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Passive Dynamics of High Frequency Bat Wing Flapping with an Anisotropic Membrane

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We investigate how unmanned aerial vehicles (UAVs) with flexible wings can be designed to exploit the aeroelasticity of wing deformation that is present in bat wings, with a view to improve the efficiency of flight. We constructed a robotic bat wing with fully passive elastic wing-folding properties. The robotic wing is powered by a gearbox running two synchronised motors, effectively providing one degree of motion: the upstroke and down-stroke of the wing. Through numerical simulations and setup experiments, we observed that by integrating a span-wise elastic network into the bat wing, we were able to achieve passive wing-folding that mimics the 8-shape wing-folding seen in bats' high speed flight. This way, we were able to reduce the complexity and additional actuation associated with wing-folding in a robotic wing.
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Passive Dynamics of High Frequency Bat Wing
Flapping with an Anisotropic Membrane
Michael Zheng, S.M.Hadi Sadati*, Pendar Ghalamchi and Thrishantha Nanayakkara
Center for Robotics Research (CoRe), Department of Informatics
King's College London
London, United Kingdom
Seyedmohammadhadi.sadati@kcl.ac.uk
Abstract—We investigate how unmanned aerial vehicles
(UAVs) with flexible wings can be designed to exploit the
aeroelasticity of wing deformation that is present in bat wings,
with a view to improve the efficiency of flight. We constructed a
robotic bat wing with fully passive elastic wing-folding properties.
The robotic wing is powered by a gearbox running two
synchronised motors, effectively providing one degree of motion:
the upstroke and down-stroke of the wing. Through numerical
simulations and setup experiments, we observed that by
integrating a span-wise elastic network into the bat wing, we were
able to achieve passive wing-folding that mimics the 8-shape wing-
folding seen in bats’ high speed flight. This way, we were able to
reduce the complexity and additional actuation associated with
wing-folding in a robotic wing.
Keywords—Bat; Flapping; Passive; Anisotropic Membrane;
Simulation; Experiment
I. INTRODUCTION
The bat wing has an anisotropic stiffness distribution of
elasticity. It exhibits high stiffness strength along the digits,
compared to high failure strain in the perpendicular direction [1].
This distribution not only prevents high shear forces from
developing between the bones and the wing membrane, but also
helps to store energy by extending the membrane during the
down-stroke. It is interesting to note that exploitation of passive
dynamics arising from special distributions of body stiffness is
seen not only in flapping flight, but also in other forms of
locomotion such as swimming [2]. In [2], it has been
demonstrated that a dead trout can passively start to swim
against a stream of water by generating productive vortexes
purely based on passive resonance of constructive body
movements in hydraulic turbulence behind a cylindrical obstacle
placed in the path of a water stream. These biological examples
suggest that the management of the distribution of body
elasticity plays a vital role in efficient locomotion. This opens
the scientific question as to how the morphology of a deformable
winged UAV should be designed to be able to tune to the flight
environment without off-line planning.
By mimicking the properties of the bat wing, we may be able
to increase the efficiency of airborne vehicles, an exciting
prospect from an engineering perspective. Recently,
advancements in engineering materials, actuators and controls
have allowed us to consider mimicking flight behaviour in the
natural world [3]. There has been analysis on a resonant drive to
reduce the average battery power consumption for DC motor-
driven flapping wing robots [4]. They developed a methodology
using a non-dimensional analysis of a motor driven compliant
system. Using this, they were able to guide the mechanical
design and predict the optimal operating point based on power
efficiency. A prototype of a biologically inspired UAV imitating
the hovering flight of humming birds and dragonflies shows
great potential in developing a high performance flapping micro-
UAV [5]. There have been previous attempts to develop a bat
inspired UAV, such as BATMAV [6], RoboBat [7], and recently
in [8][9]. Here the authors aim to develop flexible wings
actuated by artificial muscles, rather than exploiting the aero-
elastic properties of the bat wing to improve the efficiency of
flight; while similar research on insect size flyers showed
advantages of anisotropic membrane in MAV’s flight
performance and control [10].
When considering the application of flapping flight, it is
advantageous to reduce the weight of the ornithopter as much as
possible. We seek to eliminate the need for active actuation of
wing folding during flight which reduces the energetic cost on
the upstroke of flapping flight [11]. Therefore, we look to the
aeroelasticity of the bat wing membrane as inspiration to
construct a passive wing folding technique that utilises the
elasticity of the wing.
Flyers’ flapping kinematics are different depending on the
wing structure and flight speed [10][12] for which the
aeroelasticity mechanisms should be investigated individually.
Researchers at Brown University have developed a 3D printed
articulated bat wing skeleton with a silicon membrane [13]. This
study in particular highlights the advantages of wing folding, not
only on energy conservation, but also in altering the
aerodynamic qualities of the wing. Our aim is to build upon this
foundation by focusing on the aeroelasticity of the bat wing as
major factor in efficient high speed flight, in particular, how we
can derive inspiration into wing-folding kinematics of high
frequency flapping.Different species of bats have different
properties [1]. Our aim is not to mimic the flight of bats, or one
particular species. Rather we seek a solution with feasible
applications in robotics and biomimetic, as well as the potential
for further study. Here, we investigated the passive role of
anisotropic wing membrane stiffness in reducing the complexity
of the flapping motion.
978-1-4799-4598-6/14/$31.00 © 2014 IEEE
II. MODELLING
A. Kinematics
Fig. 1 shows our 3D bat wing model with three links (arm,
forearm and hand) and four degrees of freedom (DOF). The
shoulder joint is attached to the base frame origin. Base frame
has an inclination equals to the wing geometrical angle of attack
(AoA) () with gravity direction (g). The wing is approximated
by a trapezoid with variable span but parallel root (cr) and tip
chords (ct). The membrane is modelled a series of linear springs
as the elastic elements along local chord-wise sweep directions.
The model parameters are derived using a bat wing design [13]
using Solidworks 2013. The shoulder rotation about the base
frame x-axis (q1) assumes a cosinusoidal form as in (1) and other
three joints are not actuated actively and their axes of rotation
are the local frames z-axis (q2, q3, q4). The centre of mass (COM)
for each link is centred at its midpoint. For simplicity and based
on observation of a real bat flapping, the following constraints
are being used between angles to reduce the under actuated order
of the model to one.
()=−A.cos(ω.+)+
−2×
+20°2×=0

Linear and angular velocity vectors of each element derived
using 3×3 rotation (R(qi)) and 4×4 transformation matrices
(TR(R,rf)) as in (2) where qi is the angle of rotation, rf is the row
offset vector between two consecutive joint, rc is the COM
absolute position vector (w.r.t. base frame) represented in base
frame and
ω
ω
is the absolute angular velocity vector represented
in local frame (attached to each link at its first joint with the link
along its y axis and the first joint rotates along its z axis) for each
link. a, f and h are subscripts for frames attached to, and the
properties of the arm, forearm and hand links respectively. li is
the link length.
()=10 0
0cos (
)−sin (
)
0sin (
)cos (
)
()=cos ()−sin (
)0
sin ()cos (
)0
001
(,)=
0× 1×
=().[̇00
]+[00̇]
=().+[00̇]
=().+[00̇]
=(().(),[000
])
=((),[0 0])
=((),[0
0])
=.[0 /2 0]
=..[0 /2 0]
=...[0 /2 0]

B. Dynamics
We use a matrix representation for the equation of motion
(EOM) in (3) using the TMT method in (4) to derive the dynamic
model because of simplicity and efficient numerical evaluation
as in [14]. q= [q1, q2, q3, q4] is the generalised coordinates vector,
M is the inertial matrix in the Lagrange equation, Tcn is the
constrains Jacobian matrix on the generalised coordinates, λ is
the Lagrange multipliers vector, dEOM is the vector of the other
terms in the Lagrange equation, and dλ is the vector of the other
terms in the constraint equations vector (c(q)) derivatives. c(q)
is differentiated multiple times, so its order of differentiation
equals that of the EOM, namely two (6).

 0+̈
−=

Fig. 1. Schematic model of a bat model: (a) base and wing frames, and apparent air stream due to free air stream and wing flapping motion at
quarter
chord of each element; (b) wing shematic with span-wise elastic elements; (c) aerodynamic forces on each element
. b is the subscripts for the base
frame and w is for the one attached to the wing surface whose origins are at the shoulder joint. Geometrical and real AoA are showed in left
figure
while they are approximated to be equal at the right-down figure.
(a)
(b)
(c)
Here T is the Jacobian matrix of xCOM which is the
combination of links COM position (rc) and pseudo-rotation
(∫.d) 3×1 vectors in terms of the generalised coordinates,
mi is ith link mass, li is the ith link 3×3 inertia matrix, fg is the
vector of conservative forces acting on each element such as
gravity, and Qc and Qnc are the virtual work vectors of other
conservative (here Qk accounts for membrane elasticity (k)
effect) and non-conservative forces (here Qdamp accounts for
joints’ rotational viscous damping (cv) and Qaero for aerodynamic
forces (lift (fL) and drag (fD) effect) in generalized coordinate
space [14].
 [×]=[∫∫∫]
[×]=()/
[×]=−((.̇)/).̇
[×]=diag[,,,[×] , …], (: a,f, h)
=−g.[.sin(),0,.cos(),0,0,0,]×,(:a,f,h)
=+ , =
=−c.̇×
= 
=[−.]++
There is no need to find pseudo-rotation vectors. Here since
we have (=.̇) as the combination of links’ absolute linear
and angular velocity vectors (vb), we simply rearrange the
absolute angular velocity vectors in (2), in the form of (=
.̇) and then place the 3×4 coefficient matrices (Tω) at their
right place in T which is a 18×4 matrix (elements in the 9-18th
rows).
Tcn is derived based on the three constraints in (1).
̈()=̈+
 =()
 =1000
0−210
00−2 1
=−[(+)00
]
C. Membrane Model
Membrane is modelled as a trapezoid by integrating span-
wise elastic network of linear springs with elastic coefficient k
and initial length l0 as in Fig. 1. Membrane is rigid in chord-wise
direction and does not have lateral deflection normal to the wing
surface. Qc=Qk can be found from integrating springs’ virtual
work by having each ones deflection (lk-l0), direction (rk) and
attachment position to the wing tip (rtk) as in (6). Here rtw is hand
tip position vector in wing frame, b is wing span, lk is springs
instantaneous length,
η
is chord length ratio, xlr and xlt are
leading edge root and tip offset position from shoulder joint and
hand tip along x-axis respectively,
Λ
l,
Λ
t and
Λ
x are sweep angle
at leading edge, trailing edge and any arbitrary position along x-
axis, and fk is each spring’s force vector. We use cos(
Λ
x)1 and
tan(
Λ
x)sin(
Λ
x)
Λ
x approximations to reduce the complexity of
integration.
=((),[000
])...[0
0]
=2.,
≈/2
=/
≈−2.( −(+)) /
≈−2.((−)+−(−))/
= .(−)/(−), 
.(−)/((−)−) , <
=−().[10
]
=().[(−)+.(−(−)) /2 0]
[×]=.(−).(()/).

().d

D. Aerodynamic Model
Bat wing is approximated as a trapezoidal thin airfoil whose
aerodynamic properties addressed in common aerodynamic
handbooks widely using blade element theory and quasi-steady
method [15]. Due to flapping motion, local effective AoA (
r)
along wing span alters as the magnitude of normal velocity of
the wing element increases. For simplicity effective and
geometrical AoA (
a) are considered equal and cos(
r)1 and
sin(
r)
r which is feasible for low AoA, high speed flapping
and forward flight, however the change in local air stream along
the wing span is considered. Aerodynamic forces are exerted on
quarter-chord from leading edge at each element. Total normal
(fnw) and tangential (ftw) aerodynamic forces are derived based
on drag (CD) and lift coefficients (CL) of a finite 3-D trapezoidal
wing as in [15] to find the vector of centre of pressure (CoP)
(rpw), where the instantaneous total force can be considered to
be exerted, all in the wing frame. Here AR is the wing aspect
ratio, cy is element chord length,
Λ
0.25 is the local quarter-chord
sweep angle, a0 and a are lift curve slope for 2-D infinite and 3-
D finite thin airfoil, ew is the Oswalt (span) efficiency factor, dfL
and dfD are each element drag and lift force magnitudes,
ρ
is the
air density, and mx and my are momentum of aerodynamic forces
about wing frame x and y axes.
≈α,=2./(
.(1+))
=.(1−2..(1−)/)
tan(.)=tan()−(1−)/(.(1+))
=./(1+1+(./(.cos (.)))),
=
C=.,C
=C+C
/(..e)
d=.C.(.̇
+
)..d/2
d=.C.(.̇
+
)..d/2
 = (d+d)
/
.d
= (d+d)
/
.d
=.(d+d)
.d
= (+.tan()−/4).(d+d)
/
.d
=[/ / 0]

y element of rpw can be find by solving momentum around z
axis due to ftw too. fnw, ftw and rpw elements are derived in (8).
 =(C+C)(1+3)̇
+24
(1+)/192
=(C−C)(1+3)̇
+24
(1+)/192
 =3(1+4)̇
+40(1+)
10(1+3)̇
+240(1+)
/ =((3(1+4)tan()−(6+3+1))̇
+⋯
…40(+1)tan()
−40(++1)
)…
…/(10̇
(1+3)+240
(1+))

The virtual work of aerodynamic forces in term of
generalized coordinates (Qaero) can be derived as in (9). Here faero
is aerodynamic force vector and rp is CoP position vector, both
represented in base frame.
 =().[ 0−
.sign(̇)]
=().
[×]=(()/).

T, d, dEOM, Qk and Qaero are derived analytically using Maple
software and not represented here.
= , dEOM and (3)
are evaluated numerically afterward to be integrated using a
Runge-Kutta 4th order method.
E. Numerical Simulation
The assumptions and model parameters of the simulation are
shown in table 1. Fig.s 2 and 3 show the joints angle and the
absolute drag force vector for two consecutive flapping cycles
(0.8 second). Aerodynamic force (faero) is symmetric with
vertical component mean value near zero due to symmetric up-
stroke and down-stroke motion. It shows the wing passively
folds a little while it is flapping and wing tip follows an 8-shape
path due to the membrane elasticity and links’ inertia and weight
(Fig. 4). A sequenced graph of the wing is shown in Fig. 4 too.
III. DESIGN AND IMPLEMENTATION
A. The Bat Wing Design and Implimention
Our wing skeleton is based upon previous research [13]. During
the design phase, we opted to make a few adjustments to this
specification, particularly with regards to the design of the joints.
As our wing folding mechanism is not mechanically actuated,
we were able to reduce the number of actuating mechanisms to
one gearbox. This gearbox controls the upstroke and down-
stroke of the wing only, the other wing movements are actuated
via the elastic network of the wing. The completed design was
3D printed using ABS plastic. We created a network of 0.5mm
elastic threads, similar to the layout of fibre bundles of a bat
wing (Fig. 4) [1]. We then attached 0.25mm latex sheeting to
this network using cyanoacrylate glue, and polyvinyl acetate
glue as sealing. This elastic network serves as a structure for the
wing membrane to attach on to. It allows the wing membrane to
mimic the high stiffness strength along the digits of a live bat.
We attached elastic across the wing so as to allow the elastic to
maintain the constraints in (1). Our bat wing is powered by a
modified Tamiya 70097 twin-motor gearbox using a 58:1 gear
ratio. The gearbox was altered so that the output shafts operate
in unison with each other. The bat wing is controlled with an
Arduino Uno microcontroller board, using C++.
TABLE I. MODEL AND SIMULATION PARAMETERS
m
a
x
lr
0.2× c
r
[m]
m
f
-3 [Kg]
x
lt
0.ct [m]
m
h
-3 [Kg]
l
0
5.0e
-2 [m]
l
a
-3 [m]
k
2.7e1 [N/m]
l
f
c
v
0.0 [Nm/s]
l
h
-3 [m]
a
[deg]
c
r
.3e-3 [m]
C
D0
0.05
c
t
-3 [m]
e
w
1
ρ
[Kg/m3]
g
9.81
[m/s2]
v
l
COM
l
i / 2 (i: a, f, h) [m]
I
a (Arm inertia matrix)
diag[3.3, 0.017, 3.3]×1e
-5 [Kg.m2
]
I
f (Forearm int. matrix)
diag[6.2, 0.076, 6.3] ×1e
-5
[Kg.m
2
]
Ih (Hand inertia matrix)
diag[1.0, 0.079, 1.1] ×1e
-5
[Kg.m
2
]
Flapping
parameters:
A = 70°
,
= 5π,
q
= -10°
Fig. 2. Joint rotations for two flapping cycles. q1
for the arm
about the
base frame x-axis and q2, q3 and q4 are for the arm
, elbow and
wrist rotations about the local frame z-axes
Fig. 3. Aerodynamic force components (faero
) [N] for two consecutive
flapping cycles.
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
q
t [s]
q1
q2
q3
q4
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
t [s]
FD - x
FD - y
FD - z
B. Set-up Experiments Results
We applied a low pass filter to the data and plotted a time
series of both motors simultaneously (Fig. 5). We also plotted a
return map for peaks in the data (Fig. 6). In order to observe how
the limit cycle of the motor settles, the first half of the data for
each motor is plotted in one colour (magenta and cyan), and the
latter half in another (red and blue). We can see that the wing
quickly settles down to a steady state. In order to observe the
movement patterns of the wing, we attached an LED to the tip
of the wing, and took 10 second long exposure photographs of
the wing in motion at different speeds (Fig. 7). The wing extends
upon the down-stroke, and folds mid-upstroke. One interesting
observation is the extension that can be seen at the top of the
upstroke, similar to the motion of a real bat. The wing will then
extend during the down-stroke.
IV. DISCUSSION
In this paper we focused on studying the role of anisotropic
stiffness distribution in the bat wing membrane on the efficiency
of upstroke. Biological literature suggest that the elastic
membrane helps the bat to exploit passive collapsing of the wing
at the end of the downstroke leading to reduced drag force during
upstroke. Through numerical simulations and experiments we
show that the anisotropy of the membrane contributes to such
efficiency gains only at high speeds of flapping. We observed an
eight-shaped passive elongation-collapsing steady state attractor
at roughly 198 rpm speed of the motors. Though we expect the
attractor to change shape with larger loop areas at higher speeds,
we could not perform such experiments due to hardware
limitations. Meanwhile, it proved difficult to simulate and
construct a robotic wing that emulated the wing folding
kinematics of a real bat using only one degree of actuated
motion. Besides we can look at various wing alterations,
possibly through computer simulation. For that means, a more
precise dynamic model of the wing is needed that can
profoundly show the characteristics of the wing membrane.
We showed that mimicking the behaviour of nature, such as
the bat wing skin, can have practical and feasible applications in
robotics. Further work could look into optimization of the
structural design parameters to improve the passive folding
mechanism in moderate and low flapping speed. Besides,
different elastic networks can affect not only the timing and
behaviour of wing folding in relation to a wing-beat, but also the
flight properties of flapping wing UAVs. One such application
could be the role of this elastic network in the UAV’s ability to
perform energy efficient quick and precise manoeuvres.
Fig. 5.
Elastic network mimicking the layout of fibre bundles of a bat
wing. Humerus: 37.2mm, Radioulna: 68.1mm, Digit I: 10.0mm,
Digit II: Metacarpal
29.7mm, Proximal phalanx 6.9mm, Middle
phalanx 4.1mm, Distal phalanx 2.6mm. Digit III: Metacarpal
39.9mm, Proximal phalanx 29.1mm, Distal phalanx 37.9. Digit
IV: Metacarpal 42.61mm, Proximal phalanx 22.1mm, Distal
phalanx 22.9mm. Leg: Femur 26.2mm, Tibia 31.5mm.
Fig. 4. 8-shape path of the hand tip projection on y-z plane for a full cycle (left). The intersection of the 8-shape path is maximized (middle). S
equential
representation of small passive folding in upstroke in 3D space (right).
V. CONCLUSION
We designed and built a robotic bat wing with an anisotropic
membrane capable of performing the 8-shape wing-folding seen
in bats’ high speed flight passively. We can collect input power
data from the wing, and observe wing-beat patterns. We
conclude that the wing must maintain a minimum flapping
frequency in order to exhibit its wing extending and folding
behaviour effectively. The research potential of the anisotropic
stiffness distribution of the bat wing and its practical
applications is great. This robotic wing serves as a solid
foundation for further exploration into the possibility and
benefits of integrating this behaviour into flapping wing UAVs.
ACKNOWLEDGMENT
The authors would like to thank the UK Engineering and
Physical Sciences Research Council (EPSRC) project REINS,
grant no. EP/I028765/1, and the Seventh Framework Program of
the European Commission in the framework of EU project
STIFF-FLOP, grant agreement 287728.
REFERENCES
[1] S. M. Swartz, M. S. Groves, H. D. Kim, and W. R. Walsh, “Mechancial
properties of bat wing membrane skin,” J. Zool., vol. 239, no. 2, pp. 357–
378, 1996.
[2] D. N. Beal, F. S. Hover, M. S. Triantafyllou, J. C. Liao, and G. V. Lauder,
“Passive propulsion in vortex wakes,” J. Fluid Mech., vol. 549, no. 1, p.
385, Feb. 2006.
[3] X. Tian, J. Iriarte-Diaz, K. Middleton, R. Galvao, E. Israeli, A. Roemer,
A. Sullivan, A. Song, S. Swartz, and K. Breuer, “Direct measurements of
the kinematics and dynamics of bat flight,” Bioinspir. Biomim., vol. 1, no.
4, p. S10, 2006.
[4] S. S. Baek, K. Y. Ma, and R. S. Fearing, “Efficient resonant drive of
flapping-wing robots,” intelligent Robot. Syst., pp. 2854–2860, 2009.
[5] M. A. Fenelon, “Biomimetic flapping wing aerial vehicle,” Robot.
Biomimetics, pp. 1053–1058, 2008.
[6] G. Bunget and S. Seelecke, "BATMAV: a biologically inspired micro air
vehicle for flapping flight: kinematic modeling," In The 15th International
Symposium on: Smart Structures and Materials & Nondestructive
Evaluation and Health Monitoring, International Society for Optics and
Photonics, pp. 69282F-69282F, 2008.
[7] P. D. Kuang, M. Dorothy, and S. Chung, “RoboBat : Dynamics and
Control of a Robotic Bat Flapping Flying Testbed,” in AIAA Infotech at
Aerospace Conference, St. Louis, MO, pp. 2011-1435, 2011.
[8] J. Colorado, A. Barrientos, C. Rossi, J. W. Bahlman, and K. S. Breuer,
“Corrigendum: Biomechanics of smart wings in a bat robot: morphing
wings using SMA actuators,” Bioinspir. Biomim., vol. 3, no. 3, 2013.
[9] S. J. Furst, G. Bunget, and S. Seelecke, “Design and fabrication of a bat-
inspired flapping-flight platform using shape memory alloy muscles and
joints,” Smart Mater. Struct., vol. 22, no. 1, Jan. 2013.
[10] W. Shyy, H. Aono, S. K. Chimakurthi, P. Trizila, C.-K. Kang, C. E. S.
Cesnik, and H. Liu, “Recent progress in flapping wing aerodynamics and
aeroelasticity,” Prog. Aerosp. Sci., vol. 46, no. 7, pp. 284–327, Oct. 2010.
[11] B. Parslew, “Simulating Avian Wingbeats and Wakes,” PhD diss, The
University of Manchester, 2012.
[12] B. W. Tobalske, “Biomechanics of bird flight.,” J. Exp. Biol., vol. 210,
no. Pt 18, pp. 3135–46, Sep. 2007.
[13] J. W. Bahlman, “Design and characterization of a multi-articulated robotic
bat wing.,” Bioinspir. Biomim., vol. 8, no. 1, 2013.
[14] M. Wisse, R. Linde, and Q. van Der, Delft Pneumatic Bipeds, vol. 34.
Springer Tracts in Advanced Robotics, Berlin Heidelberg, 2007.
[15] J. J. Bertin and R. C. M., Aerodynamics for Engineers, 5th ed. Prentice
Hall, 2008.
Fig. 6.
Time series of current data after the application of a low pass
filter for downstroke and up-stroke motors
Fig. 7. Return map for peaks in the data for upstroke and downstroke
motors, showing the steady state variability of the up-
stroke and
downstroke motor currents.
Fig. 8. Inverted black and white images depicti
ng long exposures of
robotic wing flapping at different speeds. a) Shows the wing
flapping at a speed such that no wing extension and folding can
be seen. b) shows the wing flapping at a speed high enough such
that the wing passively extends and folds. The
red arrows
correspond to the downstroke, and the blue arrows correspond to
the up-stroke.
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