Journal of Bionic Engineering 9 (2012) 391–401
Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System
Without Guide Implementing Inherent Pitching Stability
Hoang Vu Phan1, Quoc Viet Nguyen1, Quang Tri Truong1, Tien Van Truong2, Hoon Cheol Park1,
Nam Seo Goo1, Doyoung Byun3, Min Jun Kim4
1. Department of Advanced Technology Fusion, Konkuk University, Seoul 143-701, Korea
2. Department of Aerospace Engineering, Konkuk University, Seoul 143-701, Korea
3. Department of Mechanical Engineering, Sungkyunkwan University, Seoul 143-701, Korea
4. Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, USA
Abstract
We briefly summarized how to design and fabricate an insect-mimicking flapping-wing system and demonstrate how to
implement inherent pitching stability for stable vertical takeoff. The effect of relative locations of the Center of Gravity (CG)
and the mean Aerodynamic Center (AC) on vertical flight was theoretically examined through static force balance consideration. We conducted a series of vertical takeoff tests in which the location of the mean AC was determined using an unsteady
Blade Element Theory (BET) previously developed by the authors. Sequential images were captured during the takeoff tests
using a high-speed camera. The results demonstrated that inherent pitching stability for vertical takeoff can be achieved by
controlling the relative position between the CG and the mean AC of the flapping system.
Keywords: beetle, flapping-wing system, insect-mimicking, insect flight, inherent pitching stability, vertical takeoff
Copyright © 2012, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.
doi: 10.1016/S1672-6529(11)60134-0
1 Introduction
In recent decades, there has been considerable
progress in developing Flapping-Wing Micro Air Vehicles (FW-MAVs) for real flight[1–6] and for basic
study[7–10]. A typical FW-MAV flies by flapping its
wings at a flapping angle of about 50 and a flapping
frequency of about 20 Hz[1]. For attitude control, most
FW-MAVs available in the literature use their horizontal
and vertical control surfaces, similar to a conventional
airplane[1–6]. However, the presence of fragile wings and
bulky tails is a drawback as it makes FW-MAVs uneasy
to handle and difficult to carry without a specially designed carrier. If we mimic insect flight to develop an
FW-MAV, we may be able to design a handy MAV
without control surfaces at the tail.
Most insects flap their wings at relatively higher
flapping frequencies with larger flapping angles to
produce aerodynamic forces[11–13]. Some very informative studies on the principles of insect flight include
works of Weis-Fogh[14], Ellington[15,16], Dickinson et
Corresponding author: Hoon Cheol Park
E-mail: hcpark@konkuk.ac.kr
al.[17,18], Sun and Tang[19], Sane[20], Wang et al.[21], Wu
and Sun[22], Ansari et al.[23], and Shyy et al.[24]. These
studies contributed to theoretically and/or experimentally explaining how an insect can produce extraordinary
aerodynamic force in an unsteady environment. However, research on flight stability of an insect is relatively
limited compared with the number of studies available
on their aerodynamics[25,26]. The main reason for this
limitation is the difficulty in direct force measurement of
an insect in free flight[27]. To overcome this situation,
computational fluid dynamics was used to estimate
aerodynamic forces produced by a bumblebee and their
derivatives in Ref. [25], and a Blade Element Theory
(BET) was used to investigate longitudinal stability of
an animal in Ref. [26]. For stable longitudinal flight of
animals, it is suggested that the Center of Gravity (CG)
be located ahead of the Aerodynamic Center (AC) and
below the AC during animal flight[26]. However, the
exact location of an insect may not be available when
using the proposed BET to derive the quasi-static pitch
equilibrium condition, because the researchers did not
392
Journal of Bionic Engineering (2012) Vol.9 No.4
include unsteady effects such as added mass and wing
rotation[28,29]. de Croon et al. suggested that best CG
location varies between hovering and forward flight for
the double-winged ornithopter DelFly[6]. Thus, the relative location of CG and AC is an important parameter for
pitch stability.
For attitude control, without control surfaces at the
tail, insects mostly rely on changes in the stroke plane
and on differential flapping motion[12]. Realization of
FW-MAVs mimicking these features requires many
creative ideas. Designing an inherently stable insect-mimicking FW-MAV involves overcoming several
hurdles. First, we cannot use the typical flapping
mechanism used in current FW-MAVs[1] because the
flapping angle of an insect is typically larger and the
flapping frequency is mostly higher than those of currently available FW-MAVs. Therefore, a new flapping-wing mechanism must be designed to accommodate features of flapping motion of insects; further, the
FW-MAV must be compact in size and light weight.
Second, maintaining symmetry in flapping motions of
paired wings is another important issue for stability of
vertical and longitudinal flight. Even if we develop such
a design, making it fly stably is another concern because
there is no control surface at the tail. Once we design a
flapping-wing mechanism, the flapping angle is typically predetermined and the stroke plane is fixed with
respect to its body axis. In other words, it is hard to find a
source of control force in an insect-mimicking FW-MAV,
and the free flight test of an insect-mimicking flapping-wing system becomes nontrivial. For example, two
thin wire guides were used to demonstrate takeoff of an
insect size flapping-wing system because its stability
was not guaranteed[8]. Thus, inherent stability should be
implemented in an insect-mimicking FW-MAV before
we install the control mechanism. Recent announcement
from AeroVironment indicates that the company has
developed a successful FW-MAV controlled by only
flapping wings[30]. However, no technical aspect or
principle on it can be acquired from literature survey.
In this study, we investigated a simple but useful
way to implement inherent pitching stability in an insect-mimicking flapping-wing system for stable vertical
takeoff. We used a flapping-wing mechanism developed
in earlier works[9,10]. The system flaps at 25 Hz to 40 Hz
and creates a large flapping angle of 145. Using this
flapping-wing system, we suggested how to determine
the mean AC and examined the effect of the mean AC
location on the pitching stability through vertical takeoff
tests. To determine the mean AC location of the flapping-wing system, we used an unsteady BET developed
in Ref. [29]. The flapping-wing system is first tested to
prove that it can produce a thrust force large enough to
overcome its weight. Finally, we demonstrated successful vertical takeoff of the flapping-wing system
without any guide and control.
2 Vertical takeoff of a beetle
Rhinoceros beetle, Allomyrina dichotoma, is one of
the largest flying insects. Therefore, it is easier to observe its body and wing structure with the naked eye and
examine its flapping-wing motion using a high-speed
camera. In an effort to mimic the flight motion of this
particular beetle[9], we observed its flight and found that
it flaps its hind wings at a frequency of 34 Hz to 37 Hz
with angles ranging from 165 to 180 in a
well-maintained stroke plane angle of around 20 (nose
down) to 10 (nose up) with respect to the horizontal line
during forward and hovering flights, respectively. A
beetle can rotate its hind wings around 140 and adjust
its cambered shape during upstrokes and downstrokes to
generate sufficient aerodynamic forces[9].
From the images taken by a high-speed camera
(Photron Fastcam Ultima APX, Japan) at 2000
frames·s1, we can analyze the takeoff mechanism of the
beetle. When preparing for takeoff, the beetle raises both
its front legs and then starts to open its elytra (forewings)
and hind wings at the same time; however, the hind
wings are still in the folded configuration at the beginning. To completely unfold the hind wings, the beetle
consecutively sweeps them forward, starts to flap them,
and fully unfolds them after two flapping strokes. It
takes about 261.5 ms to completely open the hind wings.
Thus, the beetle fully unfolds the outer part of its hind
wings during the initial flapping motion in a relatively
short time. Then, it takes off with an inclined flapping
stroke plane after two to three full flapping strokes, as
shown in Fig. 1. The duration from wing opening to
takeoff is about 327.5 ms, which is denoted by 327.5
ms at the first picture in Fig. 1. The inclined flapping
stroke plane seems to be almost parallel to the horizontal
surface or similar to the flapping stroke plane of about
10 for hovering[9], although the angle could not be exactly quantified. From the high-speed camera video, we
Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System
Without Guide Implementing Inherent Pitching Stability
393
Fig. 1 Takeoff of a beetle from the ground.
confirmed that there is no significant leg motion to push
the body up. Instead, the force produced by the flapping
of the insect’s hind wings is the main thrust for takeoff.
However, stability could not be assessed because direct
force estimation was not available. The beetle’s ability to
vertically take off gave us an inspiration to develop a
flapping-wing system that can demonstrate stable vertical takeoff.
3 Flapping-wing system
3.1 Design and fabrication
Our flapping-wing system aimed to mimic features
of a beetle, namely, Allomyrina dichotoma[9]. Here, we
briefly summarize the design and features of the flapping-wing system used in this study. More details on the
system can be found in Refs. [9,10].
(1) Fabrication of linkage and frame
In this work, we adopted the design used in Ref. [9]
for the flapping-wing system: the same linkage design,
motor weighing of 4.1 g from (Maxon motor, Switzerland), and a reduction gear ratio of 5:1. Fig. 2 shows
parts of the present flapping-wing system including the
supporting frame, links, slider, reduction gear, and motor.
The dimension of each part was chosen such that the
designed flapping angle can be around 150 by the
analysis suggested in Ref. [9]. For all the parts of the
supporting frames and linkages, we used a 0.8-mm-thick
glass/epoxy sheet, which is thinner than that used in Refs.
[9,10], to reduce the weight of the flapping-wing system.
A precision Computer Numerical Control (CNC) machine (M300S CE, resolution = 0.001 mm, Woosung
E&I Co. Ltd, Korea) was used for fabrication.
(2) Artificial wing
The artificial wings were made of carbon prepreg
strip (with a thickness of 0.1 mm and a width of 1 mm)
and thin Kapton film (with a thickness of 7.7 Pm, DuPont, USA) as explained Ref. [9]. Properly tailored three
layers of carbon prepreg strips were placed on the
Kapton film in a pattern similar to the main wing vein
structure of the beetle’s hind wing[9]. The venation
structure stiffens the wing to sustain wing loading during
the flapping motion. For a simple fabrication, we removed some veins but kept the weight and stiffness of
the wings similar to those of the previous wings, as
shown in Fig. 3[9]. The weight of each wing was about
0.065 g. More detailed dimensions and weights of the
two systems are compared in Table 1.
Vertical
columns
Output link
Couplers
Output link
shafts
Motor
Slider
Supporting frame
Front frame
Reduction gear
Fig. 2 Supporting frame, links, slider, gear, and motor for the
flapping-wing system assembly.
Fig. 3 Artificial wings: previous (left) and present (right).
Journal of Bionic Engineering (2012) Vol.9 No.4
394
Table 1 Summary of the dimension and weight of previous and
present systems
Previous system[9]
Dimensions and weight
Present system
Length (mm)
35
35
Height (mm)
22
22
Wing span (mm)
125
125
Wing area (cm2)
18
18
0.15
0.13
Wings (g)
Motor (g)
4.10
4.10
Linkage & Frame (g)
2.10
1.98
Total weight (g)
6.35
6.21
(3) Flapping angle and frequency
The actual flapping angle can be determined by the
angle difference between the end of upstroke and the end
of downstroke based on the images taken by a
high-speed camera. From the same images, we can also
determine the flapping frequency. The flapping frequency was about 39 Hz for a 12 V application, which is
similar to the typical flapping frequency of Allomyrina
dichotoma[9]. The flapping angles of the previous and
present flapping-wing systems were designed to be 145,
as shown in Fig. 4. The measured flapping angle was
found to be slightly larger than the designed flapping
angle because of bending deformation of the wings created by the aerodynamic and inertial forces acting on the
wings during the flapping motion. The flapping angle
range can be modified from that in the prototype flapping system in Ref. [9], such that location of the mean
AC can be shifted, as shown in Fig. 4. We assumed that
the mean AC is located at approximately 25% of the
wing chord from the leading edge at the middle of the
flapping stroke (i.e., the bisector of the flapping angle).
This assumption, that the mean AC is located at the
mid-stroke, is based on the mean AC estimation using a
Modified Unsteady BET (MUBET)[29]. More details are
provided in the following section.
3.2 Estimation for the mean AC
The MUBET was developed and validated with
several examples in Ref. [29]. Here, we used this theory
to locate the mean AC for thrust over a flapping cycle.
As the flapping-wing system produces mostly thrust,
and negligible lift[10], we decided to locate the mean AC
for thrust only. The schematic drawing of flapping motion of a wing is shown in Fig. 5. The stroke plane is the
xy-plane. The position of the feather axis is determined
by flapping angle . A wing section located at distance r
from the wing root (flapping axis) is demarked by the
black strip in Fig. 5a. To present the forces acting on the
wing section, we defined an orthogonal coordinate system at the wing section as shown in Fig. 5a. The
-axis is the feather axis, the -axis is tangential to the
flapping path of the wing section, and the -axis is perpendicular to the stroke plane. In the -plane, rotation
of a wing section is expressed by the rotation angle r as
shown in Fig. 5b. The flapping speed of the feather axis
and rotating speed of the wing section are denoted by \
and Tr , respectively. The aerodynamic force acting on
the wing section was decomposed into the - and
-directions, which were denoted by dF and dF (thrust
in this case), respectively, as shown in Fig. 5b. The
center of Fj (thrust) in the span-wise direction at each
instant of time t = tj of the wing was calculated using the
following equations:
R
F j]
³ dF] dr,
(1)
0
­
° x j]
°°
®
°
° y j]
°̄
R
1
dF] rdr cos\ j ,
F] j 0
³
R
(2)
1
dF] rdr sin\ j ,
F] j 0
³
End of
upstroke
25
Mid-stroke:
mean AC line
145
Mid-stroke:
mean AC line
145
10
(a)
(b)
End of downstroke
Fig. 4 Flapping angle ranges: (a) previous and (b) present system.
Fig. 5 Description of wing section and force components: (a)
definition of a wing section and (b) forces acting on a wing section
and wing rotation.
Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System
Without Guide Implementing Inherent Pitching Stability
where Fj and j are the thrust acting on the wing and the
flapping angle at an instant time tj, respectively. xj and
yj are the x, y coordinates of the center of the instant
thrust acting on the wing, respectively. Finally, the mean
AC for thrust over a flapping cycle can be determined as
­
°x
°°
®
°
°y
°̄
¦F ] y ] ,
¦F ]
¦F ] x ] ,
¦F ]
j
j
j
j
(3)
j
j
where x, y are the coordinates of the mean AC for thrust
over a flapping cycle.
For the estimation of the AC we calculated the instant thrust (Fj) and its actuation location (xj/R, yj/R) by
using Eqs. (1) and (2) for fifty instant times tj/T within a
flapping cycle of the previous flapping-wing system.
Table 2 shows the data for only twenty five instant times
among the fifty data. The instant of time tj /T = 0 corresponds to the beginning of the downstroke, which means
395
that the wing is located in the vertical position. By using
the data in Table 2 and Eq. (3), we can determine the
location of the AC for the previous flapping-wing system, which is located at a flapping angle of +20.7 and at
the 47% wing span in the wing span direction. We have
followed the same procedure to estimate the AC of the
present flapping-wing system, where flapping angle
range is shifted down for 25 compared to the previous
system as shown in Fig. 6b. The estimated AC of the
present design is located at 4.3 with respect to the
x-axis. In this case, the averaged pitching moment
around the CG over a flapping cycle caused by the thrust
was mostly eliminated for the stable vertical takeoff.
Fig. 6 shows that the mean ACs for thrust of our flapping-wing systems are located approximately at the
mid-stroke and at about mid-span.
Table 2 Instant thrust force and its location during a flapping
cycle for the previous flapping-wing system
tj / T
0.00
0.04
xj / R
0.00
0.02
yj / R
0.73
0.36
Fj (g)
0.36
0.21
0.08
0.04
0.27
0.81
0.12
0.08
0.35
1.82
0.16
0.07
0.31
0.65
0.20
0.00
0.00
0.57
0.24
0.65
1.42
0.28
0.28
0.31
0.39
6.04
0.32
0.43
0.33
6.57
0.36
0.67
0.34
1.85
0.40
0.64
0.19
2.29
0.44
0.57
0.04
4.58
0.48
0.66
0.09
3.43
0.52
1.28
0.52
0.89
0.56
0.44
0.36
3.52
0.60
0.27
0.35
9.02
0.64
0.13
0.17
0.31
0.68
0.68
0.49
2.90
0.72
0.55
0.10
12.71
0.76
0.63
0.10
4.38
0.80
4.09
1.54
0.13
0.84
0.49
0.32
6.12
0.86
0.42
0.37
11.36
0.88
0.34
0.44
15.89
0.90
0.26
0.50
15.73
0.92
0.18
0.56
10.10
0.94
0.11
0.66
3.37
0.96
0.00
0.01
0.46
0.98
0.01
0.49
1.23
1.00
0.69
0.24
0.36
y
End of upstroke
Stroke plane
25
145
0.47R
4.3
R
AC
AC
Mid-stroke
(b)
x
7.5
Wing tip path
End of downstroke
Fig. 6 Mean aerodynamic center for thrust over a flapping cycle:
(a) previous and (b) present flapping-wing system.
Journal of Bionic Engineering (2012) Vol.9 No.4
396
For the MUBET, we included the added mass force
and rotational lift to model unsteady aerodynamics.
Even though they might not perfectly model the real
unsteady nature of flow environment, it provided a good
enough aerodynamic force estimation for our flapping-wing systems, which was proven in Ref. [29].
Since the MUBET requires wing kinematics, we need to
acquire the wing kinematics by capturing the flapping
motion using more than two high-speed cameras and
post-process. Based on the images, we approximated the
wing kinematics with a series of functions. In this procedure, some error can be included. Thus, the AC estimation possesses some uncertainty. The CG location
was measured by typical hanging method. We hung the
flapping-wing system with two strings, one after another,
which are attached to the flapping-wing system at two
different locations, and captured the images. The CG
location is the intersecting point of the extended lines of
the two strings. Change of the CG location due to the
flapping wing motion should be negligible.
3.3 Modification of the flapping-wing system
The CG of a flapping-wing system can be measured
or more easily estimated. The CG of each system is
expressed with black circle in Fig. 7. As shown in Fig. 6,
the mean AC location strongly depends on the flapping
angle range for these particular flapping-wing systems.
The flapping angle range of the previous flapping-wing
system, which is shown in Fig. 4a, was chosen to expect
a “clap-fling” effect[14] to produce more aerodynamic
force. Because of this arrangement, the AC for thrust is
located above the CG, and it is misaligned in the vertical
direction as shown in Fig. 7a, which is a side view of the
previous flapping-wing system. In this case, the mean
thrust produces a nose-down or counter-clockwise
pitching moment about the CG, as described in Eq. (4)
¦M
G
I GT ,
(4)
where MG is the sum of pitching moment about the CG,
IG is the mass moment of inertial about the CG, and T is
the angular acceleration. Since the left hand side of the
equation is not zero, the pitching angle can grow with
time.
However, when the flapping angle range is shifted,
as shown in Fig. 4b, the estimated mean AC for thrust is
located close to the x-axis as shown in Fig. 6, and the CG
and mean AC are aligned in the vertical direction, as
described in Fig. 7b. Since thrust does not contribute to
pitching moment in this case, MG = 0 or
I GT 0 .
(5)
Therefore, when the initial pitching angle and the
initial angular velocity are all zeros, the modified flapping-wing system can demonstrate stable vertical takeoff. Thus, we expect that the present one possesses inherent pitching stability for vertical takeoff. Note that we
have not included a component for the side force in the
horizontal direction in this force analysis, because the
two flapping-wing systems produce negligible lift in the
horizontal direction due to the symmetric flapping motion during upstroke and downstroke.
V
T
ic
dynam
d aero e
te
a
m
ti
lin
Es
center
AC
(a)
CG
Counterclockwise
moment W
H
Fig. 7 Center of gravity and aerodynamic center locations of
flapping-wing systems: (a) previous and (b) present system.
4 Flight test of flapping-wing systems
We have conducted flight test for the present flapping-wing system that has the adjusted flapping angle
range as explained in Section 3. Through the adjustment,
the system may possess inherent pitching stability for
vertical takeoff. To confirm this, we flew the flapping-wing system at the flapping frequency of 39 Hz
without any vertical guide.
4.1 Demonstration of guided takeoff
Before the free vertical takeoff test, we set up an
experiment, as shown in Fig. 8, to confirm that the
flapping-wing system can generate sufficient vertical
Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System
Without Guide Implementing Inherent Pitching Stability
Fig. 8 Experimental setup for guided vertical takeoff.
force for a liftoff. In this test, we intentionally added a
small dummy weight to the present flapping-wing system to examine the maximum takeoff weight and to slow
down the takeoff speed. The total weight reached 6.95 g
after attaching the dummy weight and two carbon rods.
Since the dummy weight was fixed at the bottom of the
motor, it could be used to adjust the lateral location of
CG when the flapping angle range is not appropriately
shifted, which might happen during the fabrication
process.
Two small carbon rods were connected to the flapping-wing system: one at the top as a guide and the other
at the bottom as a leg. The length of each rod was 100
mm. One end of the upper rod was inserted into a glass
tube with a diameter of 9 mm, which was used to constrain the vertical flight direction of the flapping-wing
system. The flapping-wing system was powered at 12 V
by an external power supply through very thin copper
electric wires (diameter = 0.15 mm), so that the effect of
397
the electric wire on vertical takeoff can be minimized.
The stroke plane was parallel to the horizontal line when
it was installed to the apparatus, which is similar to the
stroke plane configuration of a real beetle during takeoff
from the ground as shown in Fig. 1. The takeoff motion
was captured by a high-speed camera (Photron Fastcam
Ultima APX, Japan) operated at 2000 frames·s1.
Fig. 9 shows the sequential takeoff motions of the
present flapping-wing system captured by the
high-speed camera. They show that the flapping-wing
system could take off for 80 mm in about 0.80 s, which
means that the average vertical takeoff speed is about 10
cm·s1 at the maximum takeoff weight. These images
prove that the flapping-wing system can produce a thrust
large enough to lift it in the vertical direction. Since the
previous flapping-wing system had the same flapping
mechanism, it also could take off in this test setup. Thus,
the proposed test method can be used to check whether
an insect-mimicking flapping-wing system can produce
a force large enough for takeoff without force measurement by using a load-cell. Now, if the flapping-wing
system fails to vertically take off, it is due to lack of
stability not because of lower thrust production.
4.2 Demonstration of free vertical takeoff
For the free takeoff test without any guide, we attached a carbon rod to the bottom of both the flapping-wing systems. The rod was then inserted into a
glass tube of 50 mm height firmly installed on the
ground surface, as shown in Fig. 10 and Fig. 11. The two
flapping-wing systems were powered at 12 V by an
external power supply, and the motions of flapping-wing
system were captured by a high-speed camera. The
weights of the previous and the present flapping-wing
systems were 6.40 g and 6.32 g, respectively.
Fig. 9 Guided vertical takeoff of the present flapping-wing system.
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Journal of Bionic Engineering (2012) Vol.9 No.4
Fig. 10 Demonstration of takeoff of the previous flapping-wing system.
Fig. 11 Demonstration of takeoff of the present flapping-wing system.
Fig. 10 shows a typical takeoff process of the previous flapping-wing system. After leaving the tube
within about 0.90 s, it rotates about its CG and immediately falls down at about 0.95 s. The duration from
leaving the tube to falling down is about 0.05 s. Thus, the
previous flapping-wing system could not demonstrate
pitching stability because the CG and AC were not vertically aligned, as shown in Fig. 7a. However, the present system displayed a more stable vertical takeoff after
leaving the tube, as shown in Fig. 11. After leaving the
tube at about 0.20 s, the flapping-wing system still
maintained pitching stability. The previous one spent
relatively longer time for leaving the glass tube because
it experienced large lateral motions as a result of pitching moment.
Fig. 12 shows images of three vertical takeoff tests
for the present system, which was vertically set up with
three short legs. The three images for stable takeoff tests
were included in Fig. 12 to show that they are not accidentally achieved. The same flapping-wing system was
used for the test. The three legs were symmetrically
attached at the bottom of the motor, so that they do not
change the CG location. We can see that it could stably
take off as soon as power was supplied to the system. In
Fig. 13, the trajectories of the CG of the system during
takeoff tests are demarked with circles. The arrows in
Fig. 13 indicate the direction of the body axis, which
demonstrates that the flapping-wing systems tended to
maintain stable vertical takeoff despite of disturbance
from electric wires. We conducted many takeoff tests
and all tests demonstrated similar stable takeoff if the
flapping-wing system was not damaged after multiple
takeoffs and crashed when the power was turned off.
Video clips for the stable flight of the flapping-wing
system can be found in Refs. [31,32]. Although the effect of electric wires was not fully removed in these tests,
the test results provided proof that inherent pitching
stability for vertical takeoff can be implemented by
controlling the relative positions of the CG and mean
AC.
As mentioned earlier, the force analysis in Fig. 7 is
rather simple for the present flapping-wing system, because it produces mostly thrust. For an insect-mimicking
flapping-wing system that produces thrust and significant lift, we can still theoretically locate the mean ACs
of the two force components and design a flapping-wing
system such that the pitching moments created by the
thrust and lift can be canceled out, which is how we
implement the inherent pitching stability in a flapping-wing system.
Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System
Without Guide Implementing Inherent Pitching Stability
(a) Test 1
(b) Test 2
(c) Test 3
Fig. 12 Demonstration of takeoff of the present flapping-wing system.
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Journal of Bionic Engineering (2012) Vol.9 No.4
400
(a) Test 1
(b) Test 2
(b) Test 3
Fig. 13 Trajectories of the CG during vertical takeoff tests.
5 Conclusion
References
In this work, we briefly summarized the design of
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relative position of the CG and the mean AC for an insect-mimicking flapping-wing system.
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Acknowledgments
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant no.
2011-0020438), and partially supported by the New &
Renewable Energy R&D program of the Korea Institute
of Energy Technology Evaluation and Planning
(KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 20113020070010).
M.J. Kim appreciates the financial support from National Science Foundation (OISE#1031465).
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