantly slower than Mini-Whegs 5.
Built for under $180, Mini-Whegs 7 can run at approximately 4 body lengths per second
using the same batteries as Mini-Whegs 5.
Mini-Whegs 7 can also successfully carry payloads equal to its own weight or
more. This makes the robot ideal as a starting point for the addition of a jumping
mechanism similar to the one used on Mini-Whegs 4J. The final Mini-Whegs 9J robot
weighs just 191g, less than Mini-Whegs 4J, and much less than Mini-Whegs 6J. The
robot runs about as fast as Mini-Whegs 7 and can jump almost as high as Mini-Whegs 4.
8.2 Future Work
While Mini-Whegs 9J successfully proves that independent running and jumping
can be accomplished in Mini-Whegs, there are some weaknesses in the design which
could be improved upon. As discussed at the end of Chapter 7, the transmission used to
wind the jumping spring is possibly too fragile for the large forces created by the spring.
Research into stronger transmissions or alternative methods for retracting the jumping
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98
mechanism could lead to a robot that can jump higher without risk of damage to the
components.
Some minor changes can be made in the design and manufacture of the chassis as
well. The thin plastic components tend to vibrate during machining, sometimes creating
cracks or punctures. By manufacturing the body shell using fused deposition modeling
(FDM), vibrations could be avoided, leading to a stronger robot. Ideally, the robot parts
could also be mass produced via plastic injection molding.
The most recent Mini-Whegs robots, Mini-Whegs 7, 8, and 9J, have fully
enclosed bodies which help keep foreign particles out of the drive components of the
robot. This greatly enhances their usefulness in outdoor environments. However, the
design is currently not water-tight. Grease or O-ring tubing could possibly be used to
seal a future robot to create a Mini-Whegs robot impervious to weather, or even a MiniWhegs robot which can swim.
Mini-Whegs also provides a versatile platform for research involving sensor
integration and robot group behavior as well as research in increased mobility. While
much success has already been achieved, the possibilities for further improvement are
endless.
Appendix A – Mini-Whegs Evolution
Name: Mini-Whegs 1
Built: July 2001 by Andrew Horchler
Size:
8.3cm long by 6.4cm wide by 2cm thick
Mass: 125g
Mini-Whegs 1 proved that whegs work at a small scale. It uses flexible couplings
for steering and torsional compliance.
99
Name: Mini-Whegs 2
Built: November 2001 by Andrew Horchler
Size:
7.6cm long by 5.3cm wide by 1.7cm thick
Mass: 94g
Mini-Whegs 2 was a somewhat unsuccessful attempt at creating a smaller, lighter
Mini-Whegs robot.
The batteries selected were incapable of providing the current
necessary to power the Maxon drive motor.
100
Name: Mini-Whegs 3
Built: February 2002 by Andrew Horchler
Size:
8.4cm long by 6.4cm wide by 2cm thick
Mass: 147g
Mini-Whegs 3 is an improved version of Mini-Whegs 1. Ball bearings and
Delrin® whegs improve the performance over Mini-Whegs 1.
101
Name: Mini-Whegs 4J
Built: April 2002 by Jeremy Morrey
Size:
9.4cm long by 7.6cm wide by 2.4cm thick
Mass: 209g
Mini-Whegs 4J proves that jumping can be incorporated on a Mini-Whegs
platform. It does not include any active control.
102
Name: Mini-Whegs 5
Built: July 2002 by Jeremy Morrey and Bram Lambrecht
Size:
9.1cm long by 6.9cm wide by 2cm thick
Mass: 165g
Mini-Whegs 5 is a robust platform with reliable ball and cup steering joints.
Small feet on the whegs improve mobility.
103
Name: Mini-Whegs 6J
Built: May 2003 by Jeremy Morrey and Bram Lambrecht
Size: 12.4cm long by 8.4cm wide by 2.5cm thick
Mass: 294g
Mini-Whegs 6J was an unsuccessful attempt at combining elements of MiniWhegs 4J and 5. The robot is too large and heavy to run or jump well.
104
Name: Mini-Whegs 7
Built: October 2003 by Bram Lambrecht
Size:
8.9cm long by 5.4cm wide by 1.8cm thick
Mass: 89g (108g with CR2 batteries)
Mini-Whegs 7 is a smaller, fully enclosed Mini-Whegs robot. It uses many offthe-shelf components to reduce cost and weight.
105
Name: Mini-Whegs 8
Built: April 2004 by Andrew Schifle, Elizabeth
Steva, and Bram Lambrecht
Size:
9.5cm long by 6.7cm wide by 1.8cm thick
Mass: 110g
Mini-Whegs 8 is a slightly larger version of Mini-Whegs 7 which encloses the
batteries within the body of the robot.
106
Name: Mini-Whegs 9J
Built: June 2004 by Bram Lambrecht
Size:
10.4cm long by 7.6cm wide by 2.1cm thick
Mass: 191g
Mini-Whegs 9J is a fully controllable running and jumping Mini-Whegs robot.
107
Appendix B – Calculations for the design of Mini-Whegs 6J
B.1 Chain Length Measurement
θ
p
θ
x
d
h
c
The sum of the vertical measurements is:
h + x sin θ + d/2 (1 – cos θ) = d
(1)
The sum of the horizontal measurements is:
p + 2 x cos θ + d sin θ = c
(2)
So, the total length of the chain is:
L = c + (π + θ) d + p + 2 x
(3)
The center distance c, pitch diameter d, and the chain pitch p are known; h is
measured; and x and θ can be determined from equations (1) and (2).
B.2 Slip Gear Contact Ratio
To calculate the contact ratio between the slip gear and mate, the following
formula is used:
CR =
rap2 − rbp2 + rag2 − rbg2 − ( rp + rg ) sin φ
pb
where rp is half of the pitch diameter of the slip gear, rg is half the pitch diameter of the
mate, P is the diametrical pitch, and
rbp = rp cosφ , rbg = rg cosφ , rap = rp +
1
1
π
, rag = rg + , pb = cosφ
P
P
P
108
Appendix C – Data for Mini-Whegs 7
The following tables provide data to support the results described for the miniature MiniWhegs 7 robot in Chapter 6.
C.1 Approximate cost of components
The following table gives the cost of all the components and materials used in
Mini-Whegs 7. The total is well within the target cost of $250.
Component
Manufacturer's description
Unit $
Quan.
drive servo
MPI MX-50HP
$20.99
1
$20.99
steering servo
GWS Pico/BB
19.99
1
19.99
steering joint ball
Associated Factory Team Blue
Aluminum Ball Studs (8 pack)
7.69
2
1.92
axle bearings
440C SS/ABEC 3 0.1875 Bore Plain
Ball Bearing
5.43
6
32.58
drive shaft
bearing
440C SS/ABEC 3 0.25 Bore Plain Ball
Bearing
5.49
1
5.49
radio receiver
Hitec Feather 4-Channel FM Receiver
40.98
1
40.98
steering pinion
48 pitch 14.5° 16 tooth Nylon gear
1.93
1
1.93
steering rack
48 pitch 14.5° Nylon gear rack (1 foot)
2.46
3”
0.62
wheg screws
#4-40 5/16" Black Nylon flat machine
screw (100 pack)
4.57
4
0.18
assembly screws
#2-56 3/8" Black Nylon flat machine
screw (100 pack)
4.6
4
0.18
battery
Sanyo 6.0V Lithium L544
4.25
1
4.25
109
Price
axle sprockets
0.1227 Pitch, 12 Tooth, 3/16" Bore
roller chain sprocket
1.01
2
2.02
drive sprocket
0.1227 Pitch, 9 Tooth, 1/8" Bore roller
chain sprocket
0.98
1
0.98
chain
0.1227 Pitch Acetal resin roller chain (1
foot, about 98 links)
8.04
58
links
4.76
steering rack pin
#0-80 3/8" SS pan head slotted
machine screw (100 pack)
5.26
2
0.11
steering joint pin
0.045" Music Wire
12.23
1”
0.01
axles
Precision ground 3/16" 6061 Aluminum
rod (6 feet)
30.20
5”
1.92
steering joint cup
5/16" 6061 Aluminum rod (6 feet)
4.94
2”
0.07
chassis
Black Delrin Sheet 1/2" Thick, 12"X12"
38.32
1
38.32
Total (without shipping costs)
110
$177.30
C.2 Comparison of Maxon motor to MPI servo
The values in the following table are based on the manufacturers’ specifications
for the two motors. The MPI high power servo is model number MX-50HP, distributed
by Maxx Products, Inc. Torque and speed numbers for the servo are rated at 4.8 Volts.
The Maxon motor is an RE-13, 1.2 Watt, 2.4 Volt model number 118420 with a 67:1
model number 110315 metal planetary gear transmission. The speed figure based on the
maximum allowable speed of the motor, and the maximum torque is based on the
continuous rotation figure from the transmission specifications.
MPI Servo
Maxon Motor
Speed (rpm)
125
189
Torque (mNm)
162
300
Starting current (mA)
300
1150
Mass (g)
9.1
32
$20.99
$107.40
Speed / Mass
1.00
0.43
Torque / Mass
1.00
0.53
Power / Mass
1.00
0.8
Power / Cost
1.00
0.55
Cost
Based on mass or cost value, the MPI servo has the obvious advantage.
111
C.3 Current draw for various operating conditions
The following gives the current draw of the robot for various operating
conditions. These values were read from the analog indicator on the power supply used
to run the robot for these tests. The results were identical with the drive components
removed from the drive train. All measurements are ±10 mA.
Operating condition
Current draw (mA)
Continuous full forward ............................................................ 200
Continuous full reverse ............................................................ 170
Peak, stop to full forward ......................................................... 300
Peak, full forward to full reverse............................................... 350
Peak, full forward with steering ................................................ 410
Peak, full reverse with steering ................................................ 370
C.4 Top speed calculations
The top speed was measured by counting the number of video frames required for
the robot to move between taped markings on the floor at one foot intervals. The number
of frames was converted to a measurement in seconds. The mean of these values was
calculated and converted to a measurement in body lengths per second. Here, the body
length is the distance between the centers of the whegs.
Single 6 Volt Cell
Two 3 Volt Cells
6
17
Mean time interval (s)
1.64
1.18
Standard deviation (s)
0.16
0.09
19 ± 2
26 ± 2
2.7 ± 0.3
3.8 ± 0.3
Number of samples
Speed (cm/s)
Speed (body len./s)
112
Appendix D – Torque Considerations in Mini-Whegs 9J
Maxon transmissions are rated for a maximum output torque by the manufacturer.
For the selected GP13 1119:1 transmission, model number 110317, the maximum
allowed continuous torque load is 350mNm, and the maximum allowed intermittent
torque is 530mNm. The RE13 2.5W motor, model number 118485, attached to the
transmission has a stall torque of 9.14mNm.
The maximum efficiency of the
transmission is 62%, so if the input torque is the stall torque of the motor, then the output
torque of the transmission will be 9.14×1119×0.62 = 6340mNm. Thus, if the load on the
transmission exceeds the rated torque, the motor can easily damage the transmission.
In Mini-Whegs 9J, the selected spring has a free length of 3.18cm and a spring
constant of 1.05N/mm. The preloaded length of the spring is 4.80cm, and the maximum
stretched length is 8.00cm. Thus, the spring nominally pulls the jumping mechanism leg
with a force of (8.00cm–3.18cm)×10.5N/cm = 53.7N. The lever arm of the mechanism is
2.16cm long, and the gear reduction at the slip-gear is 2:3. If the efficiency of the slipgear is assumed to be 80%, then the torque on the transmission output shaft from the
spring force is 53.7N×21.6m×2/3×0.80 = 619mNm. This torque is unfortunately greater
than the rated torque of the transmission! However, the spring used is operating outside
of its rated range as well (maximum load 25.4N), so it may not actually be exerting the
full 53.7N.
Regardless, there is little if no safety factor for the operation of the
transmission, so a solution rated for higher loads is highly desirable.
113
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