Development of a Flapping Wing Mechanism - Student Projects

Oliver Breitenstein
Development of a Flapping
Wing Mechanism
Semester Project
Autonomous Systems Lab (ASL)
Swiss Federal Institute of Technology (ETH) Zurich
Supervision
Dr. Samir Bouabdallah, Stefan Leutenegger
and
Prof. Dr. Roland Siegwart
Spring Semester 2009

Contents
Abstract iii
Acknowledgements iv
1 Introduction 1
2 Review 3
2.1 Aerodynamics of flapping wings . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Wagner Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Leading edge vortex . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.3 Clap and fling mechanism . . . . . . . . . . . . . . . . . . . . 4
2.1.4 Rotational lift . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.5 Wing-wake interactions . . . . . . . . . . . . . . . . . . . . . 6
2.1.6 Lift force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Flapping wings in nature . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Insects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Hummingbirds . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Bats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.4 Birds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Concepts 21
3.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Objective characteristics . . . . . . . . . . . . . . . . . . . . . 21
3.1.2 Flight control . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.3 Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Concepts for wing flapping . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Concept A . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Concept B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.3 Concept C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.4 Concept D . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Concepts for wing pitching . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 Active pitching . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Passive pitching . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Evaluation 35
4.1 Evaluation of concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.2 Flapping concepts . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1.3 Pitching concepts . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Expected weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Expected power consumption . . . . . . . . . . . . . . . . . . . . . . 38
i

5 CAD Design 39
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Transmission of motor torque . . . . . . . . . . . . . . . . . . . . . . 40
5.3 Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6 Conclusion 43
A Motor datasheet 45
ii

Abstract
This project aims at the development of a bio-mimetic propulsion mechanism for
a Flapping Wing Micro Aerial Vehicle, without considering the aerodynamics of
the wings in the design. This artificial bird will be the size of approximately 10-
20cm. Therefor the aerodynamic phenomena in flapping flight are studied and
summarized. It covers the leading-edge vortex (LEV), the clap-and-fling effect,
rotational lift and wing wake interactions. This is followed by a review of natural
flappers. The aerodynamic and kinematic pattern of hummingbirds, bats, insects
and small birds are summarized. Based on this review several different concepts of
mechanisms for flapping wings are generated, which are seperated for the flapping
motion and the pitching motion. Using a qualitative evaluation, the quality of
the concepts are determined according to different criteria such as weight, size,
robustness, mechanical complexity, expected power consumption and accuracy. The
best concept is used as basis for a 3D CAD design of the mechanism, which should
mainly reproduce the desired kinematics. During the design process the focus is
set more on getting a robust and simple mechanism, which could be used as a test
bench for further investigations and measurements. Concluding, the mechanism is
manufactured and assembled to prove the feasibility.
iii

Acknowledgements
I’d like to thank Dr. Samir Bouabdallah and Stefan Leutenegger for their good
guidance and the useful inputs they contributed. Specially during the last part, the
CAD-Design, when time was short, their experience was very supportive. Also I’d
like to thank Dr. Bret Tobalske from the University of Montana and Maria Jose
of Berkeley, giving me deeper informations about the hummingbird flight, which
helped me alot understanding the crucial parts of it for developing a mimicking
flapping device.
iv

List of Figures
1.1 Schematic drawing of DelFly I taken from www.delfly.nl . . . . . . . 1
1.2 Flapping wing mechanism of ROBUR taken from IROS 2007 www.flyingrobots.org 2
2.1 Leading edge vortex on the wing[19] . . . . . . . . . . . . . . . . . . 4
2.2 Evolution of a leading edge vortex in (A) two dimensions and (B)
three dimensions during linear translation starting from rest [19] . . 4
2.3 Schematic representation of the clap (A-C) and fling (D-F) [19] . . . 5
2.4 Three phases of the wing rotation [7] . . . . . . . . . . . . . . . . . . 5
2.5 Wing-wake interaction during stroke reversal [19] . . . . . . . . . . . 6
2.6 Flight forces for the drosophila during hovering [21] . . . . . . . . . . 7
2.7 General pattern for the wing motion of Drosophila Melanogaster [16] 8
2.8 Kinematics of Drosophila Melanogaster [9] . . . . . . . . . . . . . . . 8
2.9 Force production in two cycles [16] . . . . . . . . . . . . . . . . . . . 9
2.10 Wing motion relative to the body flying at velocities of 0 − 12ms −1 [2] 10
2.11 Angles describing bird-centered wing and body kinematics in rufous
hummingbirds [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.12 Variation of chord angle relative to body-plane during wingbeats at
velocities of 0 − 12ms −1 [2] . . . . . . . . . . . . . . . . . . . . . . . 12
2.13 Wake structures in frontal and side plane [17] . . . . . . . . . . . . . 13
2.14 Flow field vorticity at end of upstroke, (a) frontal view at shoulderplane,
(b) side view at midwing-plane [17] . . . . . . . . . . . . . . . 13
2.15 Anatomical structure of the bat wing [5] . . . . . . . . . . . . . . . . 14
2.16 Sequences of images from below and in front of bat during on cycle
starting at beginning of the downstroke [6] . . . . . . . . . . . . . . . 14
2.17 Example trajectories of the different wing regions for 3m/s (left) and
9m/s (right) [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.18 Example of wing tip motion [6] . . . . . . . . . . . . . . . . . . . . . 15
2.19 Velocity and vorticity fields around a bat wing in slow forward flight
(1 m/s) at the time instance when the wing is in horizontal position
during the downstroke [10] . . . . . . . . . . . . . . . . . . . . . . . . 15
2.20 Wingspan ratio as a function of flight velocity compared among bird
species [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.21 Representative wing kinematics in a zebra finch engaged in flapbounding
flight at 2m/s (A) and 12m/s (B) [4] . . . . . . . . . . . . 17
3.1 Schematic drawing of concept A1 . . . . . . . . . . . . . . . . . . . . 23
3.2 Sketch for kinematics of general structure for the flapping motion . . 24
3.3 Trajectories of centered joint for one cycle for different ratios L/r . . 24
3.4 Schematic drawing of concept A2 . . . . . . . . . . . . . . . . . . . . 25
3.5 Schematic drawing of concept B1 (left) and B2 (right) . . . . . . . . 25
3.6 Schematic drawing of concept C . . . . . . . . . . . . . . . . . . . . . 26
3.7 Calculation of the bending line . . . . . . . . . . . . . . . . . . . . . 26
3.8 Sketch for calculation of the dynamics . . . . . . . . . . . . . . . . . 27
v

3.9 Results of the force on the link and the needed torque during one
flapping cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.10 Schematic drawing of concept D . . . . . . . . . . . . . . . . . . . . 29
3.11 Actively adapting pitch angle using the trailing edge . . . . . . . . . 30
3.12 Geometric sketch for calculations of the trailing edge motion . . . . 30
3.13 Left: Trajectories of leading edge, traling edge and chord angle,
Right: Shifted graph for the leading edge motion for comparison
of the harmoinc behaviour of the trailing edge’s motion . . . . . . . 31
3.14 Actively adapting pitch angle using the leading edge . . . . . . . . . 31
3.15 Simulated chord angle for horizontal actuation of wing rod . . . . . . 32
3.16 Sketch of general principle for passive pitching at the hinge . . . . . 33
3.17 Passive pitching done at the wings . . . . . . . . . . . . . . . . . . . 33
4.1 Structure of the wing . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.1 Overview of resulting mechanism . . . . . . . . . . . . . . . . . . . . 40
5.2 Connection of motor to rotating link . . . . . . . . . . . . . . . . . . 40
5.3 Design for guiding the center joint . . . . . . . . . . . . . . . . . . . 41
5.4 Assembly of wing joint . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.5 Structure of the wing attachments . . . . . . . . . . . . . . . . . . . 42
vi

Chapter 1
Introduction
Over the past twenty-five years interest in small unmanned aerial vehicles has greatly
increased. Specially for reconnaissance and surveillance missions these vehicles are
of great use. Most of them, which are used today incorporate traditional methods
for lift and thrust, a propeller for thrust and fixed wings with an appropriate profile
to gain enough lift. Also rotary drive systems as can be seen by helicopters are used
by some. However natural flying creatures are still superiour in terms of manoeuverability,
lightweight and endurance.
This fact motivates to find a MAV, which mimics the flapping motion of small birds,
bats or insect, to have the same advantages. Also the improving technology, for instance
lightweight and robust materials and better batteries, make this task more
feasible and therefor the field of research of Flapping Wing MAVs has increased
remarkably over the past years.
Several Flapping Wing MAVs are already developed. The most successful is the
DelFly, which has been realised by a group of undergraduate students at TU Delft
in the Netherlands. Many other vehicles built so far use two wings, as it can be
observed in nature at birds. DelFly is more a copy of the dragonfly, it uses two pairs
of wings (see figure 1.1). The wings flap in counterphase and almost touch each
other when they come together, for which reason it is assumed that it makes use of
the clap-and-fling effect (Chapter 2.1.3). However the question, why this concept
works so well is still open, the investigations and measurements to reveal the secret
have just started.
Figure 1.1: Schematic drawing of DelFly I taken from www.delfly.nl
1

Chapter 1. Introduction 2
Other UAVs are yet less successful compared to the DelFly. However some other
promising projects are still ongoing. For instance ROBUR from the University of
Paris, France. It has bigger dimensions, comparable to them of a seagull, and uses
a more heavy and complex mechanism (figure 1.2), but again can perform much
more wing motions. It can independently control the pitch angle of the wing and
the flapping speed.
Figure 1.2: Flapping wing mechanism of ROBUR taken from IROS 2007
www.flyingrobots.org
Another project from the University of California, Berkely, which investigates smaller
dimensions is the robotic insect of Robert Wood [24]. It is at-scale of insects and
has a fascinating lift production for this small scale. However longer flights are not
possible, as the lift is indeed enough to let the Robotic insect fly, but also to carry
a battery and control modules is due to limitations of the actual technology not yet
possible.
In the following chapters, it is presented how a flapping wing mechanism for an
artificial bird with a size of approximately 20cm is developped. This project is the
first step into this direction. Therefor in chapter 2 a detailed literature review is
done to see which natural flapping flyer is most suitable for mimicking. Also briefly
the general aerodynamic phenomena of flapping wings are summarised, which have
to be considered and could give useful inputs. The result of this investigation is
then used as a starting point to generate different concepts (chapter 3), without
going too deep into the design and only theoretical calculations are done to check
the feasibility. In chapter 4 the concept are compared with each other and the best
is chosen to design in 3D CAD, which is briefly described in chapter 5.

Chapter 2
Review
2.1 Aerodynamics of flapping wings
Compared to fixed wing flight, flapping the wings induce in general different aerodynamic
phenomena. Most of the airflow is turbulent and due to permanently
changed wing position and orientation, more the unsteady aerodynamics have to
be considered. Because these informations could be of use for the development of a
flapping wing mechanism, in this section shortly the main aerodynamics phenomena
of flapping wings are described, using [11] as main input.
2.1.1 Wagner Effect
When a wing with a high angle of attack starts suddenly to move, the airflow vortices
do not immediately get their steadystate value. The circulation slowly approaches
to it. This delay results of a combination of two phenomena [19]. Firstly the fluid
is not perfect, meaning it has a viscous behaviour on the stagnation point and so
it takes some time to establish the Kutta condition. Also during the process the
vorticity is generated and again shed at the trailing edge, while this shed vorticity
forms a starting vortex. The velocity field near the wing, which is induced by the
shed vorticity at the trailing edge counteracts to the bounding of the vortex to the
wing. Only when the starting vortex has moved enough far away of the trailing
edge, the moved wing gets its maximum circulation. This slow developement of
circulation was first proposed by Wagner in 1925 and so is called as the Wagner
effect.
Unlike the other unsteady mechanisms described below, this effect is not as strong.
Specially at Reynolds numbers, which are typically for small birds or insects it
can be neglected for flapping wings. However for more detailed studies of the
aerodynamics, it is still considered.
2.1.2 Leading edge vortex
One of the most important effects for flapping wing flight is the leading edge vortex
(LEV), which is created at high angles of attack. Operating the wing at a high angle
of attack leads for a steady flow regime to flow separation and stall. However in
unsteady flow, the created vortex at the leading edge, stays attached to the wing for
a great part of the downstroke. This attached vortex induces a velocity downwards
and so increases the lift force as shown in figure 2.1. Only when the vorticity of the
leading edge vortex gets too large, the flow is not reattached before the trailing edge
any more and a trailing edge vortex is formed, where the wing is in state similar
to stall, which results in a sudden drop of lift. This described behaviour, for a
3

Chapter 2. Review 4
Figure 2.1: Leading edge vortex on the wing[19]
Thick black lines indicate the downwash due to the generated vortex system
two-dimensional wing motion, is called dynamic or delayed stall. The evolution of
the leading edge vortex for a translating wing starting from rest is shown in figure
2.2. For the three-dimensional case as shown in figure 2.2, the leading edge vortex
Figure 2.2: Evolution of a leading edge vortex in (A) two dimensions and (B) three
dimensions during linear translation starting from rest [19]
is more stable and no trailing edge vortex forms. Several different studies try to
explain the stability of the formed leading edge vortex [12] [3], which is only present
for the three-dimensional case. But still newer studies show, that the LEV has long
been underestimated and is far more complex than assumed so far [13].
2.1.3 Clap and fling mechanism
Another phenomenon is the clap and fling mechanism showed in figure 2.3. Here
the wings come together at the end of each upstroke to perform a so called ’clap’.
After the clap the trailing edges of the wings stay connected, while the leading edges
are increasing their distance to each other, which is called as ’fling’. So an opening
angle is created. When the wings then start their downstroke, air is sucked into this
funnel-like geometry, which induces a bound vortex at the leading edge of each of
the wings, and each created vortex acts as a starting vortex for the other wing. As
described by Weis-Fogh [22] this annihilation allows the circulation to be builded up
more rapidly, because the Wagner effect (see section 2.1.1) is suppressed. Another

5 2.1. Aerodynamics of flapping wings
Figure 2.3: Schematic representation of the clap (A-C) and fling (D-F) [19]
Black lines show trajectory of the airflow, dark blue arrows represent the by the airflow induced
velocity, light blue arrow shows the net force on the airfoil.
advantage of the clap is that the created vortices during upstroke are vanishing
during the clap, they cancel each other out as they are oriented in opposite direction.
Many insects make use of the fling to create a rotational airflow circulation, while
the clap is not performed by all insects. According to Ellington [8] the clap is
avoided by most of the insects because the permanent clapping can damage the
wings and more a ’almost’ clap is performed. Also for birds similar observations
were made, for instance during the takeoff of pigeons [14]. Although no full clap and
fling is performed, the wings almost touch each other at the back and it is assumed,
that in this way similar air circulations are produced, which give additional lift.
2.1.4 Rotational lift
Near the end of every stroke mainly insects but also some small birds (e.g. hummingbirds)
are rotating their wings, which allows to maintain a positive angle of
attack during the whole wingbeat cylce. The three different phases are shown in
Figure 2.4: Three phases of the wing rotation [7]

Chapter 2. Review 6
figure 2.4. The angles of attack during downstroke and upstroke are αd and αu respectively.
ω indicates the angular velocity. This rotation at the end of each stroke,
also gives additional lift. According to Dickinson the generated lift force strongly
depends on the the position of the rotation axis. For instance rotations about the
trailing edge show a better lift generation compared to rotations about the leading
edge for instance. Also the timing of the rotation has an effect on the produced lift,
which is analysed for instance in [7].
2.1.5 Wing-wake interactions
The back and forth motion of the wings used by insects make the wings interact with
the shed vorticity of the prior strokes, which acts positively on the lift generation.
Figure 2.5 shows the principle of wake capture. At the end of the translational
Figure 2.5: Wing-wake interaction during stroke reversal [19]
U∞ indicates the freestream velocity, dark blue arrows show the induced velocity field, light blue
arrows presents the aerodynamic force
phase (A), the wing starts the rotation (B), which causes the vortices at the edges
to shed off the wing (C). This induces a strong velocity field, which pushes against
the wing (D) and so increases the lift force at the beginning of the next halfstroke
(E). In the following translational phase, again a LEV is created (F). This wingwake
interaction also allows to let the pitch motion of the wing done passively, as
this additional lift, at the beginning of the stroke, rotates the wing to the desired
orientation, to maintain a positive angle of attack.
2.1.6 Lift force
The lift force is produced by the four unsteady effects described above. The most
important one is the LEV, because it is the only one, which is responsible for lift
during the flapping, the translational phases of the strokes. The other three effects
enhance the lift production mainly during the rotational phases. In figure 2.6 an
example of the generated lift force is shown. During hovering, the horizontal component
of the red arrows in figure 2.6 cancel out during one whole stroke cycle. The
vertical component equals the body weight.
Of course the wings play also an important role for the produced lift force. Like for
fixed wing aircraft, the wing profile determines lift and drag coefficients (CL and
CD). However for flapping flight, these also differ. For a steady state flow regime,
like for fixed wing aircraft, these two coefficients can be deteremined independently

7 2.2. Flapping wings in nature
Figure 2.6: Flight forces for the drosophila during hovering [21]
The red arrows indicate the net forces during down- and upstroke.
from each other. For an unsteady flow field they can not be seperated anymore [11].
Flapping flight is usually performed with a high angle of attack, to get the above
described LEV, which induces a force normal to the wing surface. Hence the resultant
force is drag- and lift force in one hand. Therefor to have a similar description
as for fixed wing flight Dickinson [20] defined a circulatory coefficient, which can be
merged out of the usual drag and lift coefficient.
CT = C2 D + C2 L
(2.1)
However, this coefficient also has to be determined experimentally. Also for a given
wing profile, and known lift- and drag coefficients for a steady flow regime, there
is no way around to obtain the circulatory coefficient, but to make experimental
measurements, because the unsteady effects of the flapping flight give different
results.
2.2 Flapping wings in nature
For developing a flapping wing mechanism different flying animals are studied. As
the future MAV should have the ability to hover, mainly animals with hovering capabilites
are examined. Also the dimensions should approximately match the MAV,
that for a first approach the feasibility can be taken for granted. Therefor in this
section the wing motions of hummingbirds, bats and smaller birds are summarized.
Although insects are much smaller and will not serve as main input for the flapping
wing mechanism, some ideas may be extracted and hence roughly the kinematics
and aerodynamics are summarized by the example of the Drosophila fruit fly.
2.2.1 Insects
The stroke shape in flying insects are varying remarkably. The wing tip makes
depending on the insect, different motions. Oval, figure-eight or pear-shaped trajectories
[16], or combinations of those patterns are done. Also some insects may
change the stroke trajectory for strong manoeuvers. And for increasing forward
flight again other wing motions occur. Because this is a wide range, the most simple
wing motion during hovering done by the drosophila fruit fly is investigated. For

Chapter 2. Review 8
Figure 2.7: General pattern for the wing motion of Drosophila Melanogaster [16]
further informations on the behaviour of other wing motions performed by other
insects see for instance [16] [9].
Wing motion
In the most common form of hovering in insects the wings move along an approximately
horizontal stroke plane with approximately equal and relatively high angles
of attack during the downstroke and upstroke. This is done by fast rotating the
wing at the end of each half stroke. The general pattern can be seen in figure 2.7.
The whole stroke cycle can be described by a sinusoidal motion or a triangular motion
depending on the insect. For the Drosophila Melanogaster the stroke trajectory
is more a triangular motion with an amplitude of 130-160 degrees and a flapping
frequency of 250 Hz. The stroke plane angle with respect to the horizontal is about
10 degrees, while the body angle is tilted about 60 degrees. These values measured
by [9] are presented in figure 2.8. Another important aspect is the ratio of the
duration of the downstroke compared to the upstroke, which is approximately 0.8
and shows that usually the downstroke is performed faster than the upstroke.
Figure 2.8: Kinematics of Drosophila Melanogaster [9]
(A) Wing tip trajectory in degrees, (B) Wing tip path drawn with respect to the body, which is
represented by an arrow

9 2.2. Flapping wings in nature
Aerodynamics
Insects are able to hover by using a range of possible unsteady high-lift mechanisms,
including rotational circulation, clap-and-fling and wake capture (see section 2.1).
However, arguably the most important mechanism is the leading-edge vortex, which
may generate up to 66% of the total lift in insect flight [23]. Consequently the high
angle of attack to create the LEV is crucial for generating enough lift force.
The almost symmetric stroke pattern, meaning that upstroke and downstroke are
very similar as described above, 50% of the resulting lift force comes out of the
downstroke, respectively out of the upstroke. Also the wing material is flexible, such
that a camber occurs, which additionally gives lift force. Due to no morphological
constraints this camber is inverted during the upstroke, which allows to maintain
almost the same aerodynamic forces acting on the wing as during the downstroke.
In figure 2.9 exemplary the generated forces are shown, which are taken out of
measurements made with a flapping device having the similar stroke trajectory as
the Drosophila melanogaster [16].
Figure 2.9: Force production in two cycles [16]
(A) Vertical force acting on the wing (black line), (B) Translational angular wing motion (black),
the wing’s angle of attack (blue) and heaving motion (green)
It can be seen that the lift force is generated during up and downstroke. Also the
clap and fling plays a role at the transition of the down- and upstroke and generates
extra lift force. It is important to notice that the generated lift force highly depends
on the stroke trajectory [16]. One can assume that if a wing is moved with the
same angle of attack and rotational velocity, the same lift force should occur. But
different stroke trajectories change the airflow pattern, the created vortices and so
the generated lift force. Therefore insects have in general different stroke pattern,
which are more or less effective, but at least enough to let them fly.

Chapter 2. Review 10
2.2.2 Hummingbirds
Most studies of hummingbirds are based on the rufous hummingbirds, because of
their practical properties for experimental measurements in the wind tunnel. They
can be trained and thrive well in captivity. Although they have a body mass of
3-4g and a wing span of 110mm and so would be too small and lightweight for a
prototype MAV, their wing motion still can be mimicked because the biggest existing
hummingbird, the Giant Hummingbird (Patagonia Gigas) has according to
biologists in general patterns the same kinematics, weights about 20g and has a
wingspan of 280mm.
Figure 2.10: Wing motion relative to the body flying at velocities of 0 − 12ms −1 [2]
(A) Dorsal view with bird silhouette at mid-downstroke. (B) Lateral view with bird silhouette at
start of downstroke.
Wing Motion
The rufous hummingbird flaps their wings with a frequency of 40-45 Hz. For bigger
species the flapping frequency decreases. For instance the giant hummingbird has a
flapping frequency of about 10-15 Hz. The main characteristics of the wing motion
for several different forward flight speeds (0m/s−12m/s) can be seen in figure 2.10.
Black circles indicate position of wingtips, white circles indicate position of wrists
which is approximately in the middle of the wing.

11 2.2. Flapping wings in nature
During upstroke of slow flight (0m/s and 2m/s), the tips and wrists trace in reverse
nearly the same paths that were exhibited during downstroke. The lateral view reveals
the wingtip describing an upwardly concave path, where the tips also follow
a slight horizontal figure-8 pattern. In figure 2.12 the flapping motion is shown
more detailed. The wrist elevation indicates the position of the wrist relative to the
mid-frontal plane, which is described by the bird’s torso, and the chord angle describes
the pitching of the wing with respect to this body plane. It can be seen that
the flapping motion is sinusoidal, where the downstroke is performed insignificantly
faster than the upstroke. Also the chord angle follows a sinusoidal trajectory, with
a phase shift and an offset compared to the wrist elevation.
Figure 2.11: Angles describing bird-centered wing and body kinematics in rufous
hummingbirds [2]
β is the body angle w.r.t. horizontal, γh and γb is the stroke plane angle relative to horizontal
respectively to body angle
During upstroke almost no wing folding is present. According to [2], [17] the
wingspan ratio upstroke:downstroke is about 0.98 for slow flight and decreases to
0.90 for faster flying speeds up to 12m/s, where most of the flexing is done at the
outer parts of the wing, between the wrist and the tip. As for slow speeds this
ratio stays more or less constant, the wings can be taken as kinematically ’rigid’
compared to other avian species.
As can be seen in figure 2.11 for transition from hovering to a forward flight speed
of 2m/s the stroke plane angle with respect to the body γb can be assumed to be
constant. In general mainly the body angle β is tilted to achieve a forward velocity
for slow flight speeds. For higher speeds of course more parameters are varying
significantly. For instance it can be seen in figure 2.12 that the maximal chord angle
reduces significantly for increasing forward flight speed and generally the stroke
amplitude increases.
Aerodynamics
Although the aerodynamic characteristics of the hummingbirds wingbeat are very
complex, several studies reveal some useful information. The main flow pattern
can be described as shown in figure 2.13. During the flapping motion trailing-tip
vortices are created. These vortices induce starting and stopping vortices of the
downstroke. The resultant air circulation origined of these vortices are the main
effects, besides the usual aerodynamic phenomena of flapping wings (Section 2.1),
which are adequate to support the weight of the hummingbirds. A more detailed
illustration can be seen in figure 2.14.

Chapter 2. Review 12
Figure 2.12: Variation of chord angle relative to body-plane during wingbeats at
velocities of 0 − 12ms −1 [2]
Wingbeat duration is expressed as a precentage of entire wingbeat. Broken line indicates wrist
elevation relative to body-plane. Shaded area represents downstroke. Values are means ±s.d
In the frontal view, the tip vortices of the downstroke (D) and the upstroke (U)
are indicated. In the side view, between the stopping vortex of the downstroke (D)
and the starting vortex of the upstroke (U) is a pocket of vorticity LEVD created
at the leading edge of the wing during the rapid wing pronation at the beginning
of the preceding downstroke, and carried through the downstroke to be shed during
the supination at the beginning of the upstroke. The resultant airflow downwards
gives the needed lift force for hovering.
More studies on the airflow revealed that a force asymmetry between upstroke and
downstroke is present. Hummingbirds produce 75% of their weight support during

13 2.2. Flapping wings in nature
Figure 2.13: Wake structures in frontal and side plane [17]
the downstroke and only 25% during the upstroke [17], although the kinematics of
the wing motion is symmetric, as for insects. It is assumed that this asymmetry
is present due to slight difference of the angular velocity during downstroke and
upstroke, a missing leading edge vortex during upstroke and several musculoskeletal
and planform material properties, which do not allow the hummingbird’s wing to
behave equally efficient as the insect’s wing. For instance during the downstroke
the wing is slightly cambered, while during the upstroke the wing is not capable to
invert the camber, which gives a significant loss of the produced lift force.
Figure 2.14: Flow field vorticity at end of upstroke, (a) frontal view at shoulderplane,
(b) side view at midwing-plane [17]
2.2.3 Bats
There are many bats species living on earth, which differ in size, weight and some
other anatomical aspects [15]. But as the wing motion was observed to be similar
for most of the species [18], mainly the studies about the lesser short-nosed fruit
bat Cynopterus Brachyotis are considered, which give a sufficient insight to the
aerodynamics and kinematics aspects of the bat flight.
Wing motion
As can be seen in figure 2.15 the bat wings possess more than two dozen joints, which
can be controlled independently [5] and has bones that deform adaptively during
the motions of the wingbeat cycle. Of course this anatomical structure is crucial for
the motion of the wing and so very complex trajectories are fullfilled. As can be seen
in figure 2.16 the general motion is characterized by a cambered wing during the
downstroke, and a folding of the wing during the upstroke. To simplify the upstroke
it could be described as additional delays for joints approaching the thorax with

Chapter 2. Review 14
Figure 2.15: Anatomical structure of the bat wing [5]
Figure 2.16: Sequences of images from below and in front of bat during on cycle
starting at beginning of the downstroke [6]
respect to the wing tip. So the motion of the next inner joint, the finger joint,
compared to the wingtip is delayed, while the wrist then again is delayed compared
to the finger joint and so on [5]. During downstroke the wing is approximately
stretched, with a almost synchronous movement of all joints but also with increasing
delays for the inner wing parts as can be seen on the right diagram of figure 2.17. The
shoulder is the most proximal point of the wing. The wrist is the next distal joint,
followed by the MCP III and the tip of the third digit as the furthest measurement
point of the wing. Hence the kinematics are not simple. Even if only the wing
Figure 2.17: Example trajectories of the different wing regions for 3m/s (left) and
9m/s (right) [5]
Zero represents the vertical position of the animal’s center of mass. Radius in red (lower arm),
Humerus in dark blue (upper arm), MCP in light blue (knuckle), shoulder in black
tip position is observed, it can be seen in figure 2.18 that the trajectory can not
be realised by a simple mechanical mechanism. Also for increasing flight speed for
example the wingtip elevation increases significantly, and the shoulder follows an
entirely other trajectory compared to slow flight or hovering.
According to [5] also changes in the length of the different bones and the membrane
in the wing occur, which is again a reason for the above presented complex wing
motion.

15 2.2. Flapping wings in nature
Figure 2.18: Example of wing tip motion [6]
Circles indicate the wing tip position for one whole cycle; The cross indicates the center of mass
of the bat’s thorax.
Aerodynamics
Lift mechanisms in bat flight origined of unsteady effects are not studied very detailed
yet. Regardless some measurements of the airflow using digital particle image
velocimetry were documented. According to [10] the wing camber during downstroke
is about 18% of the wing chord and the average angle of attack, where the
wing is operating is about 50 ◦ . It is important to notice that if a fixed wing operates
at such values, it would stall and lose lift, which already presumes that the bat
flight is very complex and not very simply comparable with other flying animals.
The main contribution to the lift force was found to be given by the LEV [10], which
is shown in the following more detailed. Figure 2.19 show that the flow separates
Figure 2.19: Velocity and vorticity fields around a bat wing in slow forward flight
(1 m/s) at the time instance when the wing is in horizontal position during the
downstroke [10]
at the leading edge, generating an area of high negative vorticity. Behind this area
the airflow reattaches, which results in an attached and laminar flow at the trailing

Chapter 2. Review 16
edge. The vorticity is stronger near the wingtip (C) and deacreases toward the wing
root (A).
At the trailing edge, mainly distally on the wing, an area with negative vorticity is
found, which results of a strong rotational movement before the end of the downstroke,
which also enhances lift generation (see section 2.1.4). During the upstroke
the vortex, which generates much of the lift in flapping-wing flight, is not documented
well. It does not appear to origin in the wingtips as it is the case for the
downstroke. According to biologists the starting point for the vortex seems to be
somewhere in the middle of the wing, which again shows, that the complex wing
structure, with the many joints is crucial for the whole bat flight.
2.2.4 Birds
For this section mainly the smaller birds are considered. Bigger birds are using more
aerodynamic effects as for fixed wing flight, for instance gliding. Small birds need
to generate the lift force by flapping the wings. However there are many different
types of birds, which also have different kinematics.
In general the wing can be tentatively separated into two parts, the outer wing and
the inner wing. The inner wing acts like an aircraft wing, it is the lift developing
part of the wing. When a bird flaps its wing it is the inner wing that moves the
smallest distance, thus the lift it generates is due, to a large extent, on the airstream
produced by forward momentum. The inner wing is also the most cambered part
of the wing and this is made possible by the extensive bones and connective tissue
that can hold this shape better than feathers. This means that it can generate more
lift per surface area than the outer wing, it also means that it will stall more easily.
The outer wing is the powerplant of the wing, it produces lift, but more crucially
Figure 2.20: Wingspan ratio as a function of flight velocity compared among bird
species [2]
it produces forward momentum. It is less cambered than the inner wing and more
flexible and it is this flexibility that leads to the momentum. As the wing is flapped
downward the outer wing tends to twist slightly forwards, this is due to a number
of reasons, one being that air passing under the wing tends to well up toward the

17 2.3. Summary
tip and as it does so it forces its way out under the back of the wingtip, tilting the
wing forward.
During the upstroke the feeders at the outer wing are spread to reduce the drag.
Also the wing is folded for most of the species significantly (see for instance figure
2.20).
Unfortunately, there is not much literature dealing explicitly with the aerodynamics
of small birds. Also note, that compared to hummingbirds no so detailed informations
about the kinematics could be found for flight during hovering, because of
their less practical properties for experimental tests. Nonetheless briefly the flapping
parameters are given exemplarily for the zebra finch, which belongs to the
same family as the siskins and is a good representation for most of the small birds.
Kinematics of flapping flight in the zebra finch
Zebra finches have a body mass of about 13g with a wingspan of 170mm. They
flap their wings with about 24Hz and a stroke amplitude of 135 ◦ , which decreases
significantly for increasing the flight velocity [4]. As for hummingbirds the body
angle is tilted for increased forward flight speed. For hovering the body angle with
respect to the horizontal is about 50 ◦ , which decreases down to 15 ◦ for a flight
velocity of 12m/s. The angle of incidence for the wing is for hovering about 75 ◦
and decreases for a flight velocity of 12m/s to 15 ◦ . However the chord angle stays
approximately constant for all flying velocities at about 20 ◦ .
Another important aspect, is that the finch not regularly flaps it’s wings. Depending
on the flight velocity the wing is bounded after several stroke cycles for some time
instances. For higher velocities almost 50% of the time, the small birds hold their
wings close to the body, do not flap them and can save so some energy. This
behaviour can be seen in figure 2.21, where the wingtip elevation and the wingspan
are shown for a flight speed of 2m/s (A) and 12m/s (B). As no lift is generated
Figure 2.21: Representative wing kinematics in a zebra finch engaged in flapbounding
flight at 2m/s (A) and 12m/s (B) [4]
with flapping or gliding during the bounded time span, the aerodynamic properties
of the body come to be crucial.
2.3 Summary
In the following table the characterization of the kinematics of the different investigated
flying animals (Insects-Drosophila fruit fly, rufous Hummingbirds, Shortnosed
Bats Cynopterus brachyotis) are summarized for hovering flight. Note that
morphological data and results out of biological experiments are taken either as average
values or most suited values. Specially for insects like the Drosophila fruit fly,

Chapter 2. Review 18
the accuracy of measurements is limited, because of their small size, and deduced
informations of experiments done with accurate models which represents good results
for the insect flights are presented.
Insects Hummingbirds Bats Siskin
Weight [g]

19 2.3. Summary
Siskin/Finch
Advantages -very maneuverable
-hovering and forward flight possible
Drawbacks -wing folding is significant during upstroke
-no constant flapping frequency for increasing forward flight
speed
-stroke amplitude reduces significantly for increasing forward
flight
Small birds also have an acceptable hover ability. But compared to hummingbirds
it is decreased. According to biologists, the hummingbird’s should can do more
different motions, for which reason crucial changes in the kinematics of the flapping
occur. Also the wrist, the joint at the approximate midpoint of the wing, is more
essential. Specially during upstroke the wing is folded significantly, which would
be very difficult to implement in a MAV. Also for transition from hovering to forward
flight many different flapping parameters are changing significantly, whereas
no resonable simplification for a flapping device can be estimated. Hence, the small
birds, are not taken into account for further investigations.
Bat
Advantages -very maneuverable
-hovering and forward flight possible
-low flapping frequency compared to animal’s size
-can generate greater lift for less energy due to stretchy membrane
Drawbacks -very complex wing structure, more than two dozen independently
controlled joints
-highly articulated motion and complex kinematics
-deforming bones
The study of the bat flight also exclude the bat wing motion as a main input for
developing a MAV. A simple mechanical flapping mechanism could not be realised,
because the wing motion is far too complex, with more than a dozen independently
controllled joints, which would let the MAV be too heavy. Also no simplifications
could be found, which would allow to make a simplified kinematic model and still
follows the wing’s trajectory in a similar way as the natural bat.
However some ideas could be filtered out of the bat-flight as for example, to let the
outer wing parts follow a delayed trajectory with respect to the inner wing parts,
which roughly describes the bat-flight. Also attaching the wing to the tail could be
a reasonable idea.

Chapter 2. Review 20
Hummingbird
Advantages -very maneuverable
-hovering and forward flight possible
-almost no wing folding during upstroke
-at first sight a simplified mimic wing motion is achievable with
a mechanical mechanism
-flapping frequency stays constant for every flight speed
Drawbacks -twisting phenomena along the wing axis is present like in other
birds
-kinematic parameters variation more complex for increasing
forward flight
-pitching is done actively
As can be seen the hummingbird seems to be a reasonable choice for mimicking.
Specially for transition from hovering to slow forward flight, very few kinematic
parameters are changing, which simplifies the later control challenges. For more
increasing the forward flight speed of course more parameters are varied, but for
the first approach this can be neglected. Compared to small birds almost no wing
folding is present, hence the wings can be assumed to designed without a joint, as
it is the case for insects. Although the pitching of the wing is done actively by the
hummingbird, this can be still achieved to copy. As shown above, the pitch angle
also follows a more or less harmonic pattern. The twisting phenomena along the
wing axis, also does not represent a big obstacle, as this can be solved by using
flexible wings, which adapts itself to the aerodynamic loads.
Therefor, to generate first concepts for the flapping wing mechanism, mainly the
hummingbird motion is considered, which could be extended with ideas described
for the bat-flight or simplified by some kinematic aspects of the insect.

Chapter 3
Concepts
3.1 General Considerations
3.1.1 Objective characteristics
As described above, hummingbirds are chosen to mimic. Therefor the dimensions
of the Giant Hummingbird (Patagonia gigas) are taken as a starting point for the
design. According to biologists the kinematics of the Giant Hummingbird are similar
to the above described pattern of the rufous hummingbird and so can be also
considered as the motion which the flapping mechanism has to fulfill.
Dimensions
The following table summarizes the dimensions of the Giant Hummingbird which
are used.
Weight 25g
Wingspan 280mm
Aspect Ratio 6.73
Wingchord ≈ 40mm
Body width ≈ 50mm
Wing length ≈ 115mm
Flapping motion
The general characteristics of the flapping motion are presented in the table below.
Flapping frequency 15 Hz
Stroke Amplitude ≈ 110 ◦
Body angle during hovering 50 ◦
Stroke plane angle during hovering 60 ◦
flapping pattern sinusoidal
chord angle trajectory sinusoidal
max/min chord angle 100 ◦ / -35 ◦
21

Chapter 3. Concepts 22
3.1.2 Flight control
Flapping flight is rather complex when control aspects are considered. For birds and
insects several parameters of the flapping motion are changed to perform different
maneuvers. For some control tasks several different ways can lead to the desired
result. For instance for changing the forward flight velocity the pitch angle of the
whole flying animal is changed. Therefor either the mean flapping angle is changed,
the angle of attack is altered and/or the stroke amplitude is varied. The rolling
angle can be controlled by increasing the flapping amplitude and/or the angle of
attack of the outer wing. For more complicated maneuvers many of the flapping
parameters are changed simultaneously. Of course a flapping mechanism, which can
be controlled in such a way would be much too complex and therefor too heavy for
a MAV. Of course a more deep study is needed for a good flight control, but this
can only be done, when the flapping mechanism is finished and implemented in a
MAV. But as a first approach it is adequate to consider only the simplest control
aspects.
According to biologists, studying the hummingbird’s wing motion, a simple way to
change the flight velocity is to tilt the body angle. As a first approach this can
be done by shifting the center of gravity of the MAV forward or backward and/or
using servos at the tail of the MAV. Changing other parameters of the flapping
motion and taking this into account for developing a flapping mechanism would be
to complicated at this early stage of the project.
To change the flight direction also a simple solution is needed. In general birds
change several parameters, for instance the stroke amplitude and the angle of attack,
of each wing seperately. This again would be to complex, for which reason it is
considered to change the orientation of the tail to deviate the air flow as a first
assumption. Of course this has also to be investigated more deeply, when a flapping
prototype is present.
Therefor the development of a first flapping mechanism can be done independently
of these control aspects. More precisely the flapping device needs only one actuator,
which has to generate the correct motion to produce enough lift force. The control
issues can be solved by using servos which change the orientation of the tail.
3.1.3 Actuator
To have a reasonable design for a MAV as less actuators as possible should be used
to reduce the power consumption and the mass. Also in general the mechanical
complexity then reduces, less joints and links are needed to transfer the forces of
the actuators to the wings and so is more lightweight.
A brief investigation of the available actuators showed, that no reasonable linear
actuator can be used. Either they are too big and too heavy or can not bring
up the force needed for the flapping motion or the linear displacement needed for
the stroke amplitude. As the future MAV is considered to be of a size similar to
the Giant Hummingbird piezoactuators can also be excluded due to the too small
generated forces. DC-Motors can fulfill these first constraints. Some, specially
brushless DC-motors, could be found which have a reasonable torque, an acceptable
power consumption and still a weight which is small enough to integrate in a MAV.
Therefor the flapping mechanism will be designed using a rotary drive system.

23 3.2. Concepts for wing flapping
3.2 Concepts for wing flapping
3.2.1 Concept A
To have a sinusodial flapping motion as it is present for the hummingbird (see
figure 2.12), the main structure of the flapping mechanism can be approximated
with a circular motion, which is generated with a rotational actuator and where the
movement in the direction of one main axis is transmitted to the wings according
to figure 3.1. However in such a way, the sinusodial motion of the wings only can be
approximated. The resulting trajectory of the wing tip depends on the up and down
Figure 3.1: Schematic drawing of concept A1
movement of the centered guided joint, which again depends on the parameters L
and r (see figure 3.2). Only for L going to infinity a perfect sinusodial motion with
amplitude r can be achieved. For a good approximation therefor L has to be chosen
much larger than r. The kinematic relationship is given with equations 3.1 and 3.2
and is shown in figure 3.3 for various ratios L/r 1 .
sin α =
r · cos δ
L
(3.1)
y = r · sin δ + L · cos α (3.2)
Already a ratio higher than 2:1 for L:r can be considered as an approximation
which is good enough to achieve an acceptable sinusodial motion. This can be either
done by increasing L or decreasing r. It is important to point out, that for decreasing
r, which affects the amplitude of the sinusodial movement of the centered joint, also
the distance b has to be adapted according to equation 3.3 to get the desired stroke
amplitude of βmax = 55 ◦ .
b =
r
tan (βmax)
(3.3)
To reduce this dependency of b to the amplitude r, an additional horizontal link
can be inserted according to figure 3.4. Instead one joint, the whole link is moved
up and down and is connected over two joints to the wings to transmit this motion.
Therefor the length of this link can be adjusted and assures more liberty for the
later dimensioning of the different link lengths. However an additionally joint is
needed, which of course reduces the efficiency.
1 Generated with matlab kinematic circular.m

Chapter 3. Concepts 24
Figure 3.2: Sketch for kinematics of general structure for the flapping motion
Figure 3.3: Trajectories of centered joint for one cycle for different ratios L/r
3.2.2 Concept B
This concept is based on the same general structure as concept A, as the given
sinusodial flapping motion does not let much margin for big variations. Therefor the
general kinematic pattern is the same as described above in section 3.2.1. Anyway
the structure presented in figure 3.5 can also be a good solution. The actuator’s
torque is transmitted via two gears to the associated wing. The advantage of this
concept as a starting point for the further designing is, that each wing can be
treated somehow independently of each other in terms of the flapping motion and
leaves therefor more space for further ideas to control each wing independently.
However the additional gears increase the friction and the complexity and so also
the efficiency and the weight respectively.
To increase the robustness of the design, the flapping can be actuated according
to the right side of figure 3.5. Instead of just actuating the wings, a more solid

25 3.2. Concepts for wing flapping
Figure 3.4: Schematic drawing of concept A2
Figure 3.5: Schematic drawing of concept B1 (left) and B2 (right)
tube, where the wings can be inserted in, is moved. This tube can be attached via
a rotational joint to the main structure where also the motor is attached at and
gives so more stability to the flapping device.
3.2.3 Concept C
To reduce the number of the needed joints the actuation can be done by using a
flexible part according to figure 3.6. The bending of the rod at the middle induces
a motion at the wings. For the flexible part a material can be used which has a
good flexibility and still has a enough high stability as carbon or titanium.
For a brief inspection of the feasibility of this concept the theory of mechanics for
calculating the bending line of a rod is used. The bending line can be calculated
according to equation 3.4,
d 2 w(x)
dt 2
= −My(x)
EIy
(3.4)
whereas E is the modulus of elasticity of the used flexible material. The bending
torque in the y-direction My and the moment of inertia in the y-direction of the
rod Iy is calculated as follows
My(x) =
Iy = dh3
12
F x
2
F x
2
for 0 < x < b
− F · (x − b) for b < x < 2b
(3.5)
(3.6)

Chapter 3. Concepts 26
Figure 3.6: Schematic drawing of concept C
The rod’s dimensions are specified by it’s width d and height h as shown in figure 3.7.
Using the boundary conditions 3.7 and integrating equation 3.4 gives the maximal
deflection at the midpoint between the two wing holdings needed to get the desired
stroke amplitude of β=55 ◦ (equation 3.8 2 ).
dw(0)
dt = tan 55◦ , w(0) = 0 , dw(b)
dt = 0 (3.7)
F =
w(b) =
4EIy tan 55◦
b2 −F b3
12EIy
+ b tan 55◦
2b tan 55◦
=⇒ w(b) =
3
Figure 3.7: Calculation of the bending line
(3.8)
Because the deflection of the rod needs a certain force to attain the desired
stroke amplitude, it has to be checked if an actuator can be found, which generates
enough force. Therefor the whole mechanism is modelled in a simplified way as
presented in figure 3.8. It is important to notice that also the following calculations
are just a rough approximation to check for the fundamental feasibility of this
concept and if it has to be investigated more deeply. Also the forces acting on the
wings and the wings itself are not included yet, as these forces can not be calculated
exact enough and so just would blur the results.
The behaviour of the bending rod can be modelled in a simple way as a spring with
a point mass ms, which represents the mass of the link with length L. The spring
constant c and the corresponding force Fc generated by the compressed or stretched
2 matlab file bending line flex.m

27 3.2. Concepts for wing flapping
spring for this arrangement is defined as
c = 48EIy
(2b) 3
(3.9)
Fc = c(y − y0) (3.10)
whereas y0 is the length of the unloaded spring and is set as a first instance for
δ = 0.
Figure 3.8: Sketch for calculation of the dynamics
Fs represents the force acting on the link and M the generated torque by the
actuator. The maximal value for y, which is calculated in equation ?? is equal to
the amplitude of the sinusodial motion. As L ≫ r the radius can be approximated
as r ≈ w(b). Using the laws of conservation of the momentum for the link and the
angular momentum for the rotating disc the following equations of motion can be
derived:
ms · d2 y
dt 2 = Fs cos α − cy + cL cos α0 (3.11)
θ · d2 δ
dt 2 = M − rFs cos δ − α (3.12)
for δ = 0 and θ is the inertia matrix of the rotating disc. Using
equations 3.1 and assuming a constant angular speed ˙ δ the equations for ˙α, ¨α are
where sin α0 = r
L
˙α = − ˙ δ · sin δ · Z −0.5 · r
L
¨α = − ˙ δ 2 · cos δ · Z −0.5 · r
L − ˙ δ · sin δ · r
L · −r2 ˙ δ sin 2δZ −1.5
2L2 (3.13)
(3.14)

Chapter 3. Concepts 28
with Z = 1−r2 cos δ 2
L2 .
Derivating equation 3.2 with respect to time an expression for ¨y is obtained
¨y = −r ˙ δ 2 − L¨α · sin α − L ˙α 2 · cos α (3.15)
Using equations 3.15, 3.13 and 3.14 into equation 3.11 the force on the link can
be calculated during one cycle (equation 3.16). Inserting it into equation 3.12 the
needed torque for the bending is obtained.
Fs = ms¨y − cy − cL cos α0
cos α
(3.16)
For numerical values a carbon rod with dimensions of 0.1mm x 2mm and a
modulus of elasticity of 110 ′ 000 N
mm2 is used. The parameter b is chosen according
to the estimated value of the body width of the hummingbird, which corresponds
to the distance between the two wing mountings as mentioned in chapter 3.1. The
results are presented in figure 3.9, which show the torque M needed during one cycle3 with the maximal value of slightly under 4mNm. The positive torque indicates that
the actuator has to push the link, while negative torques represents the situations
when the actuator has the break the motion of the link due to the reaction of the
spring-like behaviour of the bended rod.
Figure 3.9: Results of the force on the link and the needed torque during one
flapping cycle
It can be seen that with such dimensions for the carbon rod, an applicable
actuator could be found, which is enough lightweight and still can bring up enough
torque 4 . However if the thickness of the rod is increased to 0.2mm, already a much
higher torque is needed and the size and weight of the actuator would grow too
much. Another disadvantage is that the distance between both wing holdings can
not be reduced much more, then again a higher force is needed to bend the flexible
rod. Also the wings are not considered yet, which again increases the torque which
has to be generated by the motor.
Taking these aspects into account a working flapping device using this concept will
not be guaranteed, for too heavy wings no real flapping motion could be produced,
only the flexible part would bend withouth generating the desired motion for the
wings.
3 generated with dynamics flap rot const.m
4 see for instance: www.faulhaber.com

29 3.3. Concepts for wing pitching
3.2.4 Concept D
All the above ideas induce a linear motion between the centered joint and the wing
holding, because of the relatively high stroke amplitude. To get rid off the linear
motion a structure as shown in figure 3.10 could be used. The wing is attached
similar as in concept B2 to a connector, which is attached to the main structure
and can rotate about one axis, allowing to flap the wing in one plane. Between the
connector and the actuation point three joints are arranged so that the link in the
middle does not just move up and down, but rather adopts its orientation that the
joint most proximal to the wing is routed on a circular trajectory and therefor does
not induce a linear motion into the direction of the connector. The kinematics are
Figure 3.10: Schematic drawing of concept D
similar to those described in section 3.2.1. The only difference is that the parameters
have changed places. Here y is determined, it is actuated in a sinusodial way, and
the angle δ, which above described the state of the cycle is now the flapping angle
(see figure 3.10). Note that δ with the additionally inserted joint not makes a
whole cycle. By adapting the correct link lengths and the actuating amplitude,
the maximum opening angle of 55 ◦ can be obtained. The general equations for the
kinematics can therefor easily be taken out of equations 3.1 and 3.2. Hence also no
exact sinusodial flapping motion is present, but using the same convention as above
(L ≫ r) a good approximation can be found.
However this would be a nice solution, this concept needs the most joints of the
described concepts above. Also for implementing this concept later on for a real
MAV could be difficult because the links and the joints have to be guided and
supported to increase the stability of this arrangement.
3.3 Concepts for wing pitching
3.3.1 Active pitching
As showed in chapter 2.2.2 the hummingbird controls the pitch angle (chord angle)
of the wing approximately in a harmonic sinusodial motion for one flapping cycle.
Therefor to mimic the wing motion an obvious solution would include also to control
the pitch angle actively with the same actuator. As showed in chapter 3.2 an
approximated sinusodial flapping trajectory could be produced. By optimizing the
offset between the sine wave of the flapping and the chord angle, setting up the
desired pitch angle for every state of the whole cycle with the same rotary actuator
should be possible. The remaining question, at which point to actuate the wing to
set up the pitch angle has to be investigated.

Chapter 3. Concepts 30
Actuating the wing’s trailing edge
One idea could be to attach the trailing edge of the wing to the main body, where it
is connected to the actuator and is moved according to the flapping cycle to achieve
the desired pitch angle as showed in figure 3.11. As a first approximation roughly
Figure 3.11: Actively adapting pitch angle using the trailing edge
the values of the hummingbird’s flapping trajectory as can be seen in figure 2.12 are
taken. Note that the studies base on the smaller rufous hummingbirds and not the
giant hummingbird, for which reason the dimensions of the rufous hummingbirds
[2] are taken to check the feasibility. The wrist elevation is taken as a cosine wave,
Figure 3.12: Geometric sketch for calculations of the trailing edge motion
while the trajectory of the chord angle has an offset of about 190 degrees to it.
According to the geometric drawing (figure 3.12) the following equation relates the
position of the trailing edge of the wing to the position of the leading edge, which
is described by the wrist elevation.
yT = yL − c sin(α) (3.17)
The resulting trajectories are shown in figure 3.13 5 . The left graph shows the
actual motion of the leading edge, the trailing edge and the original chord angle.
On the right side the cosine wave of the leading edge is shifted over the wave of the
trailing edge to clarify the result. There it can be seen that the trailing edge is not
moved totally harmonic. One half of the cycle is performed a little faster than the
5 matlab file active pitch.m

31 3.3. Concepts for wing pitching
Figure 3.13: Left: Trajectories of leading edge, traling edge and chord angle, Right:
Shifted graph for the leading edge motion for comparison of the harmoinc behaviour
of the trailing edge’s motion
other. This anomaly increases for bigger wings and hence if the dimensions of the
giant hummingbird are used the inaccuracy increases also. If this way of setting up
the pitch angle is used, it has to be considered, that the wing has to be made of a
stretchy material. If the actuation is not done absolutely exact, which is the case if
only one actuator is used, the chord length will vary and induce stress on the wing.
However a big advantage would be that the mechanism for flapping and pitching
could be done in a seperate manner, if the motor lies between both edges of the
wing.
Actuating the wing’s leading edge
As the chord angle describes a sinusodial trajectory as the flapping motion a more
acurate way to control the pitch angle would be to actuate directly the leading edge
rod of the wing as shown in figure 3.14. The pitch control can be done by just a
Figure 3.14: Actively adapting pitch angle using the leading edge
horizontal movement, with the same harmonic behaviour as the flapping motion,
actuated directly on the wing rod of the leading edge at a distance t of the center

Chapter 3. Concepts 32
of the rod. Of course the mechanical structure is not as easy as presented in figure
3.14. As the amplitude for the chord angle is more than 100 degrees, the pin on the
rod drifts away from the actuator tool. This needs a complex pitching mechanism
to have the friction reduced. A simple but not so clean way to solve this, would
be to add a spiral spring which pushes the pin constantly onto the actuator tool.
However a more difficult problem would be, that the same rod is actuated for the
flapping motion and also moves up and down. Hence this mechanism has to be as
near as possible to the body of the MAV.
Despite these design challenges, the advantage of this concept can be showed by
calculating the kinematics. The needed amplitude s of the horizontal movement is
expressed by equation 3.18.
s = t · tan ɛ (3.18)
By putting this amplitude into the same sinusodial motion as the flapping and
adjusting the offset, the simulated pitch angle can be obtained according to figure
3.15 6 . It can be seen, that also here small errors occur. But as the sine wave for the
chord angle only is an approximation and the real chord angle as showed in figure
2.12 even more equals the simulated angle, this method seems to be more accurate
than actuating the trailing edge.
Figure 3.15: Simulated chord angle for horizontal actuation of wing rod
3.3.2 Passive pitching
A more simple way to adjust the pitch angle can be done by let the wing passively
adapt it’s chord angle. This is possible as inertial and aerodynamic loads tend to
decrease the angle of attack. However this would not be as accurate as controlling
the angle actively. But as can be seen in [2] the angle of attack for the hummingbird
flight stays more or less constant during one flapping cycle. Of course at the beginning
of the upstroke and the downstroke the angle of attack will intuitively have
the biggest error according to the desired value. But several other MAV already
use this way for adjusting the pitch angle of the wing with success, for which reason
6 matlab file active pitch2.m

33 3.3. Concepts for wing pitching
this approach can be considered as suitable.
Therefor two main ideas came up. The first one can be used if the wing rod is
inserted into a tube, which is attached to the main structure and is actuated for
flapping (see Concept B2 in chapter 3.2). The main connection between the wing
rod and the tube is done with spiral springs as shown in the sketch in figure 3.16.
If the flapping is performed, the wing tends to decrease the angle of attack and
starts to rotate. As the spring induces a counter-torque to this rotation, a constant
angle of attack could be obtained. Unfortunately there is no way for calculating a
good enough approximation for the forces and torques acting on the wing. Hence
the strength of the springs has to be identified experimentally with a test bench of
the flapping device and completely designed wings. Another approach is to include
Figure 3.16: Sketch of general principle for passive pitching at the hinge
the pitching mechanism already into the wings. The general idea is adopted of
Robert Wood’s Robotic Insect [24]. As shown in figure 3.17 the fibre of the wings
could be designed using a sandwich-like structure. The middle part is made of a
flexible material and is surrounded by a more stiff material. Right beneath the
wing rod of the leading edge, which is actuated for flapping, the stiff material is
removed, and lets the wing surface rotate around the leading edge. By investigation
the maximal pitch angle can be adjusted by removing more or less of the stiff
material. If the angle increases, a touching of the outher parts occur and blocks a
further bending of the flexible material. Also the flexible material can be modelled
Figure 3.17: Passive pitching done at the wings
as a spring, wherefor like for the first approach, the correct adjustments have to be
done experimentally. However this idea saves weight and reduces the complexity
of the flapping mechanism. Another advantage is, that this approach for pitching
the wing only depends on the wings and not on the mechanism which generates the
flapping motion. In contrast the first approach, using springs, already presumes
some construction elements for the attachement of the wing to the main body.

Chapter 3. Concepts 34

Chapter 4
Evaluation
4.1 Evaluation of concepts
After generating different ideas for the flapping motion, these concepts will be evaluated
according to several criteria described below, to chose the most suitable concept
as a starting point for the CAD design. As not all exact dimensions and parameters
for the above described concepts are present yet, this evaluation is done in a more
qualitative way. Nonetheless this selection is important as it affects the whole future
design process.
4.1.1 Criteria
The concepts are evaluated according to following critera:
• Weight
• Size
• Robustness
• Mechanical complexity
• Expected power consumption
• Accuracy
Note that some criteria are overlapping and depend on each other. For instance a
mechanism which is more complex and needs more joints, also in general consumes
more power. The most important aspects for a MAV are the weight, as it has to
be minimized or should left space for further weight reduction, and the power consumption,
which also needs to be as low as possible. It would not make sense to
integrate a flapping mechanism in a MAV, which consumes too much power and
needs a bigger battery, which again increases the weight. However the expected
power consumption can not yet be determined accurate enough, to get significant
differences between the various concepts for the flapping motion, whereas mainly
the number of joints and the generated friction is taken as an indicator for the
performance in terms of power-saving.
The general dimensions are already fixed at this stage (see chapter 3.1), for which
reason the size more indicates the feasibility to minaturize the mechanism, but has
less priority as the actual dimensions are considered to be small enough for a prototype
MAV. Also the robustness plays an important role. The mechanism has to
be stable enough to achieve a flapping frequency of 15Hz. Many links decrease the
35

Chapter 4. Evaluation 36
robustness too. To stabilize them, they need to be guided somehow on the main
structure of the MAV, which would again increase the complexity and induce more
friction. The accuracy is only used for evaluating the concepts of the pitch motion,
which differ for each concept. Due to the fact that all concepts for the flapping
motion base on the same general principle, all generate the similar wing beat trajectory
as shown in chapter 3.2.1, for which reason this criterion is not used for the
flapping concepts.
Taking into account the above considerations an evaluation matrix can be generated
with weights indicating the importance of each criterion:
Criterion Weight
Weight 6
Size 1
Robustness 4
Mechanical complexity 5
Expected power consumption 5
Accuracy 3
4.1.2 Flapping concepts
Using the above matrix the concepts of chapter 3.2 are compared to each other and
a rank is assigned (6 is the best and 1 is the worst), considering the facts described
above and in chapter 3.2.
Weight Size Robust. Mech.
Complex.
Concept A1 5 3 3 5 6
Concept A2 4 2 4 4 5
Concept B1 2 6 5 3 2
Concept B2 1 6 6 2 2
Concept C 6 1 2 6 3
Concept D 3 4 1 1 4
Power
Consumpt.
The outcome of this comparison is shown in the table below, where the total points
and the rank (1 best, 6 worst) are presented.
Total Points Rank
Concept A1 100 1
Concept A2 87 3
Concept B1 63 4
Concept B2 56 5
Concept C 90 2
Concept D 51 6
As can be seen, concept A1 seems to be the most suitable to be used as a starting
point and is therefor used as a guidance for the CAD design. Concept C also seems
reasonable to be followed. Nonetheless it is neglected, due to the big uncertainty
for the feasibility, how it was described in chapter 3.2.3.
4.1.3 Pitching concepts
This process is repeated for the concepts described in chapter 3.3 and again presented
in tables below.

37 4.2. Expected weight
Weight Size Robust.
Active-Trailing Edge 2 2 2
Active-Leading Edge 1 1 1
Passive-Spring 3 3 3
Passive-Wing 4 4 4
Mech.
Complex.
Power
Consumpt.
Active-Trailing Edge 2 2 3
Active-Leading Edge 1 1 4
Passive-Spring 3 3 2
Passive-Wing 4 4 2
Total Points Rank
Active-Trailing Edge 51 3
Active-Leading Edge 33 4
Passive-Spring 69 2
Passive-Wing 90 1
Accuracy
For the pitching motion of the wing, the concepts for passive wing pitching are
superior using this evaluation method. This is certainly the case, because the evaluation
matrix is laid out in such a way, that the whole mechanism stays simple and
is as lightweight as possible. If experimental data would be available, how more lift
force with a more accurate pitching motion can be generated, the weight for the
accuracy can be adapted. For instance, if the more complex and heavier mechanism
for actively controlling the pitch motion of the wing, regains more lift force than
the additional weight needed, controlling the wing’s pitch angle actively would be
superior to the concepts for passively controlled wing pitch angles.
However, for this first approach developing a flapping mechanism, passiv wing pitching
is adequate.
4.2 Expected weight
Knowing on which concept to focus on, first speculations on the expected weight
of the MAV can be made. Using the dimensions of chapter 3.1 the weights of the
different parts can be estimated. Note that in the following only a rough approximation
is done, which is based on an internet research of several suppliers of parts
for model aircrafts 1 .
The wings are assumed to have the structure out of carbon, which is covered with
mylar as shown schematically in figure 4.1. Three carbon (1.55g/cm 3 ) rods with
diameter of 2mm can be used as support to attach the 0.0005mm thick mylar sheet
(7g/m 2 ) on it. With this design, one simple wing weights about 1.5g.
As mentioned above two servos are needed for control purposes, whereas each one
weights about 1g. Including the weight of the RC receiver (1g), the brushless DC
motor (≈ 6g) and the battery (6.5g), the electronic payload measures about 15.5g.
A reasonable approximation for the structure of the MAV, which includes the found
concept for the flapping mechanism, would be about 10g.
Therefor the expected weight of the MAV can be assumed to be ≈ 30g.
1 for instance www.microbrushless.com

Chapter 4. Evaluation 38
Figure 4.1: Structure of the wing
4.3 Expected power consumption
Using the expected weight of 30g, the needed mechanical power can be calculated.
According to [1] the mechanical power can be expressed by following equation:
W
P = W
(4.1)
2ρSE
where W = mg ≈ 0.29N is the total mass in expressed in [N], ρ = 1.29kg/m3 the
air density and SE is the effective operational area or sweeping area of both wings.
Usually the sweeping area can be considered to be about 70% of the circular disc S
swept by both wings [1]. Rewriting equation 4.1 as follows
W
S
P = W
2ρ SE
(4.2)
S
and inserting SE
≈ 70%, W
= 31.52 N
we obtain for the power P = 0.393W .
S S m
According to [1] an efficiency coefficient for the hover ability has to be included. As
the wing motion will be similar to the hummingbird’s wing motion, it is reasonable
to take the same value for the coefficient ηH = 60%. Including the mechanical
efficiency of the mechanism ηM
according to equation 4.3.
the total needed mechanical power is calculated
Ptot = P
ηHηM
(4.3)
The efficiency coefficient for the mechanism ηM can be calculated by summing up
the efficiency of the joints (≈ 80% for each joint) and the efficiency of the motor,
which is typically around 60% for the chosen brushless DC motor 2 . Considering the
above chosen concept, the total needed mechanical power is about 1.36 W.
With this estimated value, the range for finding an appropriate motor can be constrained.
However, as the objective of this project is not to build the whole robot,
this calculation just strengthens the evidence that such a motor can be found, which
can fulfill the power and the weight requirements. Also the electrical power consumption
can then be calculated, when the best matching motor could be found,
which allows to estimate the time the MAV could fly, without recharging the batteries.
2 see for instance www.wes-technik.de

Chapter 5
CAD Design
The ’winner’ concept of chapter 4.1 is now converted into a test bench, using 3D
CAD software. As the forces on the wings are still unknown and just can be identified
experimentally in a correct manner on a finished flapping mechanism, no exact
stability calculations can be done for the different parts of the flapping device. Also
those forces highly depend on the wing design. Therefor it is considered to make
the flapping mechanism as robust as possible, trying to copy the kinematic of the
hummingbird and neglect weight constraints. Hence, the weight reduction has to
be done later on, when also the wings are completely designed and measurements
are done using the designed test bench, but this is not part of this project.
5.1 Overview
The resulting mechanism can be seen in figure 5.1. It has a width of about 12cm,
a length of 14cm and a height of about 8cm. All the parts needed for flapping are
attached to 2mm thick aluminium plate, which is screwed on two shorings. These
shorings have an inclination of 10 ◦ which corresponds to the stroke plane angle
with respect to the horizontal of the hummingbird’s wing motion. A DC-motor
with a planetary gearhead (reduction ratio 3.71:1) is attached below the plate and
transmits the generated torque to a link, which starts to rotate. The datasheets
for the motor and the gearhead can be seen in the appendix. This rotating link
is connected via a pin to another link, which is guided on the other end in such a
way, that this end point is always centered between the two wing joints. Therefor
two ball bearings are needed to allow the transmission link to rotate freely. Due
to the circular motion of the rotating link, the transmission link is moved forward
and backward, which produces the same kinematic pattern as calculated in chapter
3.2.1. This movement is transmitted via another pin to two wing attachements,
which are placed on wing joints, playing the role of center of rotation for the movement
of these attachements.
Due to time constraints, all parts were printed, except the ball bearings, the aluminium
plate and the pins, which were made of steel. Therefor the dimensions of
the links had to be chosen big enough to assure the stability. However the links are
supported in the vertical direction only on one point, the connecting point to the
motor, which has to carry both links. Therefor the connection at the ball bearings
have to be very tight, to ensure that the bending moments, caused by gravity, are
as small as possible.
39

Chapter 5. CAD Design 40
Figure 5.1: Overview of resulting mechanism
5.2 Transmission of motor torque
To transmit the torque from the motor the following assembly is used (see figure
5.2). The rotating link has a fork like structure, where the motor shaft is in-between,
with the notch aligned at the face of the link. A small part, which fits between the
two legs of the link, is pushed on the motor shaft and attached to the link using
a screw. The dimensions were chosen such that, by inserting the screw, the small
part is pressed against the motor shaft. However this is not absolute necessary, as
already the notch secures the connection. Nonetheless this force fitting again gives
a more secure force transmission.
Figure 5.2: Connection of motor to rotating link

41 5.3. Joints
5.3 Joints
Assuring that the transmission link and the wing attachements can follow the considered
motion, the joints are the most important parts. However this part could
not be solved perfectly. Pushing the center joint forward and backward, the distance
between it and the wing joints changes. As the stroke amplitude is wanted
to be 110 ◦ , the variation of the distance is a bigger problem and can not be solved
with this general structure. Therefor either the center joint can be optimized, using
ball bearings to reduce friction, and at the wing joints a loose connection is needed,
or the wing joints are optimized, but then again the center joint will cause more
friction.
For increasing the stability, the second approach is better, as the wings then are
guided more accurately, for which reason the center joint is a more loose connection.
Center joint
Hence the connection of the transmission link to the wing attachements is done
according to figure 5.3. The pin is guided through big slots in the wing attachements.
During the forward and backward motion of the pin, the attachements are pushed
to follow its way. Due to the movement of the pin in the slots friction occurs. To
optimize this design the wing attachement has to be made of different materials.
The touching area with the pin could be of a material which has low friction, while
the rest should be made of a stiff and lightweight material. Nonetheless, this design
is still acceptable as a first approach, as the friction still is pretty small.
To have the center joint stay always centered, it has to be guided. This is done by
a slot in the aluminium plate, where the pin is moved in. To decrease the friction a
ball bearing is glued to the pin. Note that the diameter of the ball bearing is just
slightly smaller than the width of the slot, to assure that the ball bearing does not
brake itself, when from both sides a touching occurs.
Figure 5.3: Design for guiding the center joint

Chapter 5. CAD Design 42
Wing joint
As described above, the wingjoint is optimized. Therefor two ballbearings are used.
One inside the structure of the wing joint, the other lying above. On the upper ball
bearing the wing attachement is arranged in such a way that only the inner part of
the ball bearing is touched. The outer part is then connected only to the motionless
structure of the wing joint. To attach the wings, holes with a diameter of 2mm and
Figure 5.4: Assembly of wing joint
a depth of 20mm are made into the wing attachements as can be seen in figure 5.5.
To increase the stability, the structure is thickened around the holes.
Figure 5.5: Structure of the wing attachments

Chapter 6
Conclusion
The resulting mechanism, designed according to the kinematic requirements of the
desired flapping motion, is acceptable. Due to time constraints no exact measurements
with the manufactured mechanism could be done. Also no information of the
generated lift force can be deducted, as this is only possible to measure when the
wing designing is done, which includes the adjustment of the wing’s flexibility for
the pitching. And at this time, the mechanism consists of a mock-up of the wings.
However it can already be seen, that the flapping motion follows the kinematic
pattern as described in chapter 3.2.1, which is a good approximation for the hummingbird’s
flapping. Also first tries showed, that the flapping frequency of 15Hz is
reachable, although still many improvements can be done.
The biggest improvements can be done for instance at the center joint. There is still
relatively much friction present, which could be reduced. Also the guidance of the
center joint leaves much space for enhancement. Nonetheless the strongly varying
distance between the center joint and the wing joint, can not be eliminated with
the chosen concept, for which reason it can also be considered to choose another
approach for the design, which reduces this weakness. Another reasonable concept,
would be to pitch the wing actively using the same actuator as for the flapping (see
chapter 3.3.1), in the case the passive pitching would fail to deliver enough lift force.
But most of these investigations can only be done after the next steps, for instance
the wing design, are finished. With appropriate wings, also exact measurements
can be done and the generated lift force can be discovered. Using a high speed
camera, a more exact comparison of the resulting motion and the hummingbird’s
wing motion can be done. Further, if these tasks show good results, implementing
this motion into a real MAV would be the next step to the final objective of a flying
flapping wing MAV.
Concluding, as this project is the first step in the direction of designing a Flapping
Wing MAV, many useful informations and experience could be gathered, which for
sure support further investigations into this direction.
43

Chapter 6. Conclusion 44

Appendix A
Motor datasheet
45

Appendix A. Motor datasheet 46

Appendix A. Motor datasheet 48

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