Dynamics of the herring gull wings - an underactuated approach

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DYNAMICS OF THE HERRING GULL WINGS: AN UNDERACTUATED

APPROACH

Thesis presented

by

PAOLA ANDREA LUNA ARENAS

Advisor:

Jonathan Camargo Leyva, MSc.

Faculty of Engineering

Department of Mechanical Engineering

Bogotá D.C, Colombia

June, 2016

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LIST OF FIGURES

Figure 1. Leonardo Da Vinci's complex ornithopter (1505) ... 7

Figure 2. Flying machines developed by Otto Lilienthal. a) The Derwitzer gliding, b) The Big plane. ... 8

Figure 3. Flying machine developed by Otto Lilienthal, the “small wing flapping machine”. ... 8

Figure 4. First flight of the airplane “The Flyer” by the Wright brothers. ... 9

Figure 5. Asimo: Honda’s humanoid robot, 2015. ... 10

Figure 6. Passive dynamic robot. ... 11

Figure 7. Festo’s SmartBird. ... 12

Figure 8. Representation of lift, weight, drag and thrust. ... 12

Figure 9. Primary and secondary parts of a wing. ... 14

Figure 10. Wings analysis from Festo’s SmartBird animation. ... 15

Figure 11. 2D mechanism and parts. ... 16

Figure 12. Positions accomplished by the 2D mechanism. ... 16

Figure 13. Gear system. ... 17

Figure 14. Hearts, shafts and gears of the mechanism. ... 18

Figure 15. Heart, secondary parts and joints of the mechanism. ... 18

Figure 16. Primary part, servomotor and servo support. ... 19

Figure 17. Wing’s ribs. ... 19

Figure 18. Mechanism wing’s shape compare to a real herring gull’s wing... 20

Figure 19. Wood prototype. ... 21

Figure 20. Carbon Fiber prototype. ... 21

Figure 21. Carbon fiber prototype. ... 22

Figure 22. Human knee’s cruciate ligaments. ... 23

Figure 23. Wing joint’s cruciate ligments. ... 23

Figure 24. a) Motor and b) Servomotor used for the mechanism. ... 24

Figure 25. Encoder installed. ... 25

Figure 26. Prototype’s wing cover with the skin. ... 25

Figure 27. Final prototype and aluminum support. ... 25

Figure 28. Lift wind tunnel assembly. ... 26

Figure 29. Prototype hanged upside-down during lift experiment. ... 27

Figure 30. Propulsion wind tunnel assembly ... 27

Figure 31. Strain gages calibration assembly. ... 31

Figure 32. Strain gages calibration assembly. ... 32

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LIST OF GRAPHS

Graph 1. Motor power vs. Crank gear angular velocity. ... 24 Graph 2. Lift coefficient vs. Crank position and angle of attack for the lift experiment. ... 28 Graph 3. Propulsion vs. Time for angles of attack of -10º, -20º, -30º, -40º (from top to bottom

respectively)... 29 Graph 4. Mass vs. Electrical resistance. Strain gages calibration for the lift experiment. ... 32 Graph 5. Mass vs. Electrical resistance. Strain gages calibration for the propulsion experiment. ... 33

LIST OF TABLES

Table 1. Gears information. ... 17 Table 2. Final features of the prototype. ... 25

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5 ACKNOWLEDGEMENTS

The completion of this project could not have been possible without the help of so many people. Their contributions in many ways are sincerely appreciated.

First of all, I am grateful to God for enlighten me during my career and all the way to my final project. Without his help none of this would have been possible.

Thanks to my thesis advisor Jonathan Camargo MSc, for being my mentor and partner and for your enthusiasm and support from the very first moment I started this project.

Special gratefulness to my father Pedro Luna who stood by my side day and night and to my mother who has always given me words of love and wisdom. To my brother, thank you for everything. I love you all.

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6 ABSTRACT

The bird’s movement is considerably more effective when using the available energy than any aircraft created. Throughout this project the movement of the herring gull’s wings was analyzed in order to obtain a deeper knowledge of their flapping motion. Using the gathered information combined with aerodynamics and control systems principles, an underactuated mechanism capable of simulating the herring gull's wings motion was designed and manufactured. After the manufacture, two experiments were made to analyze the response of the system for different angles of attack. To analyze the lift generated during the up-stroke a quasi-static experiment was made and the best results were obtained for an angle of attack of 30º. On the other hand, to analyze the propulsion generated during the down-stroke, a dynamic experiment was made and the best results were obtained for an angle of attack of -10º.

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7 1. INTRODUCTION

Humans have always been interested in flying and what better way to understand this phenomenon than analyzing the bird’s flight. Some of the earliest studies reported are the ones by Leonardo Da Vinci where he studied the structure and movement of the bird’s wings. Leonardo drew “over 500 sketches related to flying machines, the flight of birds and the flow of air…These drawings are mainly of ornithopters (figure 1), or flapping mechanisms designed to emulate the movement of bird’s wings by human pilot” (Moon, 2007). At that time, there was little knowledge about the aerodynamic principles and so, a long time would pass before a flying machine could actually fly.

Figure 1. Leonardo Da Vinci's complex ornithopter (1505)

In 1891, Otto Lilienthal succeeded on building the first manned aircraft in the world, the “Derwitzer glider” (Figure 2a), which was able to fly distances of up to 25 meters. Between 1891 and 1896, Lilienthal kept building improved gliding machines like the “Big plane” (figure 2b) and even started developing machines based on the bird’s flapping (ornithopters), like the “small wing flapping machine” (figure 3).

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Figure 2. Flying machines developed by Otto Lilienthal. a) The Derwitzer gliding, b) The Big plane.

Figure 3. Flying machine developed by Otto Lilienthal, the “small wing flapping machine”.

Otto’s achievements were perhaps the ones that inspired the Wright brothers the most, their perseverance lead to the first successful flight occurred on December 17, 1903. “The flyer” (Figure 4), name given by the Wright brothers themselves, was the result of many designs, calculations and experiments.

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Figure 4. First flight of the airplane “The Flyer” by the Wright brothers.

From this point on, the aircraft development has been growing day after day. Nowadays the main problem is not strictly the aerodynamic principles needed to make an aircraft fly, but the attainment of new and optimized ways of flying. Today’s airplanes work beautifully, as Russ Tedrake (2015) says, modern airplanes are extremely effective for steady-level flight in still air and their propellers produce thrust very efficiently. Saying this, one would think that there’s nothing left to learn from the bird’s movement. That’s not entirely true, modern airplanes are very conservative and they use low angle-of-attack flight regime where the aerodynamics are well understood. In contrast, the natural and harmonic motion of flying animals and its capability of reacting to complex environments, compared with those achieved by human-build aircrafts, are the reason why the flapping movement of bird’s wings is this project’s central focus.

The bird’s movement is considerably more effective when using the available energy than any aircraft created. Throughout this project the flight motion of the herring gull and specifically its wings will be analyzed in order to obtain a deeper knowledge of its flapping motion. By making use of the gathered information combining it with aerodynamics and control systems principles, a mechanism capable of simulating the herring gull's wings motion will be designed and manufactured.

2. PROJECT OVERVIEW

This document is divided into three sections: Prior work, theoretical framework and objectives, design process, manufacture process and testing, results and conclusions.

First, important prior work on the subject will be mentioned along with the explanation of essential concepts for the project. After that, the general and specific objectives of the project will be presented.

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The next section covers the model design of the prototype which was divided into four stages: The analysis of the herring gull wing’s motion, the 2D synthesis and modeling of the mechanism, the design of the mobility system and the 3D structure design.

After the design process, comes section three: model manufacture. During this section, the selection process to pick the structure’s material will be mentioned along with the manufacture and assembly of the prototype’s structure and mobility system. Then, the selection process of the material used for the skin and ligaments will be shown, followed by a brief explanation on the ligaments. Next, the development of the motion control will be presented as well as the last steps to get to the final prototype.

Finally, the two experiments made will be explained in detail together with their respective results. In the end, the conclusions will be presented.

3. PRIOR WORK AND THEORETICAL FRAMEWORK

Throughout time, many companies and people have developed simple and complex mechanisms that try to imitate the human or animal behavior. There is ASIMO (figure 5), the humanoid robot designed by Honda Motor Co. announced in late 1996. Even though ASIMO have incredible features that at that time had never been seen, it was clear that its movement while walking didn’t look very natural. The passive dynamic walker is another example, this robot has no motors or controllers and it still walks a lot more like a human while going down a ramp (figure 6).

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Figure 6. Passive dynamic robot.

The above was mention in order to explain the importance of underactuated mechanisms but more further the importance of “building control systems which use the natural dynamics of the machines in an attempt to achieve extraordinary performance in terms of speed, efficiency, or robustness” (Russ Teadrake, 2015). In a passive dynamic walker, the natural dynamics are exploited to the maximum: the initial swing of one of the legs allows the robot to keep walking down the ramp and a kneecap can be used to prevent the leg from inverting. On the contrary, ASIMO’s high-gain feedback cancels out the natural dynamics of the machine to do the tasks it was created for; in consequence this robot requires a lot more energy than any human to move and has an unnatural look.

The definition of an underactuated control system is “those in which the control input cannot accelerate the state of the robot in arbitrary directions” (Tedrake, 2015). According to Newton’s second law (F=ma), the state of a general second-order controllable dynamical system is given by its position and velocity at a given time. The general form for this dynamical system is:

𝑞̈ = 𝑓(𝑞, 𝑞̇, 𝑢, 𝑡)

Where q,

𝑞̇ and

𝑞̇

are the position, velocity and acceleration respectively of the mechanism and u the control inputs. The dynamics for many robots turn out to be affine in commanded torque, so this form can be considered:

𝑞̈ = 𝑓

₁

(𝑞, 𝑞̇, 𝑡) + 𝑓

2

(𝑞, 𝑞̇, 𝑡)𝑢

Given this, an underactuated system is described at any given time if it is not able to command an arbitrary instantaneous acceleration in q:

𝑟𝑎𝑛𝑘 [𝑓

2

(𝑞, 𝑞̇, 𝑡)] < dim [𝑞]

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On the other hand, there are companies and researchers that have created multiple mechanisms that imitate the animal behavior. In this case we are interested in talking about Festo’s “SmartBird” (figure 7) presented to the world in 2011. This robot succeeded in imitating the flight of the herring gull, being capable of taking off, flying and landing autonomously. The knowledge acquired by Festo will be of great help and will be implemented along this project.

Figure 7. Festo’s SmartBird.

The wings of the Smart Bird can move up and down and twist at specific angles thanks to an active articulated torsion drive in conjunction with a complex control system (Festo, 2011); this motion allows the bird to fly without any other additional lift devices. The motion of the SmartBird and other details will be analyzed later.

In order to handle correctly the motion of the wings, some aerodynamic principles need to be correctly understood and applied. Firstly, the concepts of thrust and lift are to be explained: Thrust is the force that moves an aircraft through the air while overcoming the drag forces while lift is the force that opposes the weight of an aircraft and holds it in the air (Figure 8).

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The lift coefficient (CL) is also an important concept that will be used during this project. Equation 1 expresses the ratio between the lift force generated by a lifting body and the area of the wings and speed and density of the fluid around it.

𝐶𝐿=

2𝐿 𝜌 𝑣2_𝐴 (1)

𝑤ℎ𝑒𝑟𝑒: 𝐿 = 𝐿𝑖𝑓𝑡

𝜌 = 𝐴𝑖𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑣 = 𝑊𝑖𝑛𝑔 𝑠𝑝𝑒𝑒𝑑 𝐴 = 𝑊𝑖𝑛𝑔 𝐴𝑟𝑒𝑎

4. OBJECTIVES

i. General objective: To design and develop a mechanical model which emulates the flapping motion of the herring gull’s wings.

ii. Specific objectives:

To Identify and characterize the herring gull’s wings movement in order to comprehend the specific motion of the wings.

To synthesize a mechanism that can imitate a herring gull’s wings motion.

To implement a control system capable of regulating the inputs of the mechanism in order to gain control of the flapping motion.

To create a physical prototype of the wings in order to characterize their weight, energy usage, propulsion and lift generation.

5. MODEL DESIGN

i. ANALYSIS OF THE HERRING GULL WING’S MOTION

In order to analyze the motion of the herring gull, it is important to understand the basic concepts of a wing; in figure 9 it can be seen that the herring gull has two parts in each wing, the primary and the secondary part. The secondary part is the one in charge of the lift, its shape and angle of attack help create

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a pressure differential. On the other hand, the primary part is the one in charge of the propulsion during the down-stroke while it also generates lift during the up-stroke.

Besides the mere movement of the wings, the feathers help as well. During the down-stroke, the feathers overlap in such way that the wind can’t pass through them, but in the up-stroke, the feathers delaminate allowing the wind to flow in between them, thus decreasing the resistance.

Figure 9. Primary and secondary parts of a wing.

Subsequently, a qualitative analysis of the herring gull’s wing motion was made. Given the limited time, the analysis wasn’t taken from a real life video. Instead, the video “SmartBird Animation” (link) by Festo was used to analyze the motion. The analysis that can be seen in figure 10 shows that during the down-stroke the wings push down the wind and while the secondary part of the wing keeps a constant positive angle of attack, the primary part has a negative angle of attack; this generates lift and thrust. On the contrary, during the up-stroke, the wings shorten its length while bending thus decreasing the surface area and leading to a lower wind resistance. During this time, both the primary and the secondary parts of the wings have a positive angle of attack and this generates lift.

During the analysis, three important positions were identified. The first one is the lowest position of the wings at which they are completely horizontal; this represents the position at which birds glide. Then, as the wings go up, the secondary part reaches 40° and it stops and waits for the primary part to reach the same position. This is the third important position and the highest; once the wings have reached it, they start to go down.

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Figure 10. Wings analysis from Festo’s SmartBird animation.

ii. SYNTHESIS AND MODELING OF THE MECHANISM

The mechanism developed was design to imitate the herring gull’s flapping wings while exploiting the natural dynamics of its design with little to none control system. As it was mentioned before, this project was inspired by Festo’s SmartBird and thus the design process was too. The analysis of the herring gull’s motion has already been made and now was the time to synthesize a mechanism that could imitate this movement. The program Working Model 2D was used to synthesize and make a dynamic simulation of the two-dimension mechanism (figure 11). First, the primary and secondary parts were added; the mechanism was designed so that it will move only by the rotation of one crank connected to the secondary part. To make the motion even more natural and to have control over the primary part, a joint was added between the secondary and the primary part of each wing. In order to restrict the secondary part, two supports and a “pin” were required; they let the secondary part rotate, but keep it from falling by the action of gravity and also prevents the wing from exceeding the 40°. Finally, three damper-spring sets where placed to imitate the work that the skin and the ligaments make to set the primary part of the wing in place at every moment.

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Figure 11. 2D mechanism and parts.

In figure 12, it can be seen that the mechanism obtained accomplishes the motion analyzed before. In the initial position, the wing is completely horizontal. In the same way, in the highest position the secondary and primary parts are aligned and at 40° with the horizontal.

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17 iii. MOBILITY

The design of the gear mechanism in charge of the mobility of the wings was the next step. Since the two wings move simultaneously the most energy effective option is for one motor to move both gears (one gear per crank). With this in mind, the gear connected to the motor will be “gear 1”, this gear will transmit its movement to one of the crank gears (gear 2) and this one will be connected to the other crank gear (gear 3). Since gears 2 and 3 have the same size and number of teeth, the torque and angular velocity of both are the same. In order to make the mechanism easier to handle and to make it more efficient, two more gears (gear 4 and gear 5) were added (figure 13). The dimensions and number of teeth of each gear can be seen in table 1. With the final design and dimensions of the mechanism, the power transfer is as follows: Gear 1 transmits its force to gear 4 multiplying the torque by 2. Then, gear 4 transmits its torque to gear 5 through a shaft. After that, gear 5 which is connected to the left crank gear transmits its force and multiplies the torque by 2,5. Finally, gear 2 transmits the force to gear 3 giving a final ratio of 5 between gear 1 and the crank gears.

Figure 13. Gear system.

Table 1. Gears information.

iv. STRUCTURE’S DESIGN

With the 2D model designed, we proceeded with the 3D structure using the same dimensions and positions obtained. The first step was to design the gears and gear structure in charge of the mobility of the model, this process was described above. Autodesk inventor was used to create each one of the pieces of the prototype. In the figure 14, the hearts, shafts and gears of the mechanism can be seen. The hearts

Gear Torque [N.m] Radius [m] Force

1 0,01 a 0,01 a

4 0,02 a 0,02 a

5 0,02 a 0,008 2,5 a

2 0,05 a 0,02 2,5 a

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support the whole structure and they are connected to each other through shafts. There are two types of shafts, the blue ones that hold the gears and the red ones that represent the “pins” mentioned before.

Figure 14. Hearts, shafts and gears of the mechanism.

After the central part was designed, the secondary part of each wing and the joints were added (figure 15). The tubes on the secondary part of the wings are being hold by small supports located in the extremities. Also, as it can be seen the “pins” were attached to the secondary part and an “extra shaft” was added to strengthen the structure; the wings will revolve around these pins. Finally, a crossbar was added to make the structure more robust but also to restrict the wings movement in the y direction.

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Next, the primary part of the wings was designed (figure 16). Given that the tip of the wing needs to rotate in the x axis, a support for a servomotor was added.

Figure 16. Primary part, servomotor and servo support.

Finally in order to make the “ribs” (figure 17) of each wing, the airfoil goe358-il was picked from Airfoil tools. For each section of the wings, the length of the airfoil was modified in order to give the wings a similar shape (figure 18) to the real wings of a herring gull.

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Figure 18. Mechanism wing’s shape compare to a real herring gull’s wing.

6. MODEL MANUFACTURE

During the manufacture process, two different materials where tried: wood and carbon fiber. For the wood prototype (figure 19) only one wing was build and no gears were used. Instead of the crank gear, a wood wheel was used and while operating it by hand, the whole structure moved as expected (https://youtu.be/sk3cHkqFpww). For the manufacture, cedar sticks of 3 and 5 mm where used for the shafts and MDF was laser cut to make all the pieces, except for the crossbar which was 3D printed. This prototype had its pros and cons, in one hand a weight of 158 g was a good start and also the motion was very natural. In the other hand, the structure didn’t resist the skin’s strength (simulated by a couple of elastics); after various cycles some of the pieces and shafts broke.

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Figure 19. Wood prototype.

The problems found with the wood structure lead to the search for a new material. Acrylic was considered because it was tougher but given its fragility and density (higher than wood’s), it was discarded. The next and final material used was carbon fiber (figures 20 and 21). Even though the density of this material is 50% higher than the MDF’s, its considerably higher resistance allowed a 1 mm thickness reduction in every piece. The shafts were also replaced by thin (0,125 in OD and 0,06 in ID) and thick (0,210 in OD and 0,132 in ID) carbon fiber tubes. With the carbon fiber prototype done, the gears were 3D printed and assembled as well. In the end, the weight of the structure plus the gears was measured with a result of 270 g.

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Figure 21. Carbon fiber prototype.

7. SKIN AND LIGAMENTS

For the skin, an elastic and light material was needed. Two materials were tried: The first one was Ecoflex, a material with an excellent elasticity but unfortunately too heavy for the structure. After that, a material as elastic as the Ecoflex but a lot less heavy was desired. Pure latex was tried but a lot of layers were needed to avoid breakage and the weight started to rise. To solve this problem a fiber (panty hose) was used as a first layer and then only three more layers of latex were needed to get the desired result. The obtained material was light, with good elasticity and impermeable.

The ligaments were based on the anatomy of the human knee. The cruciate ligaments (figure 22) stabilize the knee joint against shifting movements of the leg and return it to its natural position. This idea was adapted to the wing joint and two cruciate ligaments were added to the structure (figure 23). The material for the ligaments was the same as for the skin but with more layers of latex to increase the material’s constant. The process to choose the amount of latex layers necessary was iterative giving a result of six layers needed.

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Figure 22. Human knee’s cruciate ligaments.

Figure 23. Wing joint’s cruciate ligments.

8. MOTION CONTROL

For the motion control, two elements had to be picked: the servomotors and the motor. The servomotors chosen are the ones with higher torque (9 g) available in the local market. Unfortunately, even though they work fine when there are no counter forces; when the skin was added and the wind was blowing during the tests, the servomotors torque wasn’t enough. For future work, servomotors with higher torque are advised.

For the servomotors control, the code used synchronizes the servos with an encoder that reads the angular velocity of gear 4. The angle of attack as explained before must be positive during the upstroke and negative during the down stroke. The angle changes almost instantly as the wings go up and changes again when they start to go down (https://youtu.be/Vc5uU6PDQpw).

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The motor was chosen after an analysis with the final prototype. Because the gears, the friction and the action of the skin and ligaments increase the torque needed to move the structure, the analysis made with the wood prototype was useless. In the end, a 2 kg motor was chosen. No control was needed for the motor, only a voltage input.

The power characterization of the motor is shown in graph 1; the voltage and current were taken for multiple angular velocities and then the power was computed. The current measured was the highest which corresponds to the part of the cycle where the wings are going up.

Graph 1. Motor power vs. Crank gear angular velocity.

As the graph shows, the lower power needed for the wings to start moving is 2,1 W with an angular velocity of 47 RPM.

9. FINAL PROTOTYPE

For the final prototype, all of the above was connected. With the prototype and gears assembled, the motor (figure 24 a), the servomotors (figure 24 b) and the encoder were installed (figure 25). After the synchronization was successful, the ligaments were added and finally the skin was placed to cover the wings (figure 26). For a better stability, an aluminum support seen in figure 27 was attached at the bottom of the hearts. Some final features of the prototype are in table 2.

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Figure 25. Encoder installed.

Figure 26. Prototype’s wing cover with the skin.

Figure 27. Final prototype and aluminum support.

Table 2. Final features of the prototype.

Weight 310 g

Wingspan 0,845 m

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26 10. TESTING

For the testing, two experiments were made: the first one had the purpose to find the lift generated at different angles of attack during the up-stroke and the second one to find the propulsion generated during the down-stroke at different angles of attack.

a. LIFT (Up-stroke)

For the lift experiment the assembly is shown in figure 28. First a block of wood was assembled on top of the tunnel, after that an aluminum bar (bar 1) with 2 strain gages in the half bridge II configuration was placed in cantilever (see appendix 1 for the strain gages calibration). Next, an extra aluminum bar (bar 2) with 2 degrees of freedom (the one depending on the movement of bar 1 and the one that depends on the wind) was pinned to the tip of bar 1. To prevent the prototype from rotating, an extra bar (green bar) was placed in the bottom. Finally, the prototype was hanged upside down (figure 29) in order for the strain gages to sense both weight and lift as positive values. Given that the lift experiment was done quasi-static, the fact that the wings are upside down made no difference.

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Figure 29. Prototype hanged upside-down during lift experiment.

For the experiment, the wind speed was fixed at 6 m/s and the data was taken for six different angles of attack during the up-stroke: 0°, 10°, 15°, 20°, 30° and 40°. For each angle of attack, the change in the gage value was taken for ten different crank positions (between 0° and 180°).

b. PROPULSION (Down-stroke)

The assembly used for the propulsion experiment was the same as for the lift experiment with the difference that it was put upside down (figure 30). During this experiment, the strain gages were calibrated again (see appendix 2). The assembly was change because this experiment was made while the wings were flapping and in this case, the result would have been affected by the gravity. In real life, during the down-stroke the gravity allows the wings to flap harder; if the prototype is upwards, the gravity would go against the down-stroke thus altering the results.

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For this experiment, the wind speed was fixed at 5 m/s. The data was taken while the wings were flapping and the motor speed was at 60 rev/min. The angles of attack used during the down-stroke were -10°, -20°, -30° and -40°and during the up-down-stroke the angle of attack with the best result during the lift experiment was used. A video of the working mechanism in the wind tunnel is available in https://youtu.be/jgY74UzBiNs.

11. RESULTS

For the lift experiment, the lift coefficient was computed (see appendix 3) and 3D graphed along with the crank positions and angles of attack. In graph 2 it can be seen that the angle of attack with more lift coefficient was 30° and the angle with the lower lift coefficient was 0°. As for the crank positions, the one with higher lift coefficients was 0°. This crank position represents when the wings are completely horizontal; the result obtained proves why birds glide the way they do (Appendix 4). The two best results mentioned above merged to give the best lift coefficient of the experiment with a value of 3,45.

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The results for the propulsion experiment are displayed in graph 3, one for each angle of attack. The data was processed as shown in appendix 5. Each one of the graphs has two different types of peaks: wide peaks and narrow peaks. The wide peaks represent the down-stroke and the narrow peaks the up-stroke. During this experiment, the peaks analyzed were the wide peaks. For each graph an average higher propulsion (AHP) was computed in order to compare the results for each angle of attack. The narrow peaks kept the same average value through all the experiment because the angle of attack during de up-stoke was never changed. As it can be seen, the best results obtained were for an angle of attack of -10° with an AHP of 1,23 N.

Graph 3. Propulsion vs. Time for angles of attack of -10º, -20º, -30º, -40º (from top to bottom respectively).

12. CONCLUSIONS

A qualitative analysis of the herring gull´s wings motion was made obtaining data from the secondary a primary parts of the wings. With these results, a mechanism capable of imitating the motion was synthesized and constructed in carbon fiber. After having the prototype, the motion control was implemented successfully being able to adapt to all motor inputs. With all the mechanism working properly, tests were made. The lift experiment showed that among the angles of attack tested, the angle

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that generates more lift was 30° and among all the wing positions tested, the one that generates more lift is the horizontal position. With these results, the higher lift coefficient obtained was 3,45. As for the propulsion experiment, among the angles of attack tested for the down-stroke, the one with better results was -10° with an average higher propulsion of 1,23 N. It is important to clarify that the weight of the prototype was subtracted from all the results showed and because they were all positive, it means the wings were always capable to at least support their weight.

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31 13. APPENDICES

Appendix 1:

For the strain gages calibration, the wood bar (orange) was fixed and an aluminum bar was placed in cantilever on top of it. To this aluminum bar, 2 strain gages were stick in the half bridge II configuration. After that, another aluminum bar was placed on the tip of the first aluminum bar and finally, the aluminum support on figure 27 was welded to the second aluminum bar.

After having the assembly (figure 31), the strain gages were connected to the data collector and the program LabVIEW was used to read this data. The change in the electrical resistance was taken for different weights between 0g and 1211 g. With the information obtained, graph 4

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Graph 4. Mass vs. Electrical resistance. Strain gages calibration for the lift experiment.

Appendix 2:

For the strain gages calibration, the steps of appendix two were repeated with the difference that the assembly was upside-down (figure 32). After having the assembly, the change in the electrical resistance of the strain gages was taken for weights between 50 g and 800 g and graph 5 was created.

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Graph 5. Mass vs. Electrical resistance. Strain gages calibration for the propulsion experiment.

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Appendix 4:

Figure 33. Herring gull gliding.

Dynamics of the herring gull wings - an underactuated approach