development of flapping wing mechanism

Oliver Breitenstein

Development of a FlappingWing Mechanism

Semester Project

Autonomous Systems Lab (ASL)Swiss Federal Institute of Technology (ETH) Zurich

Supervision

Dr. Samir Bouabdallah, Stefan Leuteneggerand

Prof. Dr. Roland Siegwart

Spring Semester 2009

Contents

Abstract iii

Acknowledgements iv

1 Introduction 1

2 Review 32.1 Aerodynamics of flapping wings . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Wagner Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 Leading edge vortex . . . . . . . . . . . . . . . . . . . . . . . 32.1.3 Clap and fling mechanism . . . . . . . . . . . . . . . . . . . . 42.1.4 Rotational lift . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.5 Wing-wake interactions . . . . . . . . . . . . . . . . . . . . . 62.1.6 Lift force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Flapping wings in nature . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Insects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 Hummingbirds . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.3 Bats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.4 Birds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Concepts 213.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Objective characteristics . . . . . . . . . . . . . . . . . . . . . 213.1.2 Flight control . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.3 Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Concepts for wing flapping . . . . . . . . . . . . . . . . . . . . . . . 233.2.1 Concept A . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.2 Concept B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.3 Concept C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.4 Concept D . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Concepts for wing pitching . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Active pitching . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Passive pitching . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Evaluation 354.1 Evaluation of concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1.1 Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.2 Flapping concepts . . . . . . . . . . . . . . . . . . . . . . . . 364.1.3 Pitching concepts . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Expected weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3 Expected power consumption . . . . . . . . . . . . . . . . . . . . . . 38

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5 CAD Design 395.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.2 Transmission of motor torque . . . . . . . . . . . . . . . . . . . . . . 405.3 Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6 Conclusion 43

A Motor datasheet 45

ii

Abstract

This project aims at the development of a bio-mimetic propulsion mechanism fora Flapping Wing Micro Aerial Vehicle, without considering the aerodynamics ofthe wings in the design. This artificial bird will be the size of approximately 10-20cm. Therefor the aerodynamic phenomena in flapping flight are studied andsummarized. 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 naturalflappers. The aerodynamic and kinematic pattern of hummingbirds, bats, insectsand small birds are summarized. Based on this review several different concepts ofmechanisms for flapping wings are generated, which are seperated for the flappingmotion and the pitching motion. Using a qualitative evaluation, the quality ofthe concepts are determined according to different criteria such as weight, size,robustness, mechanical complexity, expected power consumption and accuracy. Thebest concept is used as basis for a 3D CAD design of the mechanism, which shouldmainly reproduce the desired kinematics. During the design process the focus isset more on getting a robust and simple mechanism, which could be used as a testbench for further investigations and measurements. Concluding, the mechanism ismanufactured and assembled to prove the feasibility.

iii

Acknowledgements

Id like to thank Dr. Samir Bouabdallah and Stefan Leutenegger for their goodguidance and the useful inputs they contributed. Specially during the last part, theCAD-Design, when time was short, their experience was very supportive. Also Idlike to thank Dr. Bret Tobalske from the University of Montana and Maria Joseof Berkeley, giving me deeper informations about the hummingbird flight, whichhelped me alot understanding the crucial parts of it for developing a mimickingflapping device.

iv

List of Figures

1.1 Schematic drawing of DelFly I taken from www.delfly.nl . . . . . . . 11.2 Flapping wing mechanism of ROBUR taken from IROS 2007 www.flyingrobots.org 2

2.1 Leading edge vortex on the wing[19] . . . . . . . . . . . . . . . . . . 42.2 Evolution of a leading edge vortex in (A) two dimensions and (B)

three dimensions during linear translation starting from rest [19] . . 42.3 Schematic representation of the clap (A-C) and fling (D-F) [19] . . . 52.4 Three phases of the wing rotation [7] . . . . . . . . . . . . . . . . . . 52.5 Wing-wake interaction during stroke reversal [19] . . . . . . . . . . . 62.6 Flight forces for the drosophila during hovering [21] . . . . . . . . . . 72.7 General pattern for the wing motion of Drosophila Melanogaster [16] 82.8 Kinematics of Drosophila Melanogaster [9] . . . . . . . . . . . . . . . 82.9 Force production in two cycles [16] . . . . . . . . . . . . . . . . . . . 92.10 Wing motion relative to the body flying at velocities of 0 12ms1 [2] 102.11 Angles describing bird-centered wing and body kinematics in rufous

hummingbirds [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.12 Variation of chord angle relative to body-plane during wingbeats at

velocities of 0 12ms1 [2] . . . . . . . . . . . . . . . . . . . . . . . 122.13 Wake structures in frontal and side plane [17] . . . . . . . . . . . . . 132.14 Flow field vorticity at end of upstroke, (a) frontal view at shoulder-

plane, (b) side view at midwing-plane [17] . . . . . . . . . . . . . . . 132.15 Anatomical structure of the bat wing [5] . . . . . . . . . . . . . . . . 142.16 Sequences of images from below and in front of bat during on cycle

starting at beginning of the downstroke [6] . . . . . . . . . . . . . . . 142.17 Example trajectories of the different wing regions for 3m/s (left) and

9m/s (right) [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.18 Example of wing tip motion [6] . . . . . . . . . . . . . . . . . . . . . 152.19 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 positionduring the downstroke [10] . . . . . . . . . . . . . . . . . . . . . . . . 15

2.20 Wingspan ratio as a function of flight velocity compared among birdspecies [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.21 Representative wing kinematics in a zebra finch engaged in flap-bounding flight at 2m/s (A) and 12m/s (B) [4] . . . . . . . . . . . . 17

3.1 Schematic drawing of concept A1 . . . . . . . . . . . . . . . . . . . . 233.2 Sketch for kinematics of general structure for the flapping motion . . 243.3 Trajectories of centered joint for one cycle for different ratios L/r . . 243.4 Schematic drawing of concept A2 . . . . . . . . . . . . . . . . . . . . 253.5 Schematic drawing of concept B1 (left) and B2 (right) . . . . . . . . 253.6 Schematic drawing of concept C . . . . . . . . . . . . . . . . . . . . . 263.7 Calculation of the bending line . . . . . . . . . . . . . . . . . . . . . 263.8 Sketch for calculation of the dynamics . . . . . . . . . . . . . . . . . 27

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3.9 Results of the force on the link and the needed torque during oneflapping cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.10 Schematic drawing of concept D . . . . . . . . . . . . . . . . . . . . 293.11 Actively adapting pitch angle using the trailing edge . . . . . . . . . 303.12 Geometric sketch for calculations of the trailing edge motion . . . . 303.13 Left: Trajectories of leading edge, traling edge and chord angle,

Right: Shifted graph for the leading edge motion for comparisonof the harmoinc behaviour of the trailing edges motion . . . . . . . 31

3.14 Actively adapting pitch angle using the leading edge . . . . . . . . . 313.15 Simulated chord angle for horizontal actuation of wing rod . . . . . . 323.16 Sketch of general principle for passive pitching at the hinge . . . . . 333.17 Passive pitching done at the wings . . . . . . . . . . . . . . . . . . . 33

4.1 Structure of the wing . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.1 Overview of resulting mechanism . . . . . . . . . . . . . . . . . . . . 405.2 Connection of motor to rotating link . . . . . . . . . . . . . . . . . . 405.3 Design for guiding the center joint . . . . . . . . . . . . . . . . . . . 415.4 Assembly of wing joint . . . . . . . . . . . . . . . . . . . . . . . . . . 425.5 Structure of the wing attachments . . . . . . . . . . . . . . . . . . . 42

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Chapter 1

Introduction

Over the past twenty-five years interest in small unmanned aerial vehicles has greatlyincreased. Specially for reconnaissance and surveillance missions these vehicles areof great use. Most of them, which are used today incorporate traditional methodsfor lift and thrust, a propeller for thrust and fixed wings with an appropriate profileto gain enough lift. Also rotary drive systems as can be seen by helicopters are usedby some. However natural flying creatures are still superiour in terms of manoeu-verability, 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 in-stance lightweight and robust materials and better batteries, make this task morefeasible and therefor the field of research of Flapping Wing MAVs has increasedremarkably over the past years.Several Flapping Wing MAVs are already developed. The most successful is theDelFly, which has been realised by a group of undergraduate students at TU Delftin the Netherlands. Many other vehicles built so far use two wings, as it can beobserved in nature at birds. DelFly is more a copy of the dragonfly, it uses two pairsof wings (see figure 1.1). The wings flap in counterphase and almost touch eachother when they come together, for which reason it is assumed that it makes use ofthe clap-and-fling effect (Chapter 2.1.3). However the question, why this conceptworks so well is still open, the investigations and measurements to reveal the secrethave 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 otherpromising projects are still ongoing. For instance ROBUR from the University ofParis, France. It has bigger dimensions, comparable to them of a seagull, and usesa more heavy and complex mechanism (figure 1.2), but again can perform muchmore wing motions. It can independently control the pitch angle of the wing andthe flapping speed.

Figure 1.2: Flapping wing mechanism of ROBUR taken from IROS 2007www.flyingrobots.org

Another project from the University of California, Berkely, which investigates smallerdimensions is the robotic insect of Robert Wood [24]. It is at-scale of insects andhas a fascinating lift production for this small scale. However longer flights are notpossible, as the lift is indeed enough to let the Robotic insect fly, but also to carrya battery and control modules is due to limitations of the actual technology not yetpossible.

In the following chapters, it is presented how a flapping wing mechanism for anartificial bird with a size of approximately 20cm is developped. This project is thefirst step into this direction. Therefor in chapter 2 a detailed literature review isdone to see which natural flapping flyer is most suitable for mimicking. Also brieflythe general aerodynamic phenomena of flapping wings are summarised, which haveto be considered and could give useful inputs. The result of this investigation isthen used as a starting point to generate different concepts (chapter 3), withoutgoing too deep into the design and only theoretical calculations are done to checkthe feasibility. In chapter 4 the concept are compared with each other and the bestis 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 aero-dynamic phenomena. Most of the airflow is turbulent and due to permanentlychanged wing position and orientation, more the unsteady aerodynamics have tobe considered. Because these informations could be of use for the development of aflapping wing mechanism, in this section shortly the main aerodynamics phenomenaof 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 vorticesdo not immediately get their steadystate value. The circulation slowly approachesto it. This delay results of a combination of two phenomena [19]. Firstly the fluidis not perfect, meaning it has a viscous behaviour on the stagnation point and soit takes some time to establish the Kutta condition. Also during the process thevorticity is generated and again shed at the trailing edge, while this shed vorticityforms a starting vortex. The velocity field near the wing, which is induced by theshed vorticity at the trailing edge counteracts to the bounding of the vortex to thewing. Only when the starting vortex has moved enough far away of the trailingedge, the moved wing gets its maximum circulation. This slow developement ofcirculation was first proposed by Wagner in 1925 and so is called as the Wagnereffect.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 itcan be neglected for flapping wings. However for more detailed studies of theaerodynamics, 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 angleof attack leads for a steady flow regime to flow separation and stall. However inunsteady flow, the created vortex at the leading edge, stays attached to the wing fora great part of the downstroke. This attached vortex induces a velocity downwardsand so increases the lift force as shown in figure 2.1. Only when the vorticity of theleading edge vortex gets too large, the flow is not reattached before the trailing edgeany more and a trailing edge vortex is formed, where the wing is in state similarto 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 ofthe leading edge vortex for a translating wing starting from rest is shown in figure2.2. 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) threedimensions during linear translation starting from rest [19]

is more stable and no trailing edge vortex forms. Several different studies try toexplain the stability of the formed leading edge vortex [12] [3], which is only presentfor the three-dimensional case. But still newer studies show, that the LEV has longbeen 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. Herethe 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 edgesare increasing their distance to each other, which is called as fling. So an openingangle is created. When the wings then start their downstroke, air is sucked into thisfunnel-like geometry, which induces a bound vortex at the leading edge of each ofthe wings, and each created vortex acts as a starting vortex for the other wing. Asdescribed by Weis-Fogh [22] this annihilation allows the circulation to be builded upmore 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 inducedvelocity, light blue arrow shows the net force on the airfoil.

advantage of the clap is that the created vortices during upstroke are vanishingduring 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, whilethe clap is not performed by all insects. According to Ellington [8] the clap isavoided by most of the insects because the permanent clapping can damage thewings and more a almost clap is performed. Also for birds similar observationswere made, for instance during the takeoff of pigeons [14]. Although no full clap andfling 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. hum-mingbirds) are rotating their wings, which allows to maintain a positive angle ofattack 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 d and u re-spectively. indicates the angular velocity. This rotation at the end of each stroke,also gives additional lift. According to Dickinson the generated lift force stronglydepends on the the position of the rotation axis. For instance rotations about thetrailing edge show a better lift generation compared to rotations about the leadingedge 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 withthe 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 bluearrows presents the aerodynamic force

phase (A), the wing starts the rotation (B), which causes the vortices at the edgesto shed off the wing (C). This induces a strong velocity field, which pushes againstthe 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 wing-wake interaction also allows to let the pitch motion of the wing done passively, asthis additional lift, at the beginning of the stroke, rotates the wing to the desiredorientation, 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 mostimportant one is the LEV, because it is the only one, which is responsible for liftduring the flapping, the translational phases of the strokes. The other three effectsenhance the lift production mainly during the rotational phases. In figure 2.6 anexample of the generated lift force is shown. During hovering, the horizontal com-ponent of the red arrows in figure 2.6 cancel out during one whole stroke cycle. Thevertical component equals the body weight.Of course the wings play also an important role for the produced lift force. Like forfixed wing aircraft, the wing profile determines lift and drag coefficients (CL andCD). 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 abovedescribed LEV, which induces a force normal to the wing surface. Hence the resul-tant force is drag- and lift force in one hand. Therefor to have a similar descriptionas for fixed wing flight Dickinson [20] defined a circulatory coefficient, which can bemerged out of the usual drag and lift coefficient.

CT =C2D + C

2L (2.1)

However, this coefficient also has to be determined experimentally. Also for a givenwing profile, and known lift- and drag coefficients for a steady flow regime, thereis no way around to obtain the circulatory coefficient, but to make experimentalmeasurements, because the unsteady effects of the flapping flight give differentresults.

2.2 Flapping wings in nature

For developing a flapping wing mechanism different flying animals are studied. Asthe future MAV should have the ability to hover, mainly animals with hovering ca-pabilites are examined. Also the dimensions should approximately match the MAV,that for a first approach the feasibility can be taken for granted. Therefor in thissection 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 flappingwing mechanism, some ideas may be extracted and hence roughly the kinematicsand 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 makesdepending on the insect, different motions. Oval, figure-eight or pear-shaped tra-jectories [16], or combinations of those patterns are done. Also some insects maychange the stroke trajectory for strong manoeuvers. And for increasing forwardflight again other wing motions occur. Because this is a wide range, the most sim-ple 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 otherinsects see for instance [16] [9].

Wing motion

In the most common form of hovering in insects the wings move along an approxi-mately horizontal stroke plane with approximately equal and relatively high anglesof attack during the downstroke and upstroke. This is done by fast rotating thewing 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 mo-tion depending on the insect. For the Drosophila Melanogaster the stroke trajectoryis more a triangular motion with an amplitude of 130-160 degrees and a flappingfrequency of 250 Hz. The stroke plane angle with respect to the horizontal is about10 degrees, while the body angle is tilted about 60 degrees. These values measuredby [9] are presented in figure 2.8. Another important aspect is the ratio of theduration of the downstroke compared to the upstroke, which is approximately 0.8and 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 isrepresented by an arrow


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, whichmay generate up to 66% of the total lift in insect flight [23]. Consequently the highangle of attack to create the LEV is crucial for generating enough lift force.The almost symmetric stroke pattern, meaning that upstroke and downstroke arevery similar as described above, 50% of the resulting lift force comes out of thedownstroke, respectively out of the upstroke. Also the wing material is flexible, suchthat a camber occurs, which additionally gives lift force. Due to no morphologicalconstraints this camber is inverted during the upstroke, which allows to maintainalmost 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 ofmeasurements made with a flapping device having the similar stroke trajectory asthe 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 wings angle of attack (blue) and heaving motion (green)

It can be seen that the lift force is generated during up and downstroke. Also theclap and fling plays a role at the transition of the down- and upstroke and generatesextra lift force. It is important to notice that the generated lift force highly dependson the stroke trajectory [16]. One can assume that if a wing is moved with thesame angle of attack and rotational velocity, the same lift force should occur. Butdifferent stroke trajectories change the airflow pattern, the created vortices and sothe 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 oftheir practical properties for experimental measurements in the wind tunnel. Theycan be trained and thrive well in captivity. Although they have a body mass of3-4g and a wing span of 110mm and so would be too small and lightweight for aprototype MAV, their wing motion still can be mimicked because the biggest ex-isting hummingbird, the Giant Hummingbird (Patagonia Gigas) has according tobiologists in general patterns the same kinematics, weights about 20g and has awingspan of 280mm.

Figure 2.10: Wing motion relative to the body flying at velocities of 0 12ms1 [2](A) Dorsal view with bird silhouette at mid-downstroke. (B) Lateral view with bird silhouette atstart of downstroke.

Wing Motion

The rufous hummingbird flaps their wings with a frequency of 40-45 Hz. For biggerspecies the flapping frequency decreases. For instance the giant hummingbird has aflapping frequency of about 10-15 Hz. The main characteristics of the wing motionfor several different forward flight speeds (0m/s12m/s) can be seen in figure 2.10.Black circles indicate position of wingtips, white circles indicate position of wristswhich is approximately in the middle of the wing.


During upstroke of slow flight (0m/s and 2m/s), the tips and wrists trace in reversenearly the same paths that were exhibited during downstroke. The lateral view re-veals the wingtip describing an upwardly concave path, where the tips also followa slight horizontal figure-8 pattern. In figure 2.12 the flapping motion is shownmore detailed. The wrist elevation indicates the position of the wrist relative to themid-frontal plane, which is described by the birds torso, and the chord angle de-scribes the pitching of the wing with respect to this body plane. It can be seen thatthe flapping motion is sinusoidal, where the downstroke is performed insignificantlyfaster than the upstroke. Also the chord angle follows a sinusoidal trajectory, witha phase shift and an offset compared to the wrist elevation.

Figure 2.11: Angles describing bird-centered wing and body kinematics in rufoushummingbirds [2]

is the body angle w.r.t. horizontal, h and b is the stroke plane angle relative to horizontalrespectively to body angle

During upstroke almost no wing folding is present. According to [2], [17] thewingspan ratio upstroke:downstroke is about 0.98 for slow flight and decreases to0.90 for faster flying speeds up to 12m/s, where most of the flexing is done at theouter parts of the wing, between the wrist and the tip. As for slow speeds thisratio stays more or less constant, the wings can be taken as kinematically rigidcompared to other avian species.As can be seen in figure 2.11 for transition from hovering to a forward flight speedof 2m/s the stroke plane angle with respect to the body b can be assumed to beconstant. In general mainly the body angle is tilted to achieve a forward velocityfor slow flight speeds. For higher speeds of course more parameters are varyingsignificantly. For instance it can be seen in figure 2.12 that the maximal chord an-gle reduces significantly for increasing forward flight speed and generally the strokeamplitude increases.

Aerodynamics

Although the aerodynamic characteristics of the hummingbirds wingbeat are verycomplex, several studies reveal some useful information. The main flow patterncan be described as shown in figure 2.13. During the flapping motion trailing-tipvortices are created. These vortices induce starting and stopping vortices of thedownstroke. The resultant air circulation origined of these vortices are the maineffects, besides the usual aerodynamic phenomena of flapping wings (Section 2.1),which are adequate to support the weight of the hummingbirds. A more detailedillustration can be seen in figure 2.14.


Figure 2.12: Variation of chord angle relative to body-plane during wingbeats atvelocities of 0 12ms1 [2]Wingbeat duration is expressed as a precentage of entire wingbeat. Broken line indicates wristelevation 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 createdat the leading edge of the wing during the rapid wing pronation at the beginningof the preceding downstroke, and carried through the downstroke to be shed duringthe supination at the beginning of the upstroke. The resultant airflow downwardsgives the needed lift force for hovering.More studies on the airflow revealed that a force asymmetry between upstroke anddownstroke is present. Hummingbirds produce 75% of their weight support during


Figure 2.13: Wake structures in frontal and side plane [17]

the downstroke and only 25% during the upstroke [17], although the kinematics ofthe wing motion is symmetric, as for insects. It is assumed that this asymmetryis present due to slight difference of the angular velocity during downstroke andupstroke, a missing leading edge vortex during upstroke and several musculoskeletaland planform material properties, which do not allow the hummingbirds wing tobehave equally efficient as the insects wing. For instance during the downstrokethe wing is slightly cambered, while during the upstroke the wing is not capable toinvert 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 shoulder-plane, (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 someother anatomical aspects [15]. But as the wing motion was observed to be similarfor most of the species [18], mainly the studies about the lesser short-nosed fruitbat Cynopterus Brachyotis are considered, which give a sufficient insight to theaerodynamics 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, whichcan be controlled independently [5] and has bones that deform adaptively duringthe motions of the wingbeat cycle. Of course this anatomical structure is crucial forthe motion of the wing and so very complex trajectories are fullfilled. As can be seenin figure 2.16 the general motion is characterized by a cambered wing during thedownstroke, and a folding of the wing during the upstroke. To simplify the upstrokeit could be described as additional delays for joints approaching the thorax with


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 cyclestarting 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 comparedto the finger joint and so on [5]. During downstroke the wing is approximatelystretched, with a almost synchronous movement of all joints but also with increasingdelays for the inner wing parts as can be seen on the right diagram of figure 2.17. Theshoulder 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 measurementpoint 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) and9m/s (right) [5]

Zero represents the vertical position of the animals 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 notbe realised by a simple mechanical mechanism. Also for increasing flight speed forexample the wingtip elevation increases significantly, and the shoulder follows anentirely 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 wingmotion.


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 massof the bats thorax.

Aerodynamics

Lift mechanisms in bat flight origined of unsteady effects are not studied very de-tailed yet. Regardless some measurements of the airflow using digital particle imagevelocimetry were documented. According to [10] the wing camber during down-stroke is about 18% of the wing chord and the average angle of attack, where thewing is operating is about 50. It is important to notice that if a fixed wing oper-ates at such values, it would stall and lose lift, which already presumes that the batflight 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], whichis 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 thedownstroke [10]

at the leading edge, generating an area of high negative vorticity. Behind this areathe airflow reattaches, which results in an attached and laminar flow at the trailing


edge. The vorticity is stronger near the wingtip (C) and deacreases toward the wingroot (A).At the trailing edge, mainly distally on the wing, an area with negative vorticity isfound, which results of a strong rotational movement before the end of the down-stroke, which also enhances lift generation (see section 2.1.4). During the upstrokethe vortex, which generates much of the lift in flapping-wing flight, is not docu-mented well. It does not appear to origin in the wingtips as it is the case for thedownstroke. According to biologists the starting point for the vortex seems to besomewhere in the middle of the wing, which again shows, that the complex wingstructure, 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 moreaerodynamic effects as for fixed wing flight, for instance gliding. Small birds needto generate the lift force by flapping the wings. However there are many differenttypes of birds, which also have different kinematics.In general the wing can be tentatively separated into two parts, the outer wing andthe inner wing. The inner wing acts like an aircraft wing, it is the lift developingpart of the wing. When a bird flaps its wing it is the inner wing that moves thesmallest distance, thus the lift it generates is due, to a large extent, on the airstreamproduced by forward momentum. The inner wing is also the most cambered partof the wing and this is made possible by the extensive bones and connective tissuethat can hold this shape better than feathers. This means that it can generate morelift 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 birdspecies [2]

it produces forward momentum. It is less cambered than the inner wing and moreflexible and it is this flexibility that leads to the momentum. As the wing is flappeddownward the outer wing tends to twist slightly forwards, this is due to a numberof 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 thewing 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 figure2.20).Unfortunately, there is not much literature dealing explicitly with the aerodynamicsof small birds. Also note, that compared to hummingbirds no so detailed informa-tions about the kinematics could be found for flight during hovering, because oftheir less practical properties for experimental tests. Nonetheless briefly the flap-ping parameters are given exemplarily for the zebra finch, which belongs to thesame 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. Theyflap their wings with about 24Hz and a stroke amplitude of 135, which decreasessignificantly for increasing the flight velocity [4]. As for hummingbirds the bodyangle is tilted for increased forward flight speed. For hovering the body angle withrespect to the horizontal is about 50, which decreases down to 15 for a flightvelocity 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 staysapproximately constant for all flying velocities at about 20.Another important aspect, is that the finch not regularly flaps its wings. Dependingon the flight velocity the wing is bounded after several stroke cycles for some timeinstances. For higher velocities almost 50% of the time, the small birds hold theirwings close to the body, do not flap them and can save so some energy. Thisbehaviour can be seen in figure 2.21, where the wingtip elevation and the wingspanare 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 flap-bounding flight at 2m/s (A) and 12m/s (B) [4]

with flapping or gliding during the bounded time span, the aerodynamic propertiesof the body come to be crucial.

2.3 Summary

In the following table the characterization of the kinematics of the different inves-tigated flying animals (Insects-Drosophila fruit fly, rufous Hummingbirds, Short-nosed Bats Cynopterus brachyotis) are summarized for hovering flight. Note thatmorphological data and results out of biological experiments are taken either as av-erage values or most suited values. Specially for insects like the Drosophila fruit fly,


the accuracy of measurements is limited, because of their small size, and deducedinformations of experiments done with accurate models which represents good re-sults for the insect flights are presented.

Insects Hummingbirds Bats SiskinWeight [g]

19 2.3. Summary

Siskin/FinchAdvantages -very maneuverable

-hovering and forward flight possibleDrawbacks -wing folding is significant during upstroke

-no constant flapping frequency for increasing forward flightspeed-stroke amplitude reduces significantly for increasing forwardflight

Small birds also have an acceptable hover ability. But compared to hummingbirdsit is decreased. According to biologists, the hummingbirds should can do moredifferent motions, for which reason crucial changes in the kinematics of the flappingoccur. Also the wrist, the joint at the approximate midpoint of the wing, is moreessential. Specially during upstroke the wing is folded significantly, which wouldbe very difficult to implement in a MAV. Also for transition from hovering to for-ward flight many different flapping parameters are changing significantly, whereasno resonable simplification for a flapping device can be estimated. Hence, the smallbirds, are not taken into account for further investigations.

BatAdvantages -very maneuverable

-hovering and forward flight possible-low flapping frequency compared to animals size-can generate greater lift for less energy due to stretchy membrane

Drawbacks -very complex wing structure, more than two dozen independentlycontrolled 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 fordeveloping a MAV. A simple mechanical flapping mechanism could not be realised,because the wing motion is far too complex, with more than a dozen independentlycontrollled joints, which would let the MAV be too heavy. Also no simplificationscould be found, which would allow to make a simplified kinematic model and stillfollows the wings 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 theouter 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 bea reasonable idea.


HummingbirdAdvantages -very maneuverable

-hovering and forward flight possible-almost no wing folding during upstroke-at first sight a simplified mimic wing motion is achievable witha mechanical mechanism-flapping frequency stays constant for every flight speed

Drawbacks -twisting phenomena along the wing axis is present like in otherbirds-kinematic parameters variation more complex for increasingforward 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 kinematicparameters are changing, which simplifies the later control challenges. For moreincreasing the forward flight speed of course more parameters are varied, but forthe first approach this can be neglected. Compared to small birds almost no wingfolding is present, hence the wings can be assumed to designed without a joint, asit is the case for insects. Although the pitching of the wing is done actively by thehummingbird, this can be still achieved to copy. As shown above, the pitch anglealso follows a more or less harmonic pattern. The twisting phenomena along thewing axis, also does not represent a big obstacle, as this can be solved by usingflexible wings, which adapts itself to the aerodynamic loads.Therefor, to generate first concepts for the flapping wing mechanism, mainly thehummingbird motion is considered, which could be extended with ideas describedfor 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 dimensionsof the Giant Hummingbird (Patagonia gigas) are taken as a starting point for thedesign. According to biologists the kinematics of the Giant Hummingbird are sim-ilar to the above described pattern of the rufous hummingbird and so can be alsoconsidered as the motion which the flapping mechanism has to fulfill.

Dimensions

The following table summarizes the dimensions of the Giant Hummingbird whichare used.

Weight 25gWingspan 280mmAspect Ratio 6.73Wingchord 40mmBody width 50mmWing length 115mm

Flapping motion

The general characteristics of the flapping motion are presented in the table below.

Flapping frequency 15 HzStroke Amplitude 110Body angle during hovering 50

Stroke plane angle during hovering 60

flapping pattern sinusoidalchord angle trajectory sinusoidalmax/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 andinsects several parameters of the flapping motion are changed to perform differentmaneuvers. For some control tasks several different ways can lead to the desiredresult. For instance for changing the forward flight velocity the pitch angle of thewhole 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 rollingangle can be controlled by increasing the flapping amplitude and/or the angle ofattack of the outer wing. For more complicated maneuvers many of the flappingparameters are changed simultaneously. Of course a flapping mechanism, which canbe controlled in such a way would be much too complex and therefor too heavy fora MAV. Of course a more deep study is needed for a good flight control, but thiscan only be done, when the flapping mechanism is finished and implemented in aMAV. But as a first approach it is adequate to consider only the simplest controlaspects.According to biologists, studying the hummingbirds wing motion, a simple way tochange the flight velocity is to tilt the body angle. As a first approach this canbe done by shifting the center of gravity of the MAV forward or backward and/orusing servos at the tail of the MAV. Changing other parameters of the flappingmotion and taking this into account for developing a flapping mechanism would beto complicated at this early stage of the project.To change the flight direction also a simple solution is needed. In general birdschange 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 isconsidered to change the orientation of the tail to deviate the air flow as a firstassumption. Of course this has also to be investigated more deeply, when a flappingprototype is present.Therefor the development of a first flapping mechanism can be done independentlyof 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 controlissues 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 usedto reduce the power consumption and the mass. Also in general the mechanicalcomplexity then reduces, less joints and links are needed to transfer the forces ofthe actuators to the wings and so is more lightweight.A brief investigation of the available actuators showed, that no reasonable linearactuator can be used. Either they are too big and too heavy or can not bringup the force needed for the flapping motion or the linear displacement needed forthe stroke amplitude. As the future MAV is considered to be of a size similar tothe Giant Hummingbird piezoactuators can also be excluded due to the too smallgenerated forces. DC-Motors can fulfill these first constraints. Some, speciallybrushless DC-motors, could be found which have a reasonable torque, an acceptablepower 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 (seefigure 2.12), the main structure of the flapping mechanism can be approximatedwith a circular motion, which is generated with a rotational actuator and where themovement in the direction of one main axis is transmitted to the wings accordingto figure 3.1. However in such a way, the sinusodial motion of the wings only can beapproximated. 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 Land r (see figure 3.2). Only for L going to infinity a perfect sinusodial motion withamplitude r can be achieved. For a good approximation therefor L has to be chosenmuch larger than r. The kinematic relationship is given with equations 3.1 and 3.2and is shown in figure 3.3 for various ratios L/r1.

sin =r cos L

(3.1)

y = r sin + L cos (3.2)

Already a ratio higher than 2:1 for L:r can be considered as an approximationwhich is good enough to achieve an acceptable sinusodial motion. This can be eitherdone by increasing L or decreasing r. It is important to point out, that for decreasingr, which affects the amplitude of the sinusodial movement of the centered joint, alsothe distance b has to be adapted according to equation 3.3 to get the desired strokeamplitude of max = 55.

b =r

tan (max)(3.3)

To reduce this dependency of b to the amplitude r, an additional horizontal linkcan be inserted according to figure 3.4. Instead one joint, the whole link is movedup 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 thelater dimensioning of the different link lengths. However an additionally joint isneeded, which of course reduces the efficiency.

1Generated with matlab kinematic circular.m


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 givensinusodial flapping motion does not let much margin for big variations. Therefor thegeneral kinematic pattern is the same as described above in section 3.2.1. Anywaythe structure presented in figure 3.5 can also be a good solution. The actuatorstorque is transmitted via two gears to the associated wing. The advantage of thisconcept as a starting point for the further designing is, that each wing can betreated somehow independently of each other in terms of the flapping motion andleaves therefor more space for further ideas to control each wing independently.However the additional gears increase the friction and the complexity and so alsothe efficiency and the weight respectively.

To increase the robustness of the design, the flapping can be actuated accordingto the right side of figure 3.5. Instead of just actuating the wings, a more solid


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 viaa rotational joint to the main structure where also the motor is attached at andgives 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 aflexible part according to figure 3.6. The bending of the rod at the middle inducesa motion at the wings. For the flexible part a material can be used which has agood 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 calculatedaccording to equation 3.4,

d2w(x)dt2

= My(x)EIy

(3.4)

whereas E is the modulus of elasticity of the used flexible material. The bendingtorque in the y-direction My and the moment of inertia in the y-direction of therod Iy is calculated as follows

My(x) ={

Fx2 for 0 < x < b

Fx2 F (x b) for b < x < 2b

(3.5)

Iy =dh3

12(3.6)


Figure 3.6: Schematic drawing of concept C

The rods dimensions are specified by its width d and height h as shown in figure 3.7.Using the boundary conditions 3.7 and integrating equation 3.4 gives the maximaldeflection at the midpoint between the two wing holdings needed to get the desiredstroke amplitude of =55 (equation 3.82).

dw(0)dt = tan 55

, w(0) = 0 , dw(b)dt = 0 (3.7)

F = 4EIy tan 55

b2

w(b) = Fb3

12EIy+ b tan 55

}= w(b) = 2b tan 55

3(3.8)

Figure 3.7: Calculation of the bending line

Because the deflection of the rod needs a certain force to attain the desiredstroke amplitude, it has to be checked if an actuator can be found, which generatesenough force. Therefor the whole mechanism is modelled in a simplified way aspresented in figure 3.8. It is important to notice that also the following calculationsare just a rough approximation to check for the fundamental feasibility of thisconcept and if it has to be investigated more deeply. Also the forces acting on thewings and the wings itself are not included yet, as these forces can not be calculatedexact enough and so just would blur the results.The behaviour of the bending rod can be modelled in a simple way as a spring witha point mass ms, which represents the mass of the link with length L. The springconstant c and the corresponding force Fc generated by the compressed or stretched

2matlab file bending line flex.m


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 = 0.

Figure 3.8: Sketch for calculation of the dynamics

Fs represents the force acting on the link and M the generated torque by theactuator. The maximal value for y, which is calculated in equation ?? is equal tothe amplitude of the sinusodial motion. As L r the radius can be approximatedas r w(b). Using the laws of conservation of the momentum for the link and theangular momentum for the rotating disc the following equations of motion can bederived:

ms d2y

dt2= Fs cos cy + cL cos0 (3.11)

d2

dt2= M rFs cos (3.12)

where sin0 = rL for = 0 and is the inertia matrix of the rotating disc. Usingequations 3.1 and assuming a constant angular speed the equations for , are

= sin Z0.5 rL

(3.13)

= 2 cos Z0.5 rL sin r

L r

2 sin 2Z1.5

2L2(3.14)


with Z = 1r2 cos 2

L2 .

Derivating equation 3.2 with respect to time an expression for y is obtained

y = r2 L sin L2 cos (3.15)

Using equations 3.15, 3.13 and 3.14 into equation 3.11 the force on the link canbe calculated during one cycle (equation 3.16). Inserting it into equation 3.12 theneeded torque for the bending is obtained.

Fs =msy cy cL cos0

cos(3.16)

For numerical values a carbon rod with dimensions of 0.1mm x 2mm and amodulus of elasticity of 110000 Nmm2 is used. The parameter b is chosen accordingto the estimated value of the body width of the hummingbird, which correspondsto the distance between the two wing mountings as mentioned in chapter 3.1. Theresults 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 thatthe actuator has to push the link, while negative torques represents the situationswhen the actuator has the break the motion of the link due to the reaction of thespring-like behaviour of the bended rod.

Figure 3.9: Results of the force on the link and the needed torque during oneflapping cycle

It can be seen that with such dimensions for the carbon rod, an applicableactuator could be found, which is enough lightweight and still can bring up enoughtorque4. However if the thickness of the rod is increased to 0.2mm, already a muchhigher torque is needed and the size and weight of the actuator would grow toomuch. Another disadvantage is that the distance between both wing holdings cannot be reduced much more, then again a higher force is needed to bend the flexiblerod. Also the wings are not considered yet, which again increases the torque whichhas to be generated by the motor.Taking these aspects into account a working flapping device using this concept willnot 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 thewings.

3generated with dynamics flap rot const.m4see 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 wingholding, because of the relatively high stroke amplitude. To get rid off the linearmotion a structure as shown in figure 3.10 could be used. The wing is attachedsimilar as in concept B2 to a connector, which is attached to the main structureand can rotate about one axis, allowing to flap the wing in one plane. Between theconnector and the actuation point three joints are arranged so that the link in themiddle does not just move up and down, but rather adopts its orientation that thejoint most proximal to the wing is routed on a circular trajectory and therefor doesnot 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 parametershave changed places. Here y is determined, it is actuated in a sinusodial way, andthe angle , which above described the state of the cycle is now the flapping angle(see figure 3.10). Note that with the additionally inserted joint not makes awhole cycle. By adapting the correct link lengths and the actuating amplitude,the maximum opening angle of 55 can be obtained. The general equations for thekinematics can therefor easily be taken out of equations 3.1 and 3.2. Hence also noexact 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 thedescribed concepts above. Also for implementing this concept later on for a realMAV could be difficult because the links and the joints have to be guided andsupported 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 controlthe pitch angle actively with the same actuator. As showed in chapter 3.2 anapproximated sinusodial flapping trajectory could be produced. By optimizing theoffset between the sine wave of the flapping and the chord angle, setting up thedesired pitch angle for every state of the whole cycle with the same rotary actuatorshould be possible. The remaining question, at which point to actuate the wing toset up the pitch angle has to be investigated.


Actuating the wings trailing edge

One idea could be to attach the trailing edge of the wing to the main body, where itis connected to the actuator and is moved according to the flapping cycle to achievethe 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 hummingbirds flapping trajectory as can be seen in figure 2.12 aretaken. Note that the studies base on the smaller rufous hummingbirds and not thegiant 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 theposition of the trailing edge of the wing to the position of the leading edge, whichis described by the wrist elevation.

yT = yL c sin() (3.17)

The resulting trajectories are shown in figure 3.135. The left graph shows theactual 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 thetrailing edge to clarify the result. There it can be seen that the trailing edge is notmoved totally harmonic. One half of the cycle is performed a little faster than the

5matlab file active pitch.m


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 behaviourof the trailing edges motion

other. This anomaly increases for bigger wings and hence if the dimensions of thegiant hummingbird are used the inaccuracy increases also. If this way of setting upthe pitch angle is used, it has to be considered, that the wing has to be made of astretchy material. If the actuation is not done absolutely exact, which is the case ifonly 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 pitchingcould be done in a seperate manner, if the motor lies between both edges of thewing.

Actuating the wings leading edge

As the chord angle describes a sinusodial trajectory as the flapping motion a moreacurate way to control the pitch angle would be to actuate directly the leading edgerod 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


of the rod. Of course the mechanical structure is not as easy as presented in figure3.14. As the amplitude for the chord angle is more than 100 degrees, the pin on therod drifts away from the actuator tool. This needs a complex pitching mechanismto have the friction reduced. A simple but not so clean way to solve this, wouldbe 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 theflapping motion and also moves up and down. Hence this mechanism has to be asnear as possible to the body of the MAV.Despite these design challenges, the advantage of this concept can be showed bycalculating the kinematics. The needed amplitude s of the horizontal movement isexpressed by equation 3.18.

s = t tan (3.18)By putting this amplitude into the same sinusodial motion as the flapping andadjusting the offset, the simulated pitch angle can be obtained according to figure3.156. It can be seen, that also here small errors occur. But as the sine wave for thechord angle only is an approximation and the real chord angle as showed in figure2.12 even more equals the simulated angle, this method seems to be more accuratethan 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 passivelyadapt its chord angle. This is possible as inertial and aerodynamic loads tend todecrease the angle of attack. However this would not be as accurate as controllingthe angle actively. But as can be seen in [2] the angle of attack for the hummingbirdflight stays more or less constant during one flapping cycle. Of course at the be-ginning of the upstroke and the downstroke the angle of attack will intuitively havethe biggest error according to the desired value. But several other MAV alreadyuse this way for adjusting the pitch angle of the wing with success, for which reason

6matlab file active pitch2.m


this approach can be considered as suitable.Therefor two main ideas came up. The first one can be used if the wing rod isinserted into a tube, which is attached to the main structure and is actuated forflapping (see Concept B2 in chapter 3.2). The main connection between the wingrod 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 andstarts to rotate. As the spring induces a counter-torque to this rotation, a constantangle of attack could be obtained. Unfortunately there is no way for calculating agood enough approximation for the forces and torques acting on the wing. Hencethe strength of the springs has to be identified experimentally with a test bench ofthe 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 ofRobert Woods Robotic Insect [24]. As shown in figure 3.17 the fibre of the wingscould be designed using a sandwich-like structure. The middle part is made of aflexible material and is surrounded by a more stiff material. Right beneath thewing rod of the leading edge, which is actuated for flapping, the stiff material isremoved, and lets the wing surface rotate around the leading edge. By investiga-tion the maximal pitch angle can be adjusted by removing more or less of the stiffmaterial. If the angle increases, a touching of the outher parts occur and blocks afurther 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 bedone experimentally. However this idea saves weight and reduces the complexityof the flapping mechanism. Another advantage is, that this approach for pitchingthe wing only depends on the wings and not on the mechanism which generates theflapping motion. In contrast the first approach, using springs, already presumessome construction elements for the attachement of the wing to the main body.

Chapter 4

Evaluation

4.1 Evaluation of concepts

After generating different ideas for the flapping motion, these concepts will be evalu-ated according to several criteria described below, to chose the most suitable conceptas a starting point for the CAD design. As not all exact dimensions and parametersfor the above described concepts are present yet, this evaluation is done in a morequalitative way. Nonetheless this selection is important as it affects the whole futuredesign 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 amechanism which is more complex and needs more joints, also in general consumesmore power. The most important aspects for a MAV are the weight, as it has tobe minimized or should left space for further weight reduction, and the power con-sumption, which also needs to be as low as possible. It would not make sense tointegrate a flapping mechanism in a MAV, which consumes too much power andneeds a bigger battery, which again increases the weight. However the expectedpower consumption can not yet be determined accurate enough, to get significantdifferences between the various concepts for the flapping motion, whereas mainlythe number of joints and the generated friction is taken as an indicator for theperformance in terms of power-saving.The general dimensions are already fixed at this stage (see chapter 3.1), for whichreason the size more indicates the feasibility to minaturize the mechanism, but hasless priority as the actual dimensions are considered to be small enough for a pro-totype MAV. Also the robustness plays an important role. The mechanism has tobe 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 mainstructure of the MAV, which would again increase the complexity and induce morefriction. 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 flappingmotion base on the same general principle, all generate the similar wing beat tra-jectory as shown in chapter 3.2.1, for which reason this criterion is not used for theflapping concepts.Taking into account the above considerations an evaluation matrix can be generatedwith weights indicating the importance of each criterion:

Criterion WeightWeight 6Size 1Robustness 4Mechanical complexity 5Expected power consumption 5Accuracy 3

4.1.2 Flapping concepts

Using the above matrix the concepts of chapter 3.2 are compared to each other anda rank is assigned (6 is the best and 1 is the worst), considering the facts describedabove and in chapter 3.2.

Weight Size Robust. Mech.Complex.

PowerConsumpt.

Concept A1 5 3 3 5 6Concept A2 4 2 4 4 5Concept B1 2 6 5 3 2Concept B2 1 6 6 2 2Concept C 6 1 2 6 3Concept D 3 4 1 1 4

The outcome of this comparison is shown in the table below, where the total pointsand the rank (1 best, 6 worst) are presented.

Total Points RankConcept A1 100 1Concept A2 87 3Concept B1 63 4Concept B2 56 5Concept C 90 2Concept D 51 6

As can be seen, concept A1 seems to be the most suitable to be used as a startingpoint and is therefor used as a guidance for the CAD design. Concept C also seemsreasonable to be followed. Nonetheless it is neglected, due to the big uncertaintyfor 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 pre-sented in tables below.

37 4.2. Expected weight

Weight Size Robust.Active-Trailing Edge 2 2 2Active-Leading Edge 1 1 1Passive-Spring 3 3 3Passive-Wing 4 4 4

Mech.Complex.

PowerConsumpt.

Accuracy

Active-Trailing Edge 2 2 3Active-Leading Edge 1 1 4Passive-Spring 3 3 2Passive-Wing 4 4 2

Total Points RankActive-Trailing Edge 51 3Active-Leading Edge 33 4Passive-Spring 69 2Passive-Wing 90 1

For the pitching motion of the wing, the concepts for passive wing pitching aresuperior using this evaluation method. This is certainly the case, because the eval-uation matrix is laid out in such a way, that the whole mechanism stays simple andis as lightweight as possible. If experimental data would be available, how more liftforce with a more accurate pitching motion can be generated, the weight for theaccuracy can be adapted. For instance, if the more complex and heavier mechanismfor actively controlling the pitch motion of the wing, regains more lift force thanthe additional weight needed, controlling the wings pitch angle actively would besuperior to the concepts for passively controlled wing pitch angles.However, for this first approach developing a flapping mechanism, passiv wing pitch-ing is adequate.

4.2 Expected weight

Knowing on which concept to focus on, first speculations on the expected weightof the MAV can be made. Using the dimensions of chapter 3.1 the weights of thedifferent parts can be estimated. Note that in the following only a rough approxi-mation is done, which is based on an internet research of several suppliers of partsfor model aircrafts1.The wings are assumed to have the structure out of carbon, which is covered withmylar as shown schematically in figure 4.1. Three carbon (1.55g/cm3) rods withdiameter of 2mm can be used as support to attach the 0.0005mm thick mylar sheet(7g/m2) on it. With this design, one simple wing weights about 1.5g.As mentioned above two servos are needed for control purposes, whereas each oneweights about 1g. Including the weight of the RC receiver (1g), the brushless DCmotor ( 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 foundconcept for the flapping mechanism, would be about 10g.Therefor the expected weight of the MAV can be assumed to be 30g.

1for 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:

P = W

W

2SE(4.1)

where W = mg 0.29N is the total mass in expressed in [N], = 1.29kg/m3 theair 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 Sswept by both wings [1]. Rewriting equation 4.1 as follows

P = W

WS

2SES(4.2)

and inserting SES 70%, WS = 31.52Nm we obtain for the power P = 0.393W .According to [1] an efficiency coefficient for the hover ability has to be included. Asthe wing motion will be similar to the hummingbirds wing motion, it is reasonableto take the same value for the coefficient H = 60%. Including the mechanicalefficiency of the mechanism M the total needed mechanical power is calculatedaccording to equation 4.3.

Ptot =P

HM(4.3)

The efficiency coefficient for the mechanism M can be calculated by summing upthe efficiency of the joints ( 80% for each joint) and the efficiency of the motor,which is typically around 60% for the chosen brushless DC motor2. Considering theabove 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 con-strained. 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, whichcan fulfill the power and the weight requirements. Also the electrical power con-sumption 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 bat-teries.

2see 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 3DCAD software. As the forces on the wings are still unknown and just can be identi-fied experimentally in a correct manner on a finished flapping mechanism, no exactstability calculations can be done for the different parts of the flapping device. Alsothose forces highly depend on the wing design. Therefor it is considered to makethe flapping mechanism as robust as possible, trying to copy the kinematic of thehummingbird and neglect weight constraints. Hence, the weight reduction has tobe done later on, when also the wings are completely designed and measurementsare 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 areattached to 2mm thick aluminium plate, which is screwed on two shorings. Theseshorings have an inclination of 10 which corresponds to the stroke plane anglewith respect to the horizontal of the hummingbirds wing motion. A DC-motorwith a planetary gearhead (reduction ratio 3.71:1) is attached below the plate andtransmits the generated torque to a link, which starts to rotate. The datasheetsfor the motor and the gearhead can be seen in the appendix. This rotating linkis connected via a pin to another link, which is guided on the other end in such away, that this end point is always centered between the two wing joints. Therefortwo ball bearings are needed to allow the transmission link to rotate freely. Dueto the circular motion of the rotating link, the transmission link is moved forwardand backward, which produces the same kinematic pattern as calculated in chapter3.2.1. 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 move-ment of these attachements.Due to time constraints, all parts were printed, except the ball bearings, the alu-minium plate and the pins, which were made of steel. Therefor the dimensions ofthe links had to be chosen big enough to assure the stability. However the links aresupported in the vertical direction only on one point, the connecting point to themotor, which has to carry both links. Therefor the connection at the ball bearingshave to be very tight, to ensure that the bending moments, caused by gravity, areas 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 figure5.2). 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 thetwo legs of the link, is pushed on the motor shaft and attached to the link usinga screw. The dimensions were chosen such that, by inserting the screw, the smallpart is pressed against the motor shaft. However this is not absolute necessary, asalready the notch secures the connection. Nonetheless this force fitting again givesa 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 con-sidered motion, the joints are the most important parts. However this part couldnot be solved perfectly. Pushing the center joint forward and backward, the dis-tance between it and the wing joints changes. As the stroke amplitude is wantedto be 110, the variation of the distance is a bigger problem and can not be solvedwith this general structure. Therefor either the center joint can be optimized, usingball 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 morefriction.For increasing the stability, the second approach is better, as the wings then areguided 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 doneaccording 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 pushedto follow its way. Due to the movement of the pin in the slots friction occurs. Tooptimize 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, whilethe rest should be made of a stiff and lightweight material. Nonetheless, this designis 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 bya slot in the aluminium plate, where the pin is moved in. To decrease the friction aball bearing is glued to the pin. Note that the diameter of the ball bearing is justslightly smaller than the width of the slot, to assure that the ball bearing does notbrake 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 ballbearing the wing attachement is arranged in such a way that only the inner part ofthe ball bearing is touched. The outer part is then connected only to the motionlessstructure 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 thedesired flapping motion, is acceptable. Due to time constraints no exact measure-ments with the manufactured mechanism could be done. Also no information of thegenerated lift force can be deducted, as this is only possible to measure when thewing designing is done, which includes the adjustment of the wings flexibility forthe 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 kinematicpattern as described in chapter 3.2.1, which is a good approximation for the hum-mingbirds flapping. Also first tries showed, that the flapping frequency of 15Hz isreachable, although still many improvements can be done.The biggest improvements can be done for instance at the center joint. There is stillrelatively much friction present, which could be reduced. Also the guidance of thecenter joint leaves much space for enhancement. Nonetheless the strongly varyingdistance between the center joint and the wing joint, can not be eliminated withthe chosen concept, for which reason it can also be considered to choose anotherapproach 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 (seechapter 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 instancethe wing design, are finished. With appropriate wings, also exact measurementscan be done and the generated lift force can be discovered. Using a high speedcamera, a more exact comparison of the resulting motion and the hummingbirdswing motion can be done. Further, if these tasks show good results, implementingthis motion into a real MAV would be the next step to the final objective of a flyingflapping wing MAV.Concluding, as this project is the first step in the direction of designing a FlappingWing MAV, many useful informations and experience could be gathered, which forsure 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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[10] et al. F. T. Muijres. Leading-edge vortex improves lift in slow-flying bats.Science 319, 1250, 2008.

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[13] Y. Lu and G. X. Shen. Three-dimensional flow structures and evolution of theleading-edge vortices on a flapping wing. Journal of Expermental Biology, 211,1221-1230, 2008.

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development of flapping wing mechanism

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