Figure-8 Flapping Micro Air Vehicle

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2011, Orlando, Florida
AIAA 2011-551
Figure-8 Flapping Micro Air Vehicle
J. C. Dawson1 and P. G. Huang2
Department of Mechanical and Material Engineering
Wright State University, Dayton, Ohio, 45435
This paper outlines an approach for creating a more efficiently flying vehicle by using a
figure -8 flapping motion. The process spanning from design concept to prototyping testing
is discussed. A simple mechanical transmission system was developed in order to create a
flap with two degrees of freedom. The figure 8 flapping motion is compared with other
designs that create a similar motion. The primary purpose of this design is to serve as the
first step towards a flapping wing MAV with fully controllably wing path dictation. The
device has been test in the load cell with some degree of success showing the ability to
generate a net force up to 50% its own weight (3.8g).
I. Introduction
Micro Air Vehicle (MAV) is designed for indoor and urban environment flight 1. Many current MAVs are
inspired from nature and achieve flight using flapping wings 1,2,3. A common difficulty encountered in creating
a flying device with flapping wings is the complexity of the transmission system needed to create a high frequency
flapping motion while keeping the total vehicle weight down. Many Flapping Wing Micro Air Vehicles (FWMAVs)
tend to be limited to a purely vertical flapping motion between 1 or 2 sets of wings5,6. Single-wing models have a
tendency to fly at higher speeds than their double-wing counterparts because a forward velocity is needed to gain
enough lift to sustain flight, meaning that they are unable to hover without complex flapping motions2. When two
sets of vertically-flapping wings are stacked on top of each other and driven 180 degrees out of phase, they produce
what is known as a the clap-and-fling18. The clap-and-fling effect occurs when two wings close together, then pull
apart. When the wings close together, they squeeze air out the back of the vehicle, producing thrust. When they pull
apart, the wings pull air in from the front of the vehicle drawing it forward. Two vertically-flapping flexible wings
utilizing the clap-and-fling effect produce a greater forward thrust than single vertical flapping wings18. By using
this technique, hovering and slow controlled flight is accomplished by pitching the aircraft upward.
While vertically-flapping FWMAVs have been able to achieve flight using one and two sets of wings, they
lack many of the desired characteristics found in natural flying insects such as snap acceleration, vertical
landing/takeoff, obstacle avoidance, and hovering. These FWMAVs are limited because they are controlled using
traditional control surfaces such as an elevator and rudder. These control surfaces cause the vehicle to fly much like
an airplane rather than an insect because they require constant airflow for operation. Ideally, a FWMAV should have
the ability to easily hover in place then quickly be accelerated in any direction through user inputs. Traditional
control surfaces limit the desired scope of aircraft control.
While birds use a pair of wings to fly, they are not necessarily efficient air vehicles. This is why most birds
need large muscles to repeat a down stroke-retraction-extension-upward motion. A hummingbird is the exception as
it behaves like insects to make use of a simple upstroke-down stroke motion which is beating at high a frequency to
achieve the needed lift and trust for flight. In practice, a flapping cycle without the retraction motion, found in larger
birds, leads to a easier design. Three types of flapping motions, commonly exhibited by insects, were the focus of
our studies (1) clap-and-fling of butterfly, (2) twin wing motion of dragon fly and (3) the figure 8 motion of the
cicada (or the hummingbird). A cicada is an ideal reference for FWMAV design because of its large weight-towing-size ratio, both high and low flight speeds, and capacity for cargo. When a cicada (or a hummingbird) is
viewed in a hover its wings are not flapping in a vertical motion with a single degree of freedom; but rather they are
producing a swimming motion in much the same way a human would tread water in pool. This swimming motion,
during a hover, traces a spherical figure-8 pattern at the wing tips. This flapping pattern, coupled with the correct
A
1
2
Graduate Research Assistant, AIAA Student Member
Professor and Chair, AIAA Associate Fellowship
1
American Institute of Aeronautics and Astronautics
Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
wing pitch adjustments causes a lift and thrust force to be produced throughout the entire flapping cycle. Minute
changes to the amplitude, frequency, and pitch of each wing allow the cicada to make instantaneous pitch, yaw, roll,
and speed adjustments. A transmission system capable of only producing a vertical flapping motion does not take
full advantage of the complex control and flight characteristics found in a natural flying insect. The figure-8 flapping
pattern is a basic high efficiency flapping motion used for hovering flight. At high frequencies, the wings can
interact with the vortices shed from the previous flapping cycle. The figure-8 motion takes advantage of these
vortices by using them as a „cushion‟ to press against for the next flapping stroke.
In order to mimic this motion, two degrees of flapping freedom are needed: vertical and horizontal. This paper
describes the development and design of a FWMAV with a flapping-motion, wing beat frequency, and flapping
amplitude control inspired by a hummingbird. The final scale of the vehicle is limited by the electrical components
used to create the flapping motion. The current model produces 50% of the vehicle weight in lift while weighing
3.8g.
A comparison between a vertically-flapping MAV and a figure-8 flapping MAV can be seen in Figure 1. The
vertically-flapping MAV creates lift during a down stroke that is canceled out by the up stroke. This means that the
only force that remains after a full flapping cycle is thrust. The figure-8 flapping MAV creates a lift and thrust force
during the entire flapping cycle and should, therefore, be more efficient.
Figure 1.
Comparison between a vertically-flapping wing and a figure-8 flapping wing.
II. Related Work
The need for an FWMAV transmission system
Slider
capable of two degrees-of-freedom (DOF) has been
recognized by many researchers as the next step in the
development of a fully controllable flying vehicle2,7. With two
independently controlled flapping DOF, executed correctly,
any wing beat pattern can be created. Research at Wright State
University has shown that different wing beat patterns are
Rotational
used for different types of flight 5. During takeoff, which can
Drive
be considered a high-power flight, an insect will flap its wings
in a U-shaped pattern in order to produce maximum lift. It has
Rotational
been proposed that this motion uses more energy, but yields
Pivot
better flight performance. Similarly, if the insect is hovering,
Figure 2.
Scotch yoke.
which can be considered a high efficiency flight, an insect will
flap its wings in a figure-8 pattern.
Eventually, onboard control circuitry, with the appropriate sensors, can control the flapping motion of each
wing autonomously and create the different types of flight, given mechanical means for making the necessary
flapping patterns is available. The first step towards accurately mimicking these insect characteristics is to develop a
mechanical transmission system capable of producing complex flapping motions.
A successfully-designed and tested transmission system capable of producing a figure-8 flapping motion
was pioneered by Galinski et al 2. Their design utilized a double-spherical Scotch yoke which allowed for both
2
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horizontal and vertical flapping motions moving about a center spherical pivot. The Scotch yoke is used to convert
the rotational motion of a motor into a linear sliding motion, as seen in Figure 2.
The Scotch yoke in Figure 2 creates a horizontal linear motion and is
a pure sine wave with respect to time given a constant rotational input
frequency. If a second slider is attached to the same rotational drive, rotated 90
degrees, and centered with the first slider and rotational pivot, then a linear
motion in the horizontal and vertical directions is produced. This is called a
double-Scotch yoke. Galinski et al 2 used this concept in a spherical manner to
produce a double-spherical Scotch yoke. This type of Scotch yoke uses
rotational sliders that rotate about a vertical and horizontal pivot, shown in
Figure 3a. The rotational drive mechanism is then used as a mounting point for
each wing as seen in Figure 3b. They designed their flapping mechanism to fit
a FWMAV scale of
grams with a
wingspan capable of
flapping at
Hz. The design is not intended to result in a flying FWMAV,
but is envisioned to serve as a test-bed for aerodynamic and mechanical
aspects of flapping insects in hovering flights.
Figure 4 shows and exploded view of the double-spherical Scotch
yoke design. While the design is insightful on the mechanics necessary for
producing a figure-8 flapping motion, it is exceedingly complicated, heavy,
and unrealistic for independent flight. Insects found in nature have not been
found to weigh more than 50 grams. In fact, the largest flying insect in the
world, the Goliathus beetle, weights 40-50 grams1. The largest insect wing
span is achieved by the
Attacus atlas at –
cm2. This suggests that
the
usefulness
of
flapping
wings
diminishes outside of
this
weight
and
wingspan.
The
Figure 3.
Double Scotch spherical
yoke visualization.
double-spherical
Scotch yoke is a
mechanism designed for a weight and wing scale above
which flapping wings are useful. In addition, the flapping
frequency used is lower than realistic insect flapping
frequencies of
Hz 16,19
Currently there are a few US patents of FWMAVs
with the ability to produce complex flapping motions20. A
common characteristic with each patented design is the
intricacy and sheer number of parts needed to produce the
flapping cycle. Two major constraints when designing
FWMAVs are weight and energy usage. Generally, a design
using many moving parts tends to lead to a higher vehicle
density. Each connecting part also corresponds to contacting
surfaces that, in-turn, reduces the overall efficiency of the
vehicle because of mechanical losses. FWMAVs achieve
flight with a high lift to weight ratio3. This is typically
accomplished in vertically-flapping models by creating a
large wing surface area relative to the overall vehicle weight.
Smaller wings, therefore, need a higher flapping frequency
and a more efficient flapping motion. However, a more
efficient flapping motion cannot be a result of a dramatic
increase in vehicle weight density. A figure-8 flapping
Figure 4.
Exploded view of the double Scotch
motion needs to be created using as few parts as possible in
spherical yoke wing flapping mechanism.
order to keep the vehicle weight to a minimum.
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III. Design of an Insect Scale Figure-8 FWMAV
In order to utilize the flight characteristics of insects, a mechanical transmission system capable of flapping
wings in both the horizontal and vertical directions is needed. The flapping mechanism must be simple, light-weight,
and strong enough to endure the rigors of high-frequency flapping; It must also have the ability to make minute
adjustments to the flapping amplitude of each wing for purposes of control. Our goal is to provide a vehicle having a
total weight of 5 grams or less and a wing span of 10 cm or less, capable of flapping one set of wings in a figure-8
pattern. In order to achieve this goal, we propose the development of a prototype for an aerodynamic and
mechanical understanding of complex flapping motions. This prototype will enable us to define design elements
needed to produce an FWMAV with enough lift and thrust to achieve flight.
A. Simplistic Figure-8 transmission system
The figure-8 shaped maneuver consists of a
combined vertical and horizontal motion driven by a
sinusoidal input, provided by an electric motor. If the
horizontal motion is driven at twice the frequency as
the vertical one, the result is a trace in the shape of an
“8”. A way to couple both directions together is to
simply use a vertical and horizontal drive linked
together, seen in Figure 5. The bottom-left corner is
fixed, and the upper-right corner is considered the
driving point.
Both the vertical and horizontal motions are
driven from one electric motor centered between two
gears. The gear used for the horizontal motion in
Figure 6 (Left) is one half the size of the vertical
component gear. This causes the horizontal frequency
to be double the frequency of the vertical motion. The
drive offset on the left-hand gear is also half the drive
offset on the right-hand gear in order to make the
Figure 5.
Figure-8 driving transmission system concept.
horizontal amplitude one-half the vertical amplitude.
Using the figure-8 driving concept in Figure
5, a conceptual model was constructed, seen in Figure 6. A quality of this drive design is a drive point that is free to
float in and out of the driving plane (in and out of the page as seen in Figure 6). This creates the possibility of
controlled flight and will be explained later.
B. Design process
The figure-8 driving mechanism is intended
to sit between two pivot points and serve as a center
driving point for two wings. As the drive follows the
figure-8 path, so will both wing tips on the opposite
sides of the pivots. With this in mind, it was
necessary to reduce the figure-8 drive prototype and
integrate it into a structure that could serve as a
realistically-sized FWMAV. This was done by using
the approach shown in Figure 7. First, a proof-ofconcept was developed and demonstrated, Figure 5.
Then the conceptual design was further developed,
solid-modeled, prototyped (Figure 7B), assembled,
and then tested. This process was repeateed until a
suitable design for testing was achieved, this can be Figure 6.
seen in Figure 8.
Figure-8 driving transmission system prototype.
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C
D
A
B
Figure 7.
Wright State University design process. A & D.) Parts produced using the AccuteX AU-300iA. B & C.)Parts
produced by the ProJet HD3000 rapid prototyping machine.
Drive
The tools used in this iteration process
Point
include 3D CAD/CAM software, a rapidprototyping machine and a wire Electric Discharge
Machining (EDM). Figure 7A and Figure 7C show
some of the parts that resulted from the design
iteration process. The scale of parts produced by
the wire EDM can be seen in Figure 7C. Figure 7B
and Figure 7D are parts that demonstrate the
resolution and printing scale of the rapidprototyping machine. These design tools made it
possible to develop and prototype the FWMAV
found in the Figure-8 MAV Design section of this
paper.
The force data collected in the testing
section of this paper, Figure 21, displays peak-to- Figure 8. Reduction to practice of the figure-8 transmission system.
peak forces of up to 4 N. Other tests performed on
this same design have shown peak-to-peak forces
up to 8N. This means device is experiencing internal forces up to 214 times larger than the vehicle weight. As a
result, some components cannot be rapid prototyped out of a plastic material and need to be produced out of 7075
aluminum. This type of aluminum was selected because of its high strength and light weight. Metals such as
Titanium, at this scale, had a tendency to elastically deform too much for high frequency flapping while the
aluminum proved to be a stiffer selection.
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IV. Figure-8 FWMAV Innovation
C. Center drive and wing pivots
The figure-8 pattern is traced between two pivot points, as seen in Figure 10. Wings are then attached to the
pivots which are actuated by the motion of the center drive. This causes the wing‟s tip to trace an enlarged spherical
figure-8 pattern. The wing pivots need to take into account the two degrees-of-freedom associated with the center
drive. Therefore, each wing pivot was designed with the ability to pitch up and down and also to rotate about the
base, as seen in Figure 11. The pivoting and rotating motions allow the wings to follow the figure-8 pattern.
The top and bottom of each wing stroke corresponds to the maximum and minimum drive positions (top
and bottom of the „8‟). Because the drive is located between two fixed pivots, this creates a spacing issue. When the
center drive is located at the top or bottom of a drive stroke, the distance between the drive point and pivot is
increased by , Figure 9.
√
√
Center Drive
Center Drive at
a maximum
Fixed pivot
point
Wing
Pivots
Center Drive at
the midpoint
Figure 9.
Displacement caused by using a center
drive.
must be compensated for during the
flapping cycle.
Figure 10.
Visualization of the prototype wing
attachment to the center drive.
There are two standard wing flapping driving techniques
used in the construction of most vertical FWMAVs. The first and
most common technique involves driving each wing individually at
points 1 and 3, with point 2 used as a pivot, Figure 12. The second
technique involves pivoting each wing at points 1 and 3, and driving
at point 2. The problem with the second technique is the change of
the distance between the drive and the pivot points, , shown in
Figure 9. To remedy this difficulty, the small hole in Figure 11 is
used to mount an elastic band that ties both pivot points firmly to
each Wing Pivot such that the elasticity of the rubber band can
account for the change in the displacement, , as shown in Figure
13. This elastic band is capable of following the two dimensional Figure 11.
Visualization of the pivoting system
drive path and stretches to compensate for the spacing error at the used to allow for a horizontal and vertical wing
top and bottom of each flapping cycle.
flapping motion.
2
1
3
Figure 12.
Driving and pivoting points for different
flapping techniques. This is a front view of an FWMAV.
The two black lines represent the leading edges of the
wings. The dashed line represents the neutral position of
driving technique 2.
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D. Elastic Center Drive
Wing
Pivot
Base
Wing
Pivot
Drive
Point
Figure 13.
The storage of kinetic energy at the end of
a flapping stroke into the stretch of the elastic band.
Figure 14.
Elastic band coupler that ties the center drive
to the wing pivots.
An additional positive effect of using an elastic coupler for spacing compensation is the potential for the
storage of kinetic energy during the flapping cycle. As the wings reach the top and bottom of each wing stroke, they
must come to a stop and then be accelerated back in the opposite direction. When an elastic band is used as the
coupler between the two wing pivots, maximum stretch occurs at the maximum and minimum points of each wing
stroke, shown in Figure 13. The elastic band stretches causing the wings to slow, and then releases the stored energy
as the wings are accelerated in the opposite direction. One problem this has caused in preliminary prototypes is wing
startup. When a gear ratio is designed for a
high flapping frequency, the motor cannot
overcome the elastic stretch for the first few
wing cycles. On the other hand, if a high-torque
gearing ratio, capable of overcoming the stretch
is used, the flapping frequency is reduced. This
same effect can be seen in high speed video of
insects during takeoff. The hummingbird flaps
at about 22-78Hz16. It was reported that when
these insects first begin to flap, the wings
require 3-10 cycles before reaching
maximum amplitude4. The introduction of
the elastic band appears to give the
Figure 15.
Prototype FWMAV with the center drive pulled left of
FWMAV qualities similar to actual insects.
center and the corresponding wing flapping amplitude change on
both sides.
E. Flight Control
The drive point in Figure 6 is free to float
to the left and right sides of its original position
because the elastic band is threaded through a hole
in the drive and tied off to each wing pivot. When
the drive point moves left or right from the center,
the angles between each pivot and the center drive
are changed and no longer equal, at the top and
bottom of each wing stroke. For example, Figure
15 shows the flapping amplitude effect on each
wing as the drive point is moved from the center
to the port side of the vehicle. As the drive point is
Prototype FWMAV with the center drive pulled left
moved to the port side, the starboard wing Figure 16.
of center and the corresponding wing flapping amplitude change on
amplitude is decreased while the port wing both sides.
amplitude is increased. This would enable the
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FWMAV to turn toward the starboard direction. Figure 16 shows an image of the actual FWMAV prototype with
the center drive moving slightly to the starboard side of the center, and the resulting wing amplitude effects. This
effect presents an opportunity for controlled flight.
With the absence of a user input, an additional effect of this drive configuration makes the drive inherently
self-centering. The center drive is inherently self-centering because of the elastic wing coupler and the triangular
shape created at the top and bottom of each wing stroke (Figure 9). When the drive is centered the triangular shape
created by the elastic band is symmetrical. In this position, the symmetrical stretch of the elastic band (between the
two fixed pivots) creates equal and opposite forces on the center drive. These forces cause a centering effect because
the legs of the triangle formed between the two pivots, and the drive, are equal and opposite. Because the drive point
is self-centering, an outside force is needed in order to cause an offset to occur to the left or right of center. For
example, the application of a set of permanent magnets and magnetic coils can cause forces perpendicular to the
drive; one coil pushes while the other pulls. This force moves the center drive from the center position. Figure 17
(Right) shows how the coils and magnets could be used together to cause the center-drive to offset in one direction
or another. However, the method used in the construction of the prototype was to sew the elastic band to each wing
pivot by hand. It is likely that this causes the tension between the port and starboard pivot to the center-drive to
behave differently. If a more precise fastening technique was used then the proposed self-centering concept should
provide for a reliable control mechanism.
Figure 17.
Copper coils and permanent magnets used to cause the center drive to shift left and right of center for
controlled flight (Right). Passively-pitching wing prototype (Left).
F. Passivly Pitching Wings
The figure-8 motion created by this design must be used in combination with passively-pitching wings in order
to create more efficient lift and thrust forces. At the top and bottom of each flapping stroke the wing must exhibit
supination and pronation postures, respectively. This pivoting action allows the wing to capture the wake from the
Figure 18.
Flapping pattern and corresponding wing pitch angles shown in the hummingbird family, Trochilidae.
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previous wing stroke12. Like treading water, at the fore or aft portions of a person‟s swimming stroke, a person will
quickly turn their hands back and press against the wake from the previous stroke. The majority of the lift produced
during this type of swimming occurs at the end of each stroke, during the wake recapture period. Similarly,
hummingbirds are swimming in air and must do the same. At the upper portion of the flapping stroke (points 7 and
8, Figure 18), the wing pitch change as the bird transitions between upward and downward strokes. This motion will
intersect with the vortices from the previous flapping stroke and cause an increase in lift. This interaction between
the two different vortices can be seen between points „8‟ and „e‟ in Figure 18. This is where the figure-8 motion is
most effective in creating lift. At the end of each stroke, vortices e and b, interact with the vortices shed from points
1 and 5 in the flapping cycle.
A set of wings was designed and prototyped with this concept in mind. Figure 17 (Left) shows the first design
which allowed the wing to passively pitch between 0 and 80 degrees. This passive motion was successfully recorded
at flapping speeds as high as 61Hz. However, between 25-50% of the upward and downward stroke was used
inefficiently, causing the wing pitch to change. The interaction between the vortices at (1,e) and (5,b) are the most
important for producing efficient lift. This means the wing pitch change at the top and bottom of each stroke cannot
be completely passive. Therefore, an outside force is needed to complete the pitch change before the wing follows
through with each stroke.
In order to deliberately change the wing pitch at the end of each flapping stroke, the following steps were taken.
First, a restoring spring was installed onto the wing to make it normally horizontal; this causes the wing to snap back
to a horizontal position before beginning the down-stroke. This allows the wing to interact with the vortices shed
from the previous up-stroke, yielding wake recapture for one half of a flapping cycle. During an upstroke, the wing
will passively pitch 80 degrees from the horizontal position (Figure 19). This pitching motion still requires 25-50%
of the upstroke before it is complete and will be mechanically actuated at the beginning of the stroke in the future.
Figure 19.
Left: Wing 80 degrees from horizontal. Center: Wing in the horizontal position. Right: Restoring spring for a
normally horizontal wing position.
V. Figure-8 Performance Testing
A full scale prototype FWMAV was mounted on a load
cell test stand within a wind tunnel environment. A single
rod protruded from the load plate, through a hole, and up
into the wind tunnel, Figure 20. A gear ratio of
was used between the motor and dominate flapping
direction (vertical) and the test was performed for a
duration of 9 seconds. Figure 20 shows the basic
configuration of the test stand from a front view (the front
of the vehicle is facing out of the page in the Y-direction
and is positive). The load cell outputs seven columns of
data:
, corresponding to time,
force and moment in x, y and z direction, respectively. Data
was collected at a rate of 1000 data points every second
Figure 20.
Test stand configuration. Y-direction is
out of the page. Horizontal flapping is in the XY plane. which is sufficient to resolve the force data at the testing
Vertical flapping is in the XZ plane. The center drive flapping frequency.
moves in the YZ plane.
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Figure 21.
directions
Raw load cell data in the x, y, and z
Figure 22.
directions
Raw load cell data in the x, y, and z
The raw force data collected from 9 seconds of
testing can be seen in Figure 21. A average net force of
is needed to lift a 3.8g FWMAV. Figure 21
shows the device fluctuated with instantaneous
magnitudes as high as 4N. This is 123 times larger than
the average force needed for flight. The three force
components, x, y, and z, will be analyzed based on the
adaptive filtering method presented by Gao et al5. This
method will be further described below.
As shown in Figure 20, lift is defined in the zdirection. A negative z-direction force corresponds to a
positive lift. Figure 22 is the Power Spectral Density
(PSD) plot of the z-direction force. The data in the PSD
plot indicates the two dominate flapping directions by
the first two peaks. The first peak is the flapping motion
Figure 23.
Z-direction force for 1 second
in the vertical direction. (Refer to Figure 20 for the
with a window size of 41 samples.
flapping directions relative to the load cell) The vertical
flapping frequency is within the range of
. The second peak in Figure 22 is the
secondary horizontal flapping and it has the frequency
range of 31.69 and 37.23 Hz. This verifies the design of
a figure-8 flapping device where the secondary flapping
is double the frequency of the primary.
Figure 23 is filtered data using a window size of 41
samples (corresponding to the frequency range of 15-20
Hz). Window sizing is part of the adaptive filtering
technique developed by Gao et al [5] and is the
definition of how segments (windows) of length 2n+1
data points overlap by n+1 points. Each segment is best
fit with a K-order polynomial. Therefore, a larger
window size provides smoothing to a larger section of
data. This scheme ensures data fitting is smooth around
Figure 24.
Z-direction force for 1 second
nonlinearities.
with a window size of 41 samples.
With a window size of 41 samples, Figure 23
displays
flapping cycles in one second of operation. Each flapping cycle produces primarily a positive lift. The
average of this lift over the entire 9 second is
which is capable of lifting 1.36 grams. Given that the total
vehicle weight is 3.8 grams, 40% of the vehicle mass is already accounted for in the z-direction.
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American Institute of Aeronautics and Astronautics
The vehicle thrust is defined as a positive y-direction
force, as shown in Figure 20. Using the same data
filtering method with a window size of 41 samples, there
are around 34 cycles in one second of operation with an
average forward force, over the entire 9 seconds, of
7.1mN. The 34 cycles is representative of the doubled
horizontal frequency relative to the vertical flapping
direction and can be seen in Figure 24.
Finally, the forces that occur in the x-direction are
referred to as control forces. In order for the vehicle to
travel in a straight line the average force must be zero.
Unfortunately, the current design shows an averaged
force of 9.8mN yield to the starboard direction. This is
most likely caused because of an imbalance between the
pitching spring tension of each wing. Also, the technique
used to fasten the elastic band may have cause the
Figure 25.
Z-direction force for 1 second
with a window size of 41 samples.
center-drive to not self-center properly.
Despite this deficiency, it is evident that the current design is capable of producing lift and thrust for the future
MAV‟s and the combination of the average net forces leads to a magnitude of
. This total force is capable
of lifting
or 50% of the total vehicle weight. Since the vehicle is oriented in a horizontal fashion on the
load cell and 80% of the total lifting capacity of the device is in the vertical direction, the figure-8 flapping motion is
demonstrating the potential for a hovering vehicle. Future models may be able to exploit this hovering characteristic
through center-of-gravity changes for instantaneous control in any direction.
VI. Conclusions
In this paper, a figure-8 FWMAV was discussed as the first step in
determining the feasibility of creating and using this type of flapping motion
as an effective means for flight. This prototype can be seen in Figures 24 and
25. There have been other attempts at creating a flapping mechanism capable
of producing this type of flapping motion, but many of them have proven to
be too complicated for actual flight. This paper discusses a simplified method
for producing a figure-8 flapping motion which consisted of a horizontally
and vertically-driven component using a four-bar linkage. The two degrees-offreedom driven motion was located between the two wing pivots. This
required a new fastening technique, capable of following a figure-8 path, to be
implemented. An elastic band was found to be capable of following the „8‟ Figure 26.
Figure-8 FWMAV (top
motion, while compensating for the change in distance between the moving view).
drive and fixed pivots. The elastic band also provides the potential for stored energy at the maximum and minimum
wing positions throughout the each flapping cycle, presenting the opportunity for a more efficient vehicle.
This model, at a relatively low flapping frequency of
Hz, produces 50% of its total weight in
total force. 80% of this total force is in the vertical direction, which presents the opportunity for a future device
capable of hovering.
Figure 27.
Figure-8 Flapping Wing Micro Air Vehicle.
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1
Golbert lachaume, "The Beetles of the World," vol. 3, 1983.
A. & Whalley, P.E.S. Watson, Dictionary of Butterflies and Moths in colour. London, England: Peerage Books,
1983.
3
Stephen L. Buchmann, Hayward Spangler Marcus J. King, "Activity of Asynchronous Flight Muscle from Two
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