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


Abstract and Figures

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
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
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
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.
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
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 (
sin ()cos (
0× 1×
=((),[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
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
while they are approximated to be equal at the right-down figure.
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)
=+ , =
= 
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
Tcn is derived based on the three constraints in (1).
 =()
 =1000
00−2 1
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,
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,
t and
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(
x)1 and
x approximations to reduce the complexity of
≈−2.( −(+)) /
= .(−)/(−), 
.(−)/((−)−) , <
=().[(−)+.(−(−)) /2 0]
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 (
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
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,
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,
is the
air density, and mx and my are momentum of aerodynamic forces
about wing frame x and y axes.
=./(1+1+(./(.cos (.)))),
 = (d+d)
= (d+d)
= (+.tan()−/4).(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)̇
 =3(1+4)̇
/ =((3(1+4)tan()−(6+3+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−
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.
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++.
0.2× c
-3 [Kg]
0.ct [m]
-3 [Kg]
-2 [m]
-3 [m]
2.7e1 [N/m]
0.0 [Nm/s]
-3 [m]
.3e-3 [m]
-3 [m]
i / 2 (i: a, f, h) [m]
a (Arm inertia matrix)
diag[3.3, 0.017, 3.3]×1e
-5 [Kg.m2
f (Forearm int. matrix)
diag[6.2, 0.076, 6.3] ×1e
Ih (Hand inertia matrix)
diag[1.0, 0.079, 1.1] ×1e
A = 70°
= 5π,
= -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.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
t [s]
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.
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
representation of small passive folding in upstroke in 3D space (right).
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.
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.
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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.
Traditional flapping-wing robots (FWRs) obtain lift and thrust by relying on the passive deformation of their wings which cannot actively fold or deform. In contrast, flying creatures such as birds, bats, and insects can maneuver agilely through active folding or deforming their wings. Researchers have developed many bio-inspired foldable or deformable wings (FDWs) imitating the wings of flying creatures. The foldable wings refer to the wings like the creatures' wings that can fold in an orderly manner close to their bodies. Such wings have scattered feathers or distinct creases that can be stacked and folded to reduce the body envelope, which in nature is beneficial for these animals to prevent wing damage and ensure agility in crossing bushes. The deformable wings refer to the active deformation of the wings using active driving mechanisms and the passive deformation under the aerodynamic force, which functionally imitates the excellent hydrodynamic performance of the deformable body and wings of the creatures. However, the shape and external profile changes of deformable wings tend to be much smaller than that of folding wings. FDWs enable the FWRs to improve flight degree of flexibility, maneuverability, and efficiency and reduce flight energy consumption. However, FDWs still need to be studied, and a comprehensive review of the state-of-the-art progress of FDWs in FWR design is lacking. This paper analyzes the wing folding and deformation mechanisms of the creatures and reviews the latest progress of FWRs with FDWs. Furthermore, we summarize the current limitations and propose future directions in FDW design, which could help researchers to develop better FWRs for safe maneuvering in obstacle-dense environments.
Full-text available
The skin of the bat wing in functionally unique among mammals: it serves as a major locomotor organ in addition to its protective and regulatory functions. We used tensile testing to investigate the mechanical capabilities of wing membrane skin, and compared stiffness, strength, load at failure, and energy absorption among specific wing regions and among a variety of bat taxa. We related these characteristics to the highly architectural fibrous supporting network of the wing membrane. We found that all material properties showed a strong anisotropy. In particular, wing membrane skin shows maximum stiffness and stregth parallel to the wing skeleton, and greatest extensibility parallel to the wing's trailing edge. We also found significant variation among wing regions. The uropatagium (tail membrane) supported the greatest load at failure, and the plagiopatagium (proximal wing membrane between laterl body wall and hand skeleton) is the weakest and most extensible part of the wing. We believe that the increased load bearing ability of the uropatagium relats to its key role in capture of insect prey, and that the great extensibility of the plagiopatagium promotes development of camber near the wing's centre of lift. In interspecific comparisons, energy absorpion and load to failure were greatest in Artibeus jamaicensis, the largest bat in our sample and the species with the highest wing loading, suggesting that wing loading may play a role in dictating the fuctional design of wing membranes.
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The overall objective of the BATMAV project is the development of a biologically inspired bat-like Micro-Aerial Vehicle (MAV) with flexible and foldable wings, capable of flapping flight. This first phase of the project focuses particularly on the kinematical analysis of the wing motion in order to build an artificial-muscle-driven actuation system in the future. While flapping flight in MAV has been previously studied and a number of models were realized using light-weight nature-inspired rigid wings, this paper presents a first model for a platform that features bat-inspired wings with a number of flexible joints which allows mimicking the kinematics of the real flyer. The bat was chosen after an extensive analysis of the flight physics of small birds, bats and large insects characterized by superior gust rejection and obstacle avoidance. Typical engineering parameters such as wing loading, wing beat frequency etc. were studied and it was concluded that bats are a suitable platform that can be actuated efficiently using artificial muscles. Also, due to their wing camber variation, they can operate effectively at a large range of speeds and allow remarkably maneuverable flight. In order to understand how to implement the artificial muscles on a bat-like platform, the analysis was followed by a study of bat flight kinematics. Due to their obvious complexity, only a limited number of degrees of freedom (DOF) were selected to characterize the flexible wing's stroke pattern. An extended analysis of flight styles in bats based on the data collected by Norberg and the engineering theory of robotic manipulators resulted in a 2 and 4-DOF models which managed to mimic the wingbeat cycle of the natural flyer. The results of the kinematical model can be used to optimize the lengths and the attachment locations of the wires such that enough lift, thrust and wing stroke are obtained.
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A dead fish is propelled upstream when its flexible body resonates with oncoming vortices formed in the wake of a bluff cylinder, despite being well outside the suction region of the cylinder. Within this passive propulsion mode, the body of the fish extracts sufficient energy from the oncoming vortices to develop thrust to overcome its own drag. In a similar turbulent wake and at roughly the same distance behind a bluff cylinder, a passively mounted high-aspect-ratio foil is also shown to propel itself upstream employing a similar flow energy extraction mechanism. In this case, mechanical energy is extracted from the flow at the same time that thrust is produced. These results prove experimentally that, under proper conditions, a body can follow at a distance or even catch up to another upstream body without expending any energy of its own. This observation is also significant in the development of low-drag energy harvesting devices, and in the energetics of fish dwelling in flowing water and swimming behind wake-forming obstacles.
Walking is simple for most of us, but two-legged robots (bipeds) are often slow, complex, inefficient, heavy, and have robotic-looking motions. What makes human walking so graceful? Can this be replicated with human-like robots? Martijn Wisse and Richard Q. van der Linde provide a detailed description of their research on pneumatic biped robots at the Delft University of Technology, The Netherlands. The book covers the basic theory - passive dynamic walking - and explains the implementation of pneumatic McKibben muscles in a series of successful prototypes.
Conference Paper
This paper investigates the control of the phase difference in between three different motions of bat flight: pitching, mapping, and lead-lag. For active control, a robotic bat test bed capable of simulating different wing motions is used to test the control of these wing motions and the phase differences using central pattern generators (CPG's). Previous work with the robotic bat is expanded upon by modifying the robotic bat test bed to allow for three dimensional motions of the entire bat, instead of only the wings. This is done by mounting the robotic bat onto a 3D pendulum. Experiments analyzing the steady state behavior of the bat's flight with varying phase differences showed a change of pitch while elevation and forward velocity remains constant. This shows promising results regarding the relation between phase differences of wing motions and longitudinal stability.
This work focuses on the development of a concept for a micro-air vehicle (MAV) based on a bio-inspired flapping motion that is generated from integrated smart materials. Since many smart materials have their own biomimetic characteristics and the potential to be highly efficient, lightweight, and streamlined, they are ideal candidates for use in structural or actuator components in MAVs. In this work, shape memory alloy (SMA) actuator wires are used as analogs for biological muscles, and super-elastic SMAs are implemented as flexible joints capable of large bending angles. While biological organisms have an intrinsic sensing array composed of nerves, the SMA wires also provide self-sensing by virtue of a phase-dependent resistance change.
Revised to reflect the technological advances and modern application in Aerodynamics, the Sixth Edition of Aerodynamics for Engineers merges fundamental fluid mechanics, experimental techniques, and computational fluid dynamics techniques to build a solid foundation for students in aerodynamic applications from low-speed through hypersonic flight. It presents a background discussion of each topic followed by a presentation of the theory, and then derives fundamental equations, applies them to simple computational techniques, and compares them to experimental data.
There are many challenges to measuring power input and force output from a flapping vertebrate. Animals can vary a multitude of kinematic parameters simultaneously, and methods for measuring power and force are either not possible in a flying vertebrate or are very time and equipment intensive. To circumvent these challenges, we constructed a robotic, multi-articulated bat wing that allows us to measure power input and force output simultaneously, across a range of kinematic parameters. The robot is modeled after the lesser dog-faced fruit bat, Cynopterus brachyotis, and contains seven joints powered by three servo motors. Collectively, this joint and motor arrangement allows the robot to vary wingbeat frequency, wingbeat amplitude, stroke plane, downstroke ratio, and wing folding. We describe the design, construction, programing, instrumentation, characterization, and analysis of the robot. We show that the kinematics, inputs, and outputs demonstrate good repeatability both within and among trials. Finally, we describe lessons about the structure of living bats learned from trying to mimic their flight in a robotic wing.