The Design and Fabrication of a Micromechanical Dragonfly

The Design and Fabrication of a Micromechanical Dragonfly
The Design and Fabrication of a Micro Mechanical Dragonfly
Project Report
Submitted March 19, 2009
Patrick J. Lingane
Senior Thesis
William D. Keat, Advisor
Department of Mechanical Engineering
Union College
Schenectady, NY
Table of Contents
1.
2.
3.
4.
5.
Abstract
Introduction
Reverse engineering of the WowWee model
The dimensional scaling analysis
Design of and modifications to the half scale prototype
5.1. Design overview
5.2. Body and frame
5.3. Motors and gearing
5.4. The linkage
5.5. The wings
5.6. The battery
5.7. Summary of design and modifications
6. Manufacture of the scaled prototype
7. Testing and results of the scaled prototype
7.1. Testing overview
7.2. Preliminary and battery testing
7.3. The frequency response to voltage
7.4. Flapping symmetry
7.5. Airfoil testing
7.6. The flapping angle response to frequency
7.7. Final result
8. Creation of an analytical model
8.1. Model overview
8.2. Positions and time derivatives of the linkage
8.3. Moments on the wings
8.4. Deflections of the wings
8.5. Results of the analytical model
9. Conclusion
10. Future work
10.1. Overview of future work
10.2. Future work on the current prototype
10.3. Future work on the analytical model
10.4. Future work and the design of a life size flapping mechanism
References
Appendix A: Characteristics and analysis of the WowWee model
Appendix B: Characteristics and analysis of the cut down WowWee model
Appendix C: Scaling and design of the scaled prototype
Appendix D: The analytical model
Appendix E: Characteristics and analysis of the scaled prototype
–2–
1. Abstract
The goal this project was to create a scaled model of a flapping wing aerial vehicle.
The design was initially based on a remote controlled model available at many toy stores.
This model was in the form of a dragonfly but about four times the size in each
dimension. My project was to scale this down, ideally to the size of a real dragonfly. This
however was difficult, and a half scaled prototype (twice life size) was constructed
instead. Scaling was done using dimensionless fluid parameters such as the Reynolds and
Strouhal numbers which effectively related the various properties of each model. Testing
and modification of the prototype were carried out, and in the process an analytical model
was made to model the dynamics. Although still not flying, the prototype will hopefully
soon be ready for testing against the theory. In the future, more testing will be completed,
and minor modifications made to get the scaled prototype flying. All of this is part of a
larger goal to miniaturize a flapping flying robot of which this project is only a part.
2. Introduction
Flight has always fascinated humans, and it has only been during the past hundred
years that humans have achieved powered flight. However the type of flight used in
nature is different from what humans use; powered flight in nature uses flapping wings
while human machines typically do not. There are advantages and disadvantages to each
design although flapping wings are the only practical method of propulsion for animals.
Typically humans have used rotating shafts or great amounts of heat to produce power,
and neither of these things is available to animals.
–3–
With the recent advances in technology, more methods are available to create
powered flight for man-made vehicles. Flapping flight provides certain challenges
especially to our understanding of its motion, but also provides certain benefits that could
not be realized without it. The fundamental difference between flapping and non-flapping
flight is that flapping flight inherently uses non-steady state aerodynamic mechanisms to
produce lift and thrust. Steady state aerodynamic technique, which has been successfully
used in the past, is easier to analyze than non-steady state, and there has not been a reason
to change. Recently however, people have realized the advantages of flapping flight, and
technology has been created to analyze it.
Flapping flight is capable of producing much more maneuverability than fixed wing
flight, and can also give sufficient lift to slower or even hovering vehicles. These
advantages are offset by an increase in sensitivity to even the smallest of changes in
motion, and control of these vehicles is much more difficult. Once these difficulties are
overcome, these vehicles can be very useful. They may be used to carry cameras to
survey a scene or find an injured person in a dangerous environment. They also give us a
better sense of how nature operates, and could be interesting to entomologists.
There are various toys available that use flapping wings to power small craft either
with or without remote control, and these can be bought cheaply. An example of this kind
of toy is the WowWee Robotic Dragonfly available at Wal-Mart® stores and shown in
Figure 1 or a similar robotic bat found at RadioShack®. My project sought to miniaturize
the WowWee model to something more close to life sized. This was broken into various
steps; the first was to create a proof of concept half-scale prototype using the same
mechanisms as the original model. This was the primary goal of the project. Further goals
–4–
included finding a mechanism that can be scaled
down past half scale, and finally building a prototype
at that smaller scale. From the beginning however it
was realized that in the time available for the project
no smaller prototype would be designed or built, but
only possibly a mechanism designed that is capable
Figure 1: The WowWee Dragonfly
of motion at this small scale.
The original WowWee model had a wingspan of 0.41 meters. Large dragonflies
have a wingspan of roughly a quarter of that. The mechanism used on this original
WowWee model uses a geared rotary motor to turn a crankshaft, which connects to the
wings through a connecting rod forming a four bar linkage for each set of two connected
wings. The wings are arranged two on top and two on bottom, with each top wing
connected rigidly to the opposite bottom wing so that the wings form an X when open.
This is an inexpensive way to provide wing motion, but has scaling limitations. The
main goal of my project was to miniaturize the existing model and mechanism, and to
arrange the new properties so that it will act and fly like the original. For any given size, a
certain weight, flapping frequency and velocity are necessary to produce flight. My first
goal was to define these variables. My second goal was to create a SolidWorks model
that exhibited the correct motion and used parts that could readily be purchased. My third
goal was to create a prototype that flew. When the first prototype did not fly, various
modifications were made. As is par for the course, new problems arose in the process of
which one in particular sparked the creation of an analytical model of the motion of the
dragonfly using Matlab®. Results from this model as well as intuition and trial and error
–5–
led to the further improvement of the prototype which, near the end of the project,
showed clear signs of forward movement while failing a flight test and crashing, still
flapping, on the ground.
Goals of future work include continued modification to make the prototype fly,
further testing and modification to update the analytical model, and finally design and
fabrication of a smaller version of the prototype more comparable to the size of a real
dragonfly.
3. Reverse engineering of the WowWee model
In order to effectively scale all the design parameters of the prototype, the original
WowWee model was completely reverse engineered to find all its important design
characteristics. Many experiments were performed during this process and are described
here; Appendix A contains all the resulting data.
As a first experiment, the WowWee dragonfly was taken outside and flown around
the yard. There were two controls for the dragonfly: throttle and turning. Each was
controlled using a joystick on the remote control. The throttle stick controlled the
frequency of flapping while the turning stick controlled the speed of a small propeller
mounted sideways in the tail of the dragonfly. The model flew easily, though it was not
easily controllable. Flight times ranged between five and thirty seconds before crashing,
depending on wind conditions and the experience of the pilot. Some altitude gain was
possible but proved difficult without stalling. A setting of beginner or expert controlled
the sensitivity of the turning stick, and while in beginner mode the dragonfly turned little,
in expert mode the turning became disruptive to the flight. One charge of the battery
–6–
produced about half an hour of fun, or about twelve to fifteen minutes of flight. The
model thus flew well overall but still had some issues relating to control. However, for
my project, control was a minor consideration and thus for my purposes the model flew
successfully.
To analyze the wing motion, the model dragonfly was secured to a black surface
and sufficient light was shown upon it. A Nikon model D300 camera was used in its
rapid exposure mode to take pictures at seven frames per second of the dragonfly from
both front and side. While taking these pictures, the dragonfly was run with a frequency
very slightly faster than the camera speed such that in each picture the wings were in a
slightly different position having just gone through slightly more than a full cycle. This
produced a series of pictures which if viewed in order gave the appearance of smooth
flapping flight which could be viewed frame by frame. In effect this was a cheap
alternative to using a high speed camera for the same purpose. Eight of these images are
arranged in Figure 2, and a more extensive set may be seen in Appendix A.
Figure 2: Motion series of the WowWee dragonfly
These pictures show that the thin, flat, flimsy airfoil of each of the WowWee
dragonfly’s wings deform during flight to become somewhat more of a traditional curved
airfoil with the forward edge leading the trailing edge, and the curvature of the wing
concave toward the direction of travel. This produces several advantages. If the wings did
–7–
not deform, no thrust would be generated by flapping. The wings operate much like the
sail in a sailboat, changing the direction of the airflow impinging on them from vertical to
backward. Although there is little wind actually traveling vertically, the flapping is a
vertical motion which causes the relative wind on the wing to be vertical. When the
wings come together, air is forced out behind the wings creating thrust. Putting a hand
behind the flapping wings verifies that some thrust is generated by the wind that can be
felt. Another advantage of the deformable wings is increased lift while gliding when the
flat airfoil deforms into a more effective shape. This lift is particularly evident if the
wings are not flapping, and only occurs during forward flight. Since the pictures in
Appendix A do not represent forward flight, this effect is not observed there; only the
flapping effect is present.
The pictures taken from the front (see Appendix A) do not provide as much
information about the flight mechanism, but do provide some information on the rigidity
of the wing rods which support the airfoils. These rods can be seen bending during
flapping such that the phase at the tip of the wing is slightly behind the phase near the
center. This is most likely undesirable, but since the magnitude of this bending is low, it
likely has a negligible effect. From these pictures we can also see the changing shape of
the airfoils as described previously.
The flapping frequency is an important parameter to measure for this mode of
flight, and it was measured using a microphone. A microphone connected to a computer
was mounted next to the model dragonfly such that at the extreme of every flap the wing
rod hit the microphone. This produced a sharp sound with every hit while the motor
sounds were steadier. Using the Sound Recorder application in Windows, the sound was
–8–
recorded for exactly ten seconds then slowed down to one eighth speed. The number of
sharp taps could now be counted. Dividing the total number of taps by the original ten
seconds provided an accurate measure of the flapping frequency at 9.45 Hz.
An experiment to determine the center of gravity of the model was completed for
both the vertical and horizontal directions. First the model was hung by a thin ribbon
attached to its tail to determine the vertical center of gravity. A picture was taken from
the side of the model such that the ribbon was vertical in the frame. Any error here was
corrected using the rotate features of Adobe Photoshop. A ruler was also mounted behind
the model to give a size comparison. A second picture was taken of the model resting on
two pointed objects to measure the horizontal center of gravity. These two objects were
uncapped pens due to lack of a better apparatus, but they proved to work well. The model
was balanced on these under the wings such that the tail was parallel to the horizontal
floor. A second photograph was taken, and any camera rotation was corrected again using
Photoshop. Vertical lines were drawn through the supports in each of these pictures to
give a center of gravity in each. Finally these two images were superimposed and
adjusted (scale, rotation, position) so that the dragonfly in each appeared in exactly the
same place. The vertical lines drawn in each picture were now perpendicular, and crossed
at the center of gravity. It is assumed that the center of gravity left to right is exactly at
the center of the model. The resulting superimposed image may be seen in Figure 3.
–9–
Figure 3: Determination of the center of gravity
The forward flight speed was determined by flying the model down a course of a
known length, and letting it crash into a wall at the end. Since it was very difficult to
control the model, a course of twenty feet was chosen at the end of a long hallway. At the
end of the course, the hallway turned a corner presenting a wall straight ahead. During
each flight, seconds were counted off verbally. This verbal timing was checked against a
clock periodically to ensure accuracy, and provided resolution to one quarter of a second.
More accuracy could have been attained using a stopwatch, but none was needed, for the
flight speed varied significantly between trials. For an even flight with few stalls or dips,
the 20 foot flight took just less than three seconds, so a speed was estimated using a time
of 2.9 seconds. This speed was 2.1 meters per second after conversions. The slowest
flight recorded had many stalls and dips, and had a speed of 1.6 meters per second. The
steady state speed was taken to be the maximum flight speed because of the absence of
dips and stalls during that trial.
– 10 –
Figure 4: The flapping mechanism
Finally, to analyze the kinematics of the motion and to measure weights and sizes of
each component, the model was disassembled. The overall mass before disassembly was
23.7 grams. The other component masses, dimensions and specifications are listed in
Appendix A. The battery had specifications printed on it. The kinematics (see Figure 4)
were comprised of two four bar linkages sharing two links. The fixed link was the body,
and a crankshaft was shared by both wings. The crank was a single component made of
bent wire, but it contained two different axes on which each linkage operated. Its
principal axis passed through the gears connected to the main motor, and it was then bent
using an offset such that a second section was parallel to the main axis but offset slightly.
A second offset bend created a third section also parallel to the main axis and offset the
same amount as the second section, but at a different angle than the second section.
Connecting rods were fitted loosely over the second and third sections and connected to
the hinges at the top that held the wings. These hinges rotated about a fixed axis, and one
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of the four wings was inserted into each side of each of the hinges. The connecting rods
connected to a point a short distance away from the axis of the hinge so that when the
crankshaft rotated the hinges also rotated. For a full revolution of the crankshaft, the
hinges moved within about 42 degrees, creating a separation at the fully open position of
85 degrees and at the closed position of 0 degrees.
4. The dimensional scaling analysis
In order to most accurately scale the WowWee model down to a smaller size, the
principles of dynamic similarity were used to find the characteristics of the smaller
design. If two objects are dynamically similar, some key dimensionless parameters will
be the same, and the fluid flow around them will be the same. In order to begin this
process, the characteristics of the WowWee model were found experimentally as
described in the previous section. Then the dimensionless quantities such as the Reynolds
number and the Strouhal number were calculated from these characteristics. Since two
models with equal dimensionless parameters will perform exactly equally, these
parameters were applied to the scaled down version. A scaling factor was chosen, and
from this and the original characteristics, new characteristics such as length, speed, and
weight were calculated.
Arguably the most important and commonly used dimensionless parameter for fluid
flows is the Reynolds number. The Reynolds number is a function of the dynamic
viscosity (µ), density (ρ), characteristic velocity (V), and characteristic length (L). In this
case the characteristic velocity was taken as the average forward velocity of the body of
the dragonfly, while the characteristic length was the chord length (from the leading to
– 12 –
the trailing edge of the wing). The Reynolds number is calculated in Equation 1:
Re =
ρVL
= 11200
µ
(1)
In the case of a dragonfly, frequency is a very important factor because of the
unsteady aerodynamics that give it lift and thrust. The only well known dimensionless
parameter that incorporates frequency is the Strouhal number. It is calculated in Equation
2 from flapping frequency (f), velocity and characteristic length.
St =
fL
= 0.362
V
(2)
One significant assumption in basic fluid mechanics is the incompressibility of air.
When air is compressible, the aerodynamic flow changes dramatically. For most
purposes, air may be considered to be incompressible if the speed of the aerodynamic
object of interest is less than three tenths the speed of sound (csound). This is specified
using the Mach number.
Ma =
V
csound
= 0.0268 < 0.3
(3)
Compressible flow must be considered when the Mach number exceeds 0.3. From this
Mach number it is clear that there is no compressibility. In a worst case scenario, where
the Mach number changes with the inverse cube of the scaling factor, there is still no
compressibility for a scaling factor of ½. Therefore future analysis disregarded the Mach
number completely.
One important specification of the design of any flying object is its weight. The
forces acting on the dragonfly must sum to zero if the object is in steady flight. For this to
be possible, the lift force must equal the weight. Since the weights may not be the same
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between the two scaled models, the lift coefficient was calculated which compares this
and other quantities using a dimensionless parameter. A is the wing area, and FL is the
force of lift which is equal to the weight.
CL =
1
2
FL
= 5.24
ρV 2 A
(4)
Lastly a scaling factor was introduced between the WowWee model and the new
“scaled down” design. This scaling factor was meant to change the geometry of the wings
in two dimensions where R is the length (radius) of the wing. This was chosen to be 0.5.
Lscaled
R
= scaled = 0.5
LWowWee RWowWee
FS =
(5)
In order to achieve dynamic similarity, it was necessary to derive the quantities that
were to change using the scaling factor and other dimensionless parameters. The
following represents a list of the quantities that changed using this analysis and the
equations which governed how they changed. These equations are simply equations 1
through 6 rewritten in various ways.
LC − scaled = LC −WowWee ⋅ FS
(5a)
Rscaled = RWowWee ⋅ FS
(5b)
V=
Re µ
ρL
(1a)
f =
StV
L
(2a)
FL = C L ⋅ 12 ρV 2 A
(4a)
This analysis produced values for certain parameters which were unattainable.
These and other parameters are listed in Table 1 under the column “Scaled Design.” For
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example, the scaled design weighs as much as the larger model, and the scaled velocity is
doubled. By studying real dragonfly behavior, other researchers have derived a range of
Reynolds numbers over which dragonflies operate. Other researchers have found
Reynolds numbers over which micro-aerial-vehicles (MAVs) typically operate. Typical
dragonfly chord based Reynolds numbers are in the range of about 103 – 103.8 (May,
332), while chord Reynolds numbers for MAVs range from 104 – 105 (Tamai, 2). Since
the Reynolds number for this design is just above 104, decreasing the Reynolds number
should not have a serious impact on the performance, especially since most dragonflies
have Reynolds numbers below this. Decreasing the Reynolds number will allow slower
flapping, slower speed, lower weight, and ultimately less power. It would seem silly to
make a dragonfly heavier simply to achieve dynamic similarity when other dragonflies of
lower Reynolds numbers are quite capable fliers.
The Reynolds number was therefore set as an independent variable with certain
constraints above and below according to the Reynolds numbers observed on real
dragonflies and MAVs. Using a preliminary SolidWorks model of the scaled down
dragonfly with motors, gears, wings, body and tail, a mass was calculated. By varying the
Reynolds number of the scaled design, it was possible to optimize the weight to fit the
SolidWorks model. The weight of the SolidWorks model was about 10 grams-force
which resulted in a Reynolds number of about 7278 or 103.86. This is well within the
acceptable range indicated by physical experiments with dragonflies. With this change,
all of the other design specifications changed besides the wing and chord lengths. The
column of Table 1 titled “Modified Scaled Design” shows the new values, many of which
are much more realistic than those for the “Scaled Design”.
– 15 –
As a preliminary test of these principles, the WowWee model was partially
disassembled, and the wings were cut down using a pair of scissors. Cutting down the
wings decreases the torque on the motor, which should affect an increase in the
frequency. This was observed but not to as great an extent as expected. Disassembling the
dragonfly and removing various non-essential parts reduced the weight.
The resulting cut down model flew but not nearly as well as the original model. It
was more stable, and did not have any tendency to stall. It could not maintain level flight
and dropped 6 feet vertically over a 2.0 second flight while traveling 12 feet horizontally.
Its un-powered flight from an altitude of 9 feet lasted 1.0 seconds, and it covered 8
horizontal feet in that time. Table 3 shows four sets of characteristics. The first column
contains characteristics of the original WowWee model, while the characteristics of the
cut down model appear in the second column.
Model
Original
Cut down
Scaled
WowWee
WowWee
Wing span (m)
0.413
0.214
0.207
0.207
Wing Chord (m)
0.081
0.070
0.040
0.040
Wing area (m)
0.0167
0.00749
0.00417
0.00417
Overall mass (g)
23.7
15.6
23.7
11.0
Freq (Hz)
9.45
11.35
37.80
25.76
flight speed (m/s)
2.1
1.6
4.2
2.9
Chord Re
11 181
7 460
11 181
7621
Lift Coefficient
5.24
13.01
5.24
5.24
Strouhal No
0.362
0.492
0.362
0.362
Power required (W)
0.45
0.18
0.90
0.28
Scaled
Table 1: Characteristics of all models
– 16 –
Modified
Because the flight of the cut down dragonfly did not satisfactorily match the flight
of the original WowWee model, it was hypothesized that the difference was simply
weight. To test this hypothesis, weights were added to the original model just above the
center of gravity. These weights were various coins, and were inserted between the foam
shell of the body and the plastic supporting the wings. The flight of this weighted model
became much more similar to the flight of the cut down model, giving good indication
that the only difference between the two was weight, and that the coefficient of lift of the
cut down model would need to be higher to produce the same flight. This may be seen
from Table 3. Likely the coefficient of lift listed is not accurate, because the model could
not sustain flight, and is actually lower than the listed value, leading to this
unsustainability.
5. Design of and modifications to the half-scale prototype
5.1 Design overview
The physical design of the scaled prototype was completed using the design
parameters found from the scaling analysis for the “Modified Scaled Design” in Table 1,
and it was done concurrently with that analysis. Designing these two things
simultaneously allowed some feedback from SolidWorks to the weight of the design
which allowed educated variation of the Reynolds number to fit this weight. Parts were
found on various websites and were integrated into the design. Later, when the parts
desired were not available, the design changed to accommodate the parts that could be
purchased. Once a prototype was built and tested, certain problems were solved by
changing the design of some components and remanufacturing them. Figure 5 shows the
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preliminary SolidWorks design, while Figures 6a and b show how that design was
modified when the parts in Figure 5 were not available.
After manufacture and preliminary testing, certain problems with the design became
obvious. The most obvious problems with the original prototype were examined and
remedied first with little knowledge of the dynamics. Once these obvious problems were
fixed, a model of the dynamics was made to help determine further necessary
modifications, and those modifications were made.
Figure 5: SolidWorks Model 1
– 18 –
Figure 6a: Overall view of SolidWorks model 2
Figure 6b: Detailed view of motor, gearbox and hinges
5.2 Body and frame
Initially, a balsa wood body was modeled in SolidWorks to hold the motor, gears,
and wires for skids and tail. The tail and skids were made using a single spring grade
stainless steel wire with a diameter of 0.029 inches. This wire was intended to be rigid to
a point and then springy if too large a load was applied that might otherwise break the
– 19 –
dragonfly. It was also purchased with some of the other components in mind. This design
may be seen in Figure 5.
When the gears and motor were not found however, a full gearbox was purchased
instead. The body of this was made of plastic and specially formed to fit the motor and
gears it contained. Once received, it was evident that it had been manufactured using a
rapid prototyping process, and, considering the availability of the school’s rapid
prototyping machine to me, this became even a better option should I need to remake this
part. This gearbox had two mounting holes near the top as can be seen in Figure 6b.
When inserted through these holes, the wire used for the frame could simultaneously be
used to create the pin on which the wings rotated. This greatly simplified the design and
manufacture as the motor and gears were replaced and the wires had a simpler
configuration. This new model can be seen in Figures 6a and b.
5.3 Motors and gearing
Since one major factor of the design is weight, small and light parts were used in
the design. Another significant parameter however in choosing a motor was the amount
of power available from such a motor. After searching for a motor with low enough
weight and high enough power within a desired frequency range, a model was selected
which was ultimately not available for purchase. Another significant consideration in the
design was the flapping frequency. This was directly controlled by the motor and gearing,
and once a motor was purchased, an approximate gear ratio was known. Small gears
however are very hard to find and few companies carried gears of the right sizes. One
company that did have some selection of miniature gears was Stock Drive
Products/Sterling Instrument (SDP/SI), although even their selection was limited.
– 20 –
The best overall option came from a company called The Ornithopter Zone that
specializes in flapping wing MAV’s for hobbyists, and who sold the integrated
motor/gearbox unit described earlier. This resolved the issue of finding an appropriate
motor and gears to fit it and reduce the frequency. The gearbox when received had a
maximum frequency of 5 Hz, but luckily the last gear in the gear train had a ratio of
12:60. So the second to last gear had the rotational speed required and the crankshaft was
inserted into this gear.
To secure the crankshaft in place and attach it securely to the appropriate gear, a
few methods were tried. First, Crazyglue® was used, but within a few seconds of
operation this had broken off. Loctite® was also tried but to little success. For a time, the
joint was held simply by melting slightly the plastic of the gear around the crankshaft so
that any gaps were filled. When the crankshaft was moved however as part of another
modification, this method failed to work again, and epoxy was used in its place. Since the
first bend in the crank is touching the gear, the geometry of this bend was used secure it
in place against the face of the gear with the epoxy.
The motor in the gearbox was a seven millimeter diameter brushed DC motor, and
the battery was a small coin cell. Both of these components were modeled in SolidWorks
of aluminum, and cut outs were made until the modeled weight matched the actual
weight of each component. The resulting model is shown in Figure 6.
5.4 The linkage
The four bar linkage of the WowWee dragonfly was replicated on a smaller scale in
the scaled design, but the components and manufacturing techniques were changed.
Initially, all of the components were made of stainless steel from two kinds of stock
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material. The same type of stainless steel wire used for the frame and tail of the dragonfly
was used in conjunction with thin tubing with an inner diameter of 0.035 inches and wall
thickness of 0.008 inches. This inner diameter was six thousandths of an inch larger than
the outer diameter of the 0.029 inch diameter wire. In some components a combination of
wire and tubing were used, and any connection between subcomponents was done using
solder. These connections were modeled in SolidWorks using fillets.
Figure 7: The gearing and linkage in final form
Three parts for this four bar linkage needed manufacture while the body served as
the fourth. The first such part was the crank. The crank was designed as a single bent
piece of wire. A long straight section was inserted through the last gear and the gearbox,
but immediately upon leaving contact with that gear the wire was bent using an offset to
create the first of the two cranks. A second offset bend was used to make the second
crank on the shaft. This crank is shown in green near the bottom of Figure 7.
– 22 –
The connecting rods, which attach to the crank, went through several
iterations before arriving at a final design. Initially, the connecting rods
were formed by bending a wire with a right angle, cutting off the excess
length, and soldering a very short section of tubing to the end again at a
right angle (see Figure 8). The tube at the bottom of the rod fit over the
crank while the horizontal wire at the top of the rod fit through a hole in
the wing hinge. After continuing testing, the connecting rods between the
crank and the wings bent slightly at the solder joint, and oftentimes the
Figure 8:
1st generation
connecting rod
connecting rod got stuck on the bends in the crank. Because the fit was so tight between
the small tube at the base of the connecting rod and the wire in the crank around which it
rotated, any bend in the crank caused the tube in the connecting rod to bind. Very often,
even the bends at each end of the crank were enough to cause this binding, and the motor
could not break free. When this binding occurred, the solder joints in the connecting rod
were stressed, and eventually led to repeated failures. To fix both these problems, plastic
connecting rods were made using the school’s rapid prototype machine. With holes
drilled in the bottom and top of these rods, they slid loosely onto the crank (with no
alterations to the crank) and provided good performance without solder joints. In the top,
these rods were attached to the wing using a simple pin joint. Unfortunately, the wing
hinge and the connecting rod tended to separate during testing. A second iteration of the
connecting rods was prototyped which incorporated a small Y at the top of the rod to be
pinned to both sides of the wing hinge as is shown in Figure 8. This held the wing much
steadier compared to the connecting rod, and so far there have been no failures of this
system.
– 23 –
The wing hinge, also seen in Figure 8, is a longer section of the same tubing as was
used in the connecting rod. It was bent at the middle to allow the wings to have a slight
upward angle when closed. Two small sections of the tubing were then soldered on the
bottom of and at a right angle to the main section. One was located in the middle to make
an axis for the wing, while the other was located a short distance away to make a hole
through which the top section of the connecting rod could pass. This design was not
modified throughout the design process and still works well.
One significant modification to the linkage was the shorting of both the crank and
the pin on which the hinges rotated. An analytical model (described later) was created to
analyze the linkage and showed that as these wires were shortened, the wing motion
improved dramatically. During this process, a new crank was required which was made
out of the same wire as the rest of the wire components instead of the provided shaft wire
that came with the gearbox.
5.5 The wings
Initially, wings were designed with the same shape as those of the WowWee
dragonfly but with each dimension half of the original. The first generation wings were
made of the material from a grocery bag which was the same thickness as the material
used in the WowWee model. After some very preliminary testing showed that these
wings were not adequate, the wing material was changed to polyester film. This material
was chosen after examining the wings on a remote control airplane and comparing them
to the wings of the WowWee model. The wings of the plane were known to be made of
polyester film, and they appeared to be the same material as the wings of the WowWee
– 24 –
model. This material had the same thickness as the grocery bags, but was more smooth,
flexible and less likely to crease making it more suitable to the application.
The wing rods at the leading edge and along the diagonal of each wing were placed
according to the placement in the WowWee model. These can be seen in Figures 5 and 6.
Initially these rods were made from the same wire as the linkages, tail and frame until
this material proved too massive. To decrease the mass of these rods, carbon fiber
composite wire was used instead. Carbon fiber composite just sinks in water indicating
that it has a density about one seventh that of steel (Beer, 747). Substituting carbon fiber
rods into the wings instead of steel rods (of the same geometry) created wings that were
about one third the original mass.
5.6 The battery
Since this MAV will fly using electric power, a battery was chosen to directly
power the motor. Initially, a 3.0 Volt alkaline coin cell was chosen with weight being a
major deciding factor along with voltage and energy storage capacity. Although this
voltage was enough to produce a flapping frequency of 24 Hz, a simple first test with the
battery however showed that the current capacity of the battery was much too low for the
motor’s needs. To remedy this problem, the battery from the WowWee model was
studied and determined to be a 3.7 Volt lithium polymer battery. Lithium polymer
batteries are rechargeable and light weight, and they have a very low internal resistance
(approximately 1 ohm). The higher voltage of these batteries also allows for increased
frequency if necessary. The energy stored by these batteries, though not as important, is
within an acceptable range allowing for extended flight. A battery with lower capacity
– 25 –
and weight was purchased from the same company as made the battery for the WowWee
model, and has performed well since.
5.7 Summary of design and modifications
The overall design of the half scale prototype is very similar to that of the WowWee
model, but each of the parts has been scaled down. Some modifications were made the
design to allow for easier manufacture with the tools available, and some further
modifications were made once certain components did not work as well as planned. This
process took place in a step by step fashion where one modification was followed by
testing and then another modification. Although slow, this allowed for evaluation of each
modification individually.
6. Manufacture of the scaled prototype
Although the design of the scaled prototype is
fairly simple, actually manufacturing the components
proved difficult. First the hinges (shown in Figure 6b in
green or in Figure 7) were created. The tubes were bent
Figure 9: Hinge and fixture
the required 10 degrees using two pairs of pliers, then
the smaller tubes serving as hinges were soldered on. However, stainless steel does not
solder easily, so liquid flux was used to clean and prepare the surfaces. It was most
effective to solder the pieces together while they were submerged in a droplet of flux
which vaporized on contact with the soldering iron tip. The distance between the small
tubes on the hinge component was critical so a fixture was created out of a small piece of
aluminum sheet metal. See Figure 9. This fixture had two small holes drilled at the
– 26 –
required distance of these tubes such that the tubes could be inserted, the main tube laid
across them, and the two solder joints made effectively. This worked well. The aluminum
material of the fixture proved important because the solder did not stick to the aluminum
even with flux, and the hinge component could be easily removed when completed.
To create the first generation connecting rod, a
piece of wire was bent at a right angle and cut to length.
A small piece of the tubing was also cut and the two were
soldered together. Because the length of this component
was again critical, two additional holes were created in
Figure 10: Connecting rod,
tool, and fixture
the aluminum fixture (see Figure 10) with diameters of 0.034 inches, and separated by the
required length of the connecting rod. The end of the connecting rod not to be soldered
was inserted through one hole while a small scrap piece of the same wire was inserted
into the other hole and the small tube fit onto that. This located both the connecting rod
and the tube, and the two could be soldered together with precise positioning.
The second and third generation connecting rods were made using the school’s
rapid prototype machine. Creation of these components was fully automatic, and the
rapid prototype machine printed accurately made parts. Typically however the holes on
these connecting rods were too small, and a small drill was used in a drill press to enlarge
these. The hole to fit over the crank was enlarged much to allow it to fit over and around
the bends of the crank. The hole used at the top to connect to the wing hinge was
enlarged to just larger than the size of the wire pin to be used.
To create the crank, an offset bend as described in Section 5.4 was needed. This
bend required an offset between the two wire centers of 0.080 inches. Needle nose pliers
– 27 –
were too large to create this, and any other existing
devices could not create the sharp corners necessary.
To create this part, a new fixture was created which
acted to stamp this bend into the wire much like an
offset bender for tubing. Since an eighty thousandths
bend was needed in spring steel, this tool was made to
bend ninety thousandths after which the wire would
spring back to the required dimension. This tool was
created by cutting a block of steel (aluminum was
Figure 11: Fixtures used in
manufacture
tried first but was too soft) in half and milling flat the two cut faces. All but 0.090 inches
of the flat face of one of the halves was milled down 0.090 inches, and 0.125 inches of
the other half was milled down the same 0.090 inches so that when put together the
pieces fit like puzzle pieces and looked like a whole. The space left between the two
halves horizontally was intended to allow the wire a place to go to prevent cutting by
shear. This fixture is shown in Figure 11. Holes were drilled in each half in
corresponding locations, such that when a pin was press fit into one half it would slide in
the other and the two halves could be pressed together and separated without any
transverse movement. When a wire was placed between the halves, and the halves were
squeezed together using a vice, the wire was bent with an offset very nearly the required
0.080 inches. To create the crank, this process was repeated twice with the first bend
placed just outside the tool so that the second offset bend would be close to the first.
Because the first generation connecting rod could not slide on the crankshaft past
the bends created, one bend was created, one of the connecting rods was slid onto the
– 28 –
shaft, and finally the other bend was created around the connecting rod. The tube in the
connecting rod in this process was placed between the halves of the offset bending tool,
but when no other forces were exerted on it the connecting rod (particularly its solder
joints) stayed intact throughout the process. If there was any breakage of the solder joint
during this operation, a soldering iron was used to re-melt the solder and make the
connection secure again using the fixture for this process. To insert the crankshaft into
the fixture for this re-solder operation, a slot was cut which intersected the hole which the
scrap wire from the original manufacture had been placed through. Because the
crankshaft was bent, it did not simply slide through the original hole and this slot was
necessary for insertion and removal.
The tail of the scaled prototype dragonfly was created by bending a two foot long
wire roughly in half with a large radius of curvature. The two ends of the wire were then
inserted into the holes in the gearbox (as shown in Figure 6b) and the wires were soldered
together on the tail side of the gearbox. This ensured that the tail did not twist
excessively. Finally the wires were bent as is shown in Figures 6a and b using pliers and
fingers. These last bends were not precise except the one used to position the hinges.
The gearbox purchased also required modification. The frequency of the output
shaft was about five times too low, To modify it, the last two gears were removed and the
second to last hole was enlarged to accept the output shaft. The included output shaft was
bent to make the crank and inserted into the second to last gear and the corresponding
hole. The gear was secured on the crankshaft using superglue. When the superglue broke
during testing, the plastic gear was melted using a soldering iron and formed a good bond
to the crankshaft. When further failures occurred after modification, epoxy was used.
– 29 –
The wings and tail surfaces were created using plastic from a grocery bag of
thickness 0.0005 inches. This was the same thickness as the wings from the original
WowWee model. These plastic sheets were secured to their respective wires using strips
of Scotch® brand tape that were cut to be 3/16 of an inch wide.
The final result of the manufacture before modification is shown in Figure 12.
Figure 12: The 1st generation scaled prototype
7. Testing and results of the scaled prototype
7.1 Testing overview
Testing of the prototype was done as a step by step process alongside modification.
Each modification was the result of a test, and after each modification, a test was done to
evaluate the change. The following sections describe each test and what modification
each evaluated.
7.2 Preliminary and battery testing
Preliminary testing was done first by hand, then by using the battery, and finally by
using a power supply. With hand testing, the prototype worked great. The wings
– 30 –
separated and came together nicely, and there were no problems. This showed that the
prototype was made with sufficient precision and was ready to be tested electrically.
Testing using the coin cell battery was done by placing the leads of the motor wires
in contact with the terminals. The motor turned, and the prototype flapped successfully.
However the flapping frequency was about 4 or 5 Hz, much lower than what it should
have been, and over the course of thirty seconds the frequency slowed further. This
showed that the battery was likely not powerful enough to run the motor. The motor
could take a maximum of 3.7 V DC input, and the batteries used were tested to be 3.2 V
but rated at 3.0 V. After running the motor using the battery for about 30 seconds, the
battery was again tested and the voltage was found to have dropped to about 2.7V.
When the lithium polymer battery was connected, the prototype flapped very
quickly. When not connected, the battery had a voltage of 3.8 V, and when connected to
the motor that voltage dropped to 3.6 V. This showed the current capabilities of this
battery and that low frequency would not be a problem caused by the battery. This battery
can power the prototype at full speed for about a minute.
7.3 The frequency response to voltage
By using a power supply, and connecting everything using a breadboard, the
voltage across the motor could be varied and monitored precisely. Even a very low
voltage produced a flapping motion that was as fast as that produced with the battery.
Further tests were done using a strobe tachometer to measure frequency. Flapping
frequency, current, and power were recorded for several voltages.
First, this data was collected for the gearbox alone without any other mechanisms or
wings attached to it. From the cut down dragonfly, it is reasonable to assume that adding
– 31 –
wings will decrease the frequency somewhat but not dramatically enough to cause the
prototype not to fly. This hypothesis was tested by adding the grocery bag and stainless
steel wings. Although an extensive analysis was not yet carried out, the flapping
frequency at 3.0 V was 20.1 Hz, slightly below the frequency without wings. When at
this setting, I placed my hand behind the dragonfly to feel the wind produced. Although
there was some wind produced it did not feel like enough to let the prototype fly.
These wings behaved fine at low frequencies, but as the frequency increased the
power increased much more dramatically and the dragonfly seemed as though it would
break apart. To remedy this, the carbon fiber wing rods were substituted in place of the
steel. Further testing was done to analyze the effect of this change, and the results from
these frequency vs. voltage tests in the various configurations – with and without wings,
carbon fiber or steel rods or no wings at all – showed that the impact of this change to
carbon fiber was significant (see Figure 13). Although there was still a slight decrease in
the frequency from no wings to carbon fiber wing rods, that decrease was much less
pronounced than the decrease from no wings to steel wing rods with polyester wings. The
steel wing rods with polyester wings had a maximum measured frequency of just over 7
Hz while the carbon fiber wing’s frequency increased with increasing voltage for all
voltage tested (maximum of ~25Hz tested). No data was taken for the steel wing rods
with grocery bag airfoils.
– 32 –
35.00
No Wings
Hinges
Frequency (Hz)
30.00
Steel Rods
CF Rods
Poly. (CF Rods)
25.00
20.00
15.00
10.00
5.00
2
y = 1.443x + 3.155x + 1.3489
0.00
0.0
1.0
2.0
Voltage (V)
3.0
4.0
Figure 13: The affect of wing mass on frequency
7.4 Flapping symmetry
If the first generation prototype was held by hand during testing with the wings
were attached, significant horizontal vibration could be felt. Since this only happened
when the wing airfoils were attached, the forces causing the vibration were likely due to
the unsteady aerodynamics at work which were not completely balanced on each wing.
When the motion was slowed down and analyzed using either the camera technique
described in Section 3 or when the gears were turned by hand, it became evident that
there was some side to side rocking; the wings closed, came together, rotated together a
few degrees passing through horizontal, and then opened again a few degrees off
horizontal. This motion was repeated when the wings were fully open but was not as
obvious. This motion can be seen in a short series of pictures in Figure 14 (especially the
5th and 6th images) or in a longer series in Appendix E which describes the characteristics
designed and measured for the scaled prototype. Any motion where the wings are not
– 33 –
flapping symmetrically about the vertical “right” plane will cause significant vibrations
beyond those expected for normal flapping.
Figure 14: Asymmetrical flapping of 1st generation scaled prototype
After the crank geometry was adjusted slightly, the wings became much more
symmetrical. Although some vibration was still evident, the frequency could be easily
increased much past the prior limit where fear of destroying the prototype limited it.
7.5 Airfoil testing
Another problem with the motion of the first generation prototype was the shape of
the deformed airfoil when flapping. For stable flight, all the airfoils should deform in the
same way, and this deformation should mimic the deformation of the airfoils in the
WowWee model. Neither of these criteria was met. The wings all deformed slightly
differently, and some deformed more on the up stroke and others more on the down
stroke. Also, although this deformation was similar in overall shape to that of the flapping
WowWee model, each wing deformed a different amount than the WowWee model.
This, even more than the asymmetry of the flapping, is likely responsible for the lack of
propulsive force felt.
When the wing material was changed to polyester, the wings deformed much more
easily and consistently, and to a better degree they mimicked the deformations in the
– 34 –
WowWee wings. Although this increased deformation is expected to have created more
thrust, a quantitative test was unfortunately not completed to evaluate this change. Some
problems arose around slack in the airfoil near the body and the trailing edge of the
wings. This slack likely caused some lack of lift due to unchecked deformation of that
part of the wing, but this problem has not yet been resolved.
7.6 The flapping angle response to frequency
It was observed in various tests that as the frequency of the wings increased, the
amplitude with which they flapped decreased dramatically. At high frequencies, the
wings just twitched and little thrust was produced. This can be seen in Figure 15. This
problem was most pronounced when using the first generation rapid prototyped
connecting rods, because in this case the pin connecting the rod to the wing hinge was
loose and was getting pushed around with very little force. This was corrected with the Y
shaped connecting rods. Data linking the flapping amplitude to frequency was taken at
several frequencies, and a plot of this data appears in dark blue in Figure 16
Flapping
Angle
6.4 Hz
19.4 Hz
(a)
(b)
Figure 15: The affect of frequency on flapping angle
After a new and shorter crank and hinge pin were made, the wings were much more
resistant to the decreasing flapping amplitude that they experienced before at high
frequency. After epoxying the crank to the gear that turned it, so that the crank would not
– 35 –
slip in the gear, a second set of data was taken. This new data from the modified
prototype appears alongside the original data in Figure 16. It can be seen from this data
that the flapping angle becomes independent of the frequency after accounting for
measurement error. It may also be noted that the average flapping angle increased to
about 42 degrees, although the reason for that has yet to be determined.
50
Average Flapping Angle (deg)
45
40
35
30
25
20
15
10
Original Prototype
5
Modified prototype
0
0.0
5.0
10.0
15.0
20.0
Frequency (Hz)
25.0
30.0
35.0
Figure 16: Effect of modifications on average flapping angle
– 36 –
7.7 Final result
Figure 17: Final Prototype
Figure 17 shows the final prototype after all testing and modification was complete.
Although the prototype did not fly as successfully as was desired, it had the same
characteristics as the original WowWee model and was very nearly half the original size.
The scaling analysis showed that the prototype has those characteristics that should allow
it to fly. The weight of the prototype with the battery, wiring and motor and all other
components is 11.0 grams, very slightly below the original target weight. The flapping
angle of roughly 42 degrees matches the flapping angle of the original WowWee design,
and the wings have a similar shape. One difference between the WowWee model and the
scaled prototype is the stiffness of the wings. The WowWee model has relatively stiff
wings that fit well onto the body and are not slack at any point. The scaled prototype’s
wings have a less tight fit, and there are places where the wings are slack and likely
provide little lift. Other possible differences between the models include the locations of
the center of lift, center of mass and center of drag. These and possible other differences
combine to influence the aerodynamics and flight characteristics of the prototype.
– 37 –
In its initial flight test, the prototype showed signs of both lift and thrust, but did not
fly. After analyzing how much resistance to put in series with the battery to reduce the
voltage across the motor and thus the speed, all components were attached to the gearbox
of the dragonfly. A small switch was created when a connector was attached to the free
lead of a resistor whose other end was attached to the battery. When turned on and gently
tossed by hand, the dragonfly first dropped before leveling out at a (very approximate)
downward 45 degree angle. Thrust was demonstrated when the dragonfly moved
forward, and lift was demonstrated when it did not tumble but instead stayed upright.
When fixed in a position and powered, it is clear to any hand placed behind the wings
that a significant amount of thrust was created.
The other significant achievement was the creation of the analytical model. The
model predicted with some accuracy how changing various parameters or dimensions
would effect changes in the flight of the dragonfly. As compared with experimental data,
the model predicted roughly the same changes in characteristics with modifications in the
various cases which it could distinguish. This model is described in Section 8.
8. Creation of an Analytical Model
8.1 Model Overview
In Figure 16 in section 7.6, we see a blue “Original Prototype” curve that looks
distinctly like a low pass filter. From intuition we know that as the frequency or flapping
angle increases the power also increases, and that physical systems will always choose
the option which uses the least power. Therefore we see that at low frequencies the power
output is small but at higher frequencies when the power output does not want to
– 38 –
increase, something must give, and that which gives is the flapping angle. That short
analysis is useless however at telling us how to fix the problem. In order to be able to
better analyze how certain factors influence the flapping amplitude at high frequency, a
computerized model using the Matlab software package was made, tested and used to
model the prototype.
The overall idea of the model is that the linkage is modeled from which
aerodynamic and inertial forces are found which contribute to a deflection analysis which
is fed back into the linkages model. Iterating this several times at each position of the
wings and crank allows a precise solution of where the wing is. Comparing the maximum
wing angle to the minimum determines the flapping angle for a given frequency.
Incrementing again over multiple frequencies allows the curve in Figure 16 to be
replicated by the program.
8.2 Positions and time derivatives of the linkage
The first step in the analysis is finding the position of the
linkages in the system. For ease of modeling, only one linkage
was modeled. Figure 18 shows how the links were set up for
analysis. Equations 7 – 10 describe the positions of each point in
the linkage. P represents the position of the point in [x,y] indicated
Figure 18: Link names
by its subscript, while L represents the length of the specified link. θ represents the angle
of the specified link with respect to the horizontal.
P1 = [0,0]
(7)
P2 = P1 + [0,− L1 ]
(8)
P3 = P2 + [cos θ 2 , sin θ 2 ]
(9)
– 39 –

− d ± d 2 − 4⋅c⋅e − d ± d 2 − 4⋅c⋅e 
P4 = a + b ⋅
,

2
⋅
c
2⋅c


2
a=
2
2
2
2
P3 x + P3 y − P1x − P1 y − L3 + L4
(10)
2
(10a)
2 ⋅ P3 x − 2 ⋅ P1x
b=
P1 y − P3 y
(10b)
P3 x − P1x
c = b2 +1
(10c)
d = 2 ⋅ a ⋅ b − 2 ⋅ b ⋅ P3 x − 2 ⋅ P3 y
(10d)
2
2
e = a 2 − 2 ⋅ a ⋅ P3 x + P3 x + P3 y − L3
2
(10e)
After modeling the positions of each of the joints and links, the velocities and
accelerations were calculated for links 3 and 4 based on an input velocity of link 2. The
angular velocity of a link is denoted by θ& while the angular acceleration is denoted by θ&& .
θ&4 =
L2 ⋅ θ&2 ⋅ sin θ 2 − L2 ⋅ θ&2 ⋅ cos θ 2 ⋅ tan θ 3
 tan θ 3 

− L4 ⋅ sin θ 4 1 −
 tan θ 3 
θ&3 =
L2 ⋅ θ&2 ⋅ cos θ 2 − L4 ⋅ θ&4 ⋅ cos θ 4
− L3 ⋅ cos θ 3
θ&&4 =
a − tan θ 3 ⋅ b
 tan θ 3 

− L4 ⋅ sin θ 4 1 −
 tan θ 4 
θ&&3 =
b + L4 ⋅ cosθ 4 ⋅ θ&&4
− L3 ⋅ cosθ 3
(11)
(12)
(13)
(14)
2
2
2
a = L2 ⋅ cos θ 2 ⋅ θ&2 + L2 ⋅ sin θ 2 ⋅ θ&&2 + L3 ⋅ cos θ 3 ⋅ θ&3 + L4 ⋅ cos θ 4 ⋅ θ&4
(13,14a)
2
2
2
b = − L2 ⋅ sin θ 2 ⋅ θ&2 + L2 ⋅ cos θ 2 ⋅ θ&&2 − L3 ⋅ sin θ 3 ⋅ θ&3 − L4 ⋅ sin θ 4 ⋅ θ&4
(13,14b)
– 40 –
8.3 Moments on the wings
After the linkages were analyzed, the moments on each wing needed to be analyzed
about the axis of rotation. The inertial moment is calculated first for a single wing. In
equation 15, ρcf is the density of carbon fiber composite wing rod, while rcf is its radius. L
is the wing length.
M inertial = ρ cf ⋅ π ⋅ rcf ⋅ 13 L3 ⋅ θ&&4
2
(15)
The aerodynamic moment is more complicated to calculate. Since the aerodynamic
moment calculation uses a drag coefficient of the wings traveling vertically through the
air, a drag coefficient was calculated using Cosmos FloWorks with SolidWorks. Many
thin airfoil geometries were tested to determine their drag coefficient, and it was found
that while the curvature of the wing did not significantly impact the drag coefficient, the
angle of attack did significantly impact this coefficient. An equation was found which
approximated this drag coefficient given an angle of attack using a third order
polynomial. In order to find the angle of attack at every point along the length of the
wing, an approximation was assumed where the trailing edge of the wing went through
the same motion as the leading edge but with a phase shift specified by an input to the
program. The program recalled past angles of the wing to determine the angle of the
trailing edge of the wing about its axis, and the tilt of the wing was initially calculated as
an arctangent of the difference of the height of a point on each edge. However in order to
calculate the overall moment created, integration was needed along the length of the
wing. Because that integration contains the arctangent of a third order polynomial, it is
difficult. It was calculated using an internet version of the Mathematica integration tool,
but the output contained a function which was not preprogrammed into Matlab, and I
– 41 –
could not program it. So some approximation was made. It was assumed for simplicity
that the wing formed a helix shape going from zero degrees at the center to the maximum
angle at the end, which was found using the arctangent function. This approximation is
shown graphically in Figure 19.
Figure 19: Tilt modeled with the arctangent (left) or helix (right)
This new function was much easier to integrate, and that integral appears in
Equation 16b as part of the calculations for the aerodynamic moment calculated in
Equation 16. In these equations, L represents the length of the wing, while W represents
the width from front to back of the wing.
θ&
2
M aerodynamic = 12 ⋅ ρ air ⋅ W ⋅ θ&4 ⋅ b ⋅ 4
θ&
(16)
4
1
L

tan −1  ⋅ sin θ 4 − sin θ trailing −edge 
L
W

(16a)
0.7925 3 7 1.5094 2 6 0.0865 5 0.8321 4
a L −
a L +
aL +
L
7
6
5
4
(16b)
a=
b=
8.4 Deflections of the wings
By adding these two moments together from equations 15 and 16 and multiplying
by the four wings, the total moment that will affect a deflection in the crank could be
calculated. Using statics, the moment on the wings could be converted to forces on the
crank and the pin wing connector. The deflections for each were then calculated using the
following equation 17. E is the Young’s modulus for the material of which the beam
– 42 –
(crank or hinge pin) is made, while I is the moment of inertia of each beam cross section.
L is the length of each beam and F is the force applied to each beam.
L3 ⋅ F
∆y =
3⋅ E ⋅ I
(17)
Using these equations, deflections in the two members were calculated. These
deflections went to update the values of P1 and P2 by simple addition. Using iteration
(with convergence typically in three to four iterations), an accurate deflection and wing
position as functions of the crank position were found. With this crank angle incremented
across all positions, a minimum and maximum wing angle could be found. The difference
provides the flapping amplitude.
8.5 Results of the analytical model
Tests were run at many frequencies, and Figure 20 shows the result of the analytical
model superimposed on the experimental data. Although the model does not precisely
predict the curves, it does show some of the same relationships of flapping angle to
frequency that the experimental data shows. When some modifications were made to the
prototype, similar changes were made to the inputs of the computer model. The results
from all four tests (unmodified and modified from the computer model and prototype)
were then superimposed in one plot which is shown in Figure 20.
– 43 –
50
Average Flapping Angle (deg)
40
30
20
Original Prototype
Original Model
Modified Prototype
Modified Model
10
0
0
10
20
30
Frequency (Hz)
40
50
Figure 20: Correlation of analytical model to experimental data
Although the curve representing the behavior of the modified prototype does not
follow exactly the curve representing the modified model, the change in shape between
the model curves is also reflected in the change in shape between the prototype curves.
This indicates that the model did a decent job at approximating the real life prototype.
Although the model saw little real use, its creation provided good understanding of which
issues were most important for improving the prototype.
9. Conclusions
The major goals of the first term were met, and on time. The only goal that was not
met was the continued testing of the scaled prototype which would result in modifications
and improvements to allow the prototype to fly. The goals of the second term were not
met with as much success. The design was modified to improve the mechanical, electrical
and aerodynamic properties of the prototype, but the prototype never successfully flew.
The model created as part of the analysis of the mechanics was a partial success due to a
– 44 –
limited understanding of the relevant factors and possibly insufficient testing. The overall
goals of the project, including making a flying prototype to test the aerodynamic scaling
theory used and designing a new flapping mechanism with the opportunity for further
scaling, were again not achieved, though the current prototype is close to being ready for
testing against aerodynamic theory. As a next step in the future, further modifications
will be made to the prototype to try to approach flight with as much success as possible.
If the prototype is successfully able to fly, this will also verify that the scaling theories
applied in this design are actually applicable.
One major downside to the mechanisms used on this dragonfly is their scalability. It
was very difficult to find parts as small as needed even for this design, and this design
only used a scale of one half. If a quarter scale design is desired, a different design of
flapping mechanism will need to be created. It is likely easiest to create this flapping
mechanism on a larger scale using parts that can be scaled down. The ultimate goal in
this specific area of research is to create a robot that mimics a dragonfly in size,
maneuverability and control, and has the option to mount a camera for viewing images
remotely. Although this goal seems far away, continued research in this area should allow
these goals to be met in the future. The WowWee model after all is only four times larger
in each dimension than a real dragonfly.
10. Future work
10.1 Overview of future work
Future work on the current prototype will be somewhat manageable, while future
work on the project as a whole could be quite extensive while trying to create a robotic
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dragonfly of the same dimensions as live ones. For improving the prototype, two
elements will be researched. First, the prototype will need further testing and
improvement. Second, the analytical model will need further analysis to make sure it is
all correct, and to add other features not currently present.
10.2 Future work on the current prototype
Partly due to a lack of time, the aerodynamics of the prototype were not nearly
tested to the point they should have been, and it is unknown how the aerodynamic forces
act. In order to learn such information, the wind tunnel available on campus can be used
to determine both the lift and the drag forces on the prototype at different airspeeds and
flapping frequencies. These should be compared to similar measurements or calculations
for both the WowWee model, and for the initial target parameters of the scaled prototype.
For example, it may be found that the lift forces on the prototype are not nearly as high as
they should be, and that further modification to the wings is necessary. In another case, it
may be found that the lift and thrust forces are sufficient, in which case another
characteristic of the prototype would need modification.
Other such characteristics are the locations of the center of mass, the center of lift,
and the center of drag. The center of mass is easily found by hanging the prototype from
a string, taking a picture, and extending the line of the string down through the prototype
as described for the WowWee model on page 8. The center of lift is more complicated,
and can only easily be found by studying the airfoils more closely. However, some trial
and error technique can be used by shifting the position of the 0.8 gram battery around
and monitoring the performance.
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Another parameter that is easily altered is the resistance in series with the battery
and the motor. While a potentiometer may be used to select a proper operating frequency
when connected to a breadboard, only a fixed resistor is small or light enough to use on
the flying prototype. Two such resistors may be seen in Figure 17. Altering the resistance
of these resistors can vary the voltage across the motor which alters the motor frequency
and thus the flapping frequency anywhere from the maximum possible with the battery of
about 30 Hz to zero. The resistors are used to protect the gears and motor from excessive
wear.
The shape of the airfoils should also be analyzed or altered to ensure that the airfoils
produce the lift required. Currently the slack in the thin airfoils allows them to deform
with little force which leads to possible low lift production for the wing area. As can be
seen from Figure 17, particularly in the upper right wing in the picture, the wing is loose,
and tightening it could provide significant benefits. Finally, the tail is still currently made
of a piece of the original grocery bag material which, although it seems to work
sufficiently well, could still possibly stand changing. It is possible as well that the size of
the tail needs to be changed. The scaling analysis was not completed originally for the
tail, except as a general scaling of the entire model by the specified amount. In updating
the airfoils, the attachment mechanism of the wings to the body could be modified from
the current method involving Scotch® tape, although the tape does work reasonably.
10.3 Future work on the analytical model
In order to continue to help the design of the prototype, work will need to be done
on the analytical model both to check the validity of what has been modeled as well as to
add new features. Any number of things may have gone wrong during the creation of the
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model, and testing should be conducted systematically on each result to verify the results.
Further improvements to the model include the addition of code relating to thrust
calculations for various situations so that results from wind tunnel testing may be
predicted. These improvements will make it easier to understand how various changes
will affect the prototype before the change is made.
10.4 Future work and the design of a life size flapping mechanism
Future work on the rest of the overall project could be very extensive. As a first
step, further research will need to be done to design a flapping mechanism which can be
scaled down at least to if not past the scale at which live dragonflies operate. Some work
has been done by researchers at other universities, especially Robert Wood at Harvard
University, in creating such flapping mechanisms. His research is a very good place to
start to look for answers, and some of his articles are listed here in the references for this
current research. Typically the methods used to create such small flapping mechanisms
use four bar linkages to magnify the motion of an actuation such as piezoelectrics or
electroactive polymers. In these mechanisms, the actuator is connected to the rocker in
the four bar linkage, while the wings are connected to the crank. This allows great
magnification potential of the motion. The four bar linkage is typically made of folded
material where the joints are the folds, and the links are sections of material where the
rigidity has been increased. Piezoelectrics have not been used in the papers I have seen to
successfully create a flying prototype due to especially the weight and to some degree the
size of the housing around the piezoelectric actuator. Electroactive polymers have a better
record, and Robert Wood of Harvard has successfully manufactured a prototype capable
of lifting its own weight (Technology Review, 2008). Of the two types of electroactive
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polymers, the more common is a sandwich of a gel material between two electrodes
which act as a capacitor. When a high voltage is applied to the electrodes, the gel is
squeezed thin and expands outward allowing an extending action. When the voltage is
released, the gel regains its original thickness and contracts lengthwise. A second type of
process is one where the material properties of the material, and how the atoms are
arranged within the molecules, change when a voltage is applied. These processes happen
at much lower voltages than in the first type of actuator, and films have been shown to
bend with significant force, displacement and speed. There is little currently written on
this technology, but it seems from the designs of the micro flapping mechanisms that the
preferred actuator is the second type of electroactive polymer described above.
Other kinds of possible actuation techniques include the use of the first type of
electroactive polymer to be used as the equivalent of a muscle to pull the wings to and
fro, or the use of very thin shape memory alloy wires to do the same. Shape memory
alloy is any one of a number of composite materials which can “remember” a shape and
transform to the shape when heated. Such a transformation typically involves the
contraction of a long wire. Typically this heating is done electrically, while cooling is
done through convection. The nature of the material is such that as the thickness
increases, the frequency at which the actuation can repeat itself decreases. While in a
dragonfly, convection of the air blowing over the wings is increased from normal, but the
wires used would still need to be very thin. Typically, wires with a diameter of 50µm
have a maximum frequency of about 1 Hz (Teh, 2007).
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Though this research could prove very extensive, it could help allow humans to
both understand better the world in which we live and to create microrobots capable of
completing tasks currently impossible.
– 50 –
References
Çengel, et all. Fluid Mechanics: Fundamentals and Applications. New York: McGraw
Hill, 2006.
Beer, Ferdinand P., et all. Mechanics of Materials. 4th ed. New York: McGraw Hill, 2003.
Mueller, T. J., Fixed and Flapping Wing Aerodynamics for Micro Vehicle Applications.
Reston, Virginia: American Institute of Aeronautics and Astronautics, Inc. 2001.
Chris Kjelgaard, Aviation. World's Smallest Camera Plane Shows Off in Public.
<http://www.aviation.com/> July 2008.
Bai, Ping, et all. A new bionic MAV’s flapping motion based on fruit fly hovering at low
Reynolds number. Beijing: China Academy of Aerospace Aerodynamics.
September 2007.
Tamai, Masatoshi, et all. Aerodynamic Performance of a Corrugated Dragonfly Airfoil
Compared with Smooth Airfoils at Low Reynolds Numbers. Beijing: Chinese
Academy of Sciences. January 2007.
Guo, Theresa. Design and Prototype of a Hovering Ornithopter Based on Dragonfly
Flight. Cambridge: MIT. June 2007.
Liu, Teresa. Design of a Flapping Mechanism for Reproducing the Motions at the Base of
a Dragonfly Wing. Cambridge: MIT. June 2007.
May, Micheal L. Dragonfly Flight: Power Requirements at High Speed and Acceleration.
New Brunswick: Rutgers. February 1991.
Mols, Bennie. Flapping micro plane watches where it goes. Delft Outlook. Delft
University of Technology. April, 2005.
Teh, Yee H. et all. Frequency Response Analysis of Shape Memory Alloy Actuators.
Canberra Australia: Australian National University. 2007.
Worley, Darren. New MAV Ornithopter – Flapping Wings Forum. Ornithopter.org.
January 2006.
Leung, Kin Y. Micro-Aerial Vehicle (MAV) Research: The Developtment of a Biplane
Ornithopter. University of New South Wales. 2002.
Technology Review – Young Innovators Under 35. Robert Wood – Harvard. Building
Robotic Flies. 2008
Weis-Fogh, Torkel. Quick Estimates of Flight Fitness in Hovering Animals, Including
Novel Mechanisms for Lift Production. Cambridge, England. January 1973.
Olson, D. H., et all. Wind Tunnel Testing and Design of Fixed and Flapping Wing Micro
Air Vehicles. Tucson: University of Arizona.
Beer, Ferdinand et all. Mechanics of Materials, 4th ed. New York: Mc Graw Hill. 2006.
Hibbeler, R. C. Engineering Mechanics: Statics & Dynamics, 11th ed. Upper Saddle
River, NJ: Pearson Prentice Hall. 2007.
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Appendix A
Characteristics and analysis of the WowWee model
Appendix B
Characteristics and analysis of the cut down WowWee model
Appendix C
Scaling and design of the scaled prototype
Appendix D
The analytical model
Appendix E
Characteristics and analysis of the scaled prototype
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