A Robotic Mechanism to Validate the Origin of Avian Flight

Received September 24, 2018, accepted October 16, 2018, date of publication October 24, 2018, date of current version November 30, 2018. Digital Object Identifier 10.1109/ACCESS.2018.2877719

A Robotic Mechanism to Validate the Origin of Avian Flight YASER SAFFAR TALORI

AND JING-SHAN ZHAO

Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

Corresponding author: Jing-Shan Zhao ([email protected]) This work was supported in part by the National Natural Science Foundation of China under Grant 51575291, in part by the National Major Science and Technology Project of China under Grant 2015ZX04002101, in part by the State Key Laboratory of Tribology, Tsinghua University, and in part by the 221 Program of Tsinghua University.

ABSTRACT A fundamental way to quantify the origin of flight is the implementation of experiments on the running bipedal with/without flapping wings in order to capture the kinematics of a bird quantitatively. To this purpose, the measured parameters should be the body rolling and the amplitude of flapping accompanied by running, while the wings can be folded and unfolded in a certain angle of attack. Here, we show the analysis and synthesis of a testrig-based bionic robot using screw theory. This paper investigates a multi-purpose bipedal robot to simulate the dynamics and kinematics of a bird from terrestrial running to aero flapping flight. The bird-like robot is composed of lower limb and forelimb mechanisms, including the motions of folding and unfolding the wings, flapping wings, and adjustment of their angle of attack. These mechanisms are integrated together with the robot’s main body in order to make a bipedal movement. The robot mounts on its test rig to create a three-degree-of-freedom model in such a way that the motion is restricted to the lateral sides and only the movement up and down is allowed. INDEX TERMS Flapping flight, forelimbs, lower limbs, folded/unfolded wings, angle of attack, screw theory. I. INTRODUCTION

The origin of avian flight is still one of the most controversial debates in Paleontology [1]–[13]. It has been debated for over 150 years ever since the first fossil of bird, Archaeopteryx, was discovered in 1861 [1]–[4]. Common recognition is that birds evolved from theropod-dinosaurs, the Maniraptora [1]–[5]. According to the information collected from feathered dinosaurs closely related to birds from the Early Cretaceous and Late Jurassic dinosaurs (such as the most primitive winged dinosaur, Caudipteryx which is clearly terrestrial), many scientists believe that avian flight evolved through a number of phases from ground-dwelling quadrupedal reptile [2]–[6], cursorial bipedal ground-dweller [1]–[5], [7], to arboreal life [2], [8] including parachuting [2], [9], [10], gliding [2], [4], [8], [10], [11] and active powered flapping flight [2], [4], [8]–[11]. However, there is increasing support from studies of juvenile birds for a ground up hypothesis in which flight evolved in a terrestrial animal and the flight stroke evolved directly without an intervening gliding stage [12], [16]. Hence, in this study, we propose a robotic testrig in order to validate cursorial possibility for the origin of avian flight. VOLUME 6, 2018

Observation of the performance, behavior and capacity of the birds for very long distance travelling teaches the engineers that they use an efficient and economic mode of motion in the nature and the efficiency of this type of propulsion must be taken into account [1], [2], [17]. In flight, the birds have a regular pathway, without any jerking movement. Its body does not move up and down while the wings move down and up. It shows that the wings carry the bird at every moment. Therefore, the total lift remains constant [18]. The speed obtained by the streamline airflow around the wings provides sufficient lift to maintain the flight [18]–[21]. The horizontal speed due to the displacement is identical along the wingspan, but the vertical speed due to the wing beat is zero at the wing base and increases gradually to the wing tip. The horizontal and vertical speeds combine together and create the angle of attack of the airstream along the wing (horizontal at the wing base and more vertical near the wing tip). Birds adapt its wing twist to keep a nearly constant angle of incidence and hence, the twist angle of the wings tip, twists negative while going down (downstroke), and positive while going up (upstroke). Therefore, twist of the wings leads the bird and allows it to fly [20], [22]. Lift is perpendicular to the plane

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Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

of the wings, thus, it leads the wing forward during descent [22], [23]. Birds are quite different in size and mass, from hummingbird to the vulture, from the insect to the ancient dinosaur, from a few milligrams to 100 kilograms and from one centimeter to ten meters in wingspans [22]–[24]. Avian flight is a complex process involving rapid action and reaction between nervous and musculoskeletal systems of bird and the external environment [25]–[27]. Thus, the accurate process of flying flight including flapping, gliding, soaring and powered flight and adjusting all flight parameters such as downstroke and upstroke still remains to be discovered [28], [29]. Ducks are popular and widespread in many different kinds. They can help the engineers to identify the characteristics of any part of duck more quickly and properly [15], [27]–[32]. Most ducks have relatively short legs and they are set far back on their body, which makes them an ungainly walk on the ground but gives them more power while swimming. It seems the legs of birds may not be considered to be an important requirement in flight but the initially required power supplies by the legs and it provides enough force during takeoff for many birds. The similar performance can be considered during landing where the legs are often utilized to tolerate the large amounts of energy that are produced during initial contact with the ground [27]–[29], [33]. Birds that have long wings and high wing loads usually rely on increasing their momentum on the ground by running until they reach a speed that obtains enough lift for takeoff but ducks do not run on the ground to get speed, instead some dabbling ducks such as the mallard, are able to launch themselves in vertical direction from the water using their strong flight muscles and then in the air they use the full strokes of their wings to continue their upward motion. The motion of the wings is controlled by the muscles and governed by the bones and joints [25], [26], [15], [29]–[33]. The free movement around the joint of the wrist of bird’s wings is omitted in order to have only movement in one plane and prevent the wings from bending up/down by the applied forces during flight. Also, elbow and wrist joints are connected in such a way that extending the elbow automatically extends the wrist. Both the ulna and the radius have their own articulation on the distal end of the humerus. The ulna is more distal to the radius on the elbow because when the elbow is bended the two bones of the forearm oppose one another and the radius is also pushed into the various carpal bones of the wrist whiles the ulna is withdrawn. Therefore, this automatically makes the forelimb flexible to be folded. In unfolding process, the opposite movement occurs. In this way, the wings are controlled by the flight muscles [25], [29]. Humans are covered in skin, birds are covered in feathers, and bats are covered in hair. From the outside, human arms, birds and bats wings look very different but from the inside there are many similarities among human, bird, and bat forearms. They have the exact same types of bones in their forearm. These organisms share the same forearm bones, because they all evolved from a common ancestor. Human, bird, and bat forelimbs’ bones include the humerus, ulna, 64982

FIGURE 1. (A) Human hand, (B) bird and (C) bat forelimb comparison. Wings evolved from the same structure as an arm, hence, they are quite similar. It is mostly the hand structure that makes the difference. Birds have most of the hand bones united in simple shapes. Bats’ fingers are very long and they also start directly from the wrist.

radius, carpals, metacarpals, and phalanges. Both birds and bats use their thumbs for precise maneuvers in flight and when the wings are folded, all of the bones try to come closer to each other (Fig. 1) [28], [29]. A basic method to understand the origin of flight is performing the experiments and tests on the extant birds or bird-like robot. This study focuses on bird-like robot and represents how to use some simple but efficient mechanisms and integrate them together to create a bipedal robot. This investigation has been done in order to better quantify the kinematics and dynamics of walking/running and flapping flight of a flying bird. In order to implement experiments on running with/without flapping of birds, a multi-purpose bipedal robot is considered. This paper investigates the architecture schemes of the lower limbs [34]–[40] and forelimbs [41]–[43] of a bipedal robot. A three-degree-of-freedom testrig based robot is designed inspiring from the biology kinematic characteristics of a duck. In lower limbs, an architecture model is first quantified and second, leg mechanism for walking/ running with the approach of Jansen’s ideal walking curve [44], [45] is analyzed. Also forelimbs including flapping, folding and unfolding wing mechanisms with the capability of changing angle of attack are investigated. The twists and constraints of the chain have been discussed with reciprocal screw theory for the kinematics of mechanisms [46], [47]. The present design gives the possibility to produce a light and very powerful mechanism that can be fabricated by 3D printer and it shows that the goals are very close to the purpose. II. OVERVIEW OF THE ROBOTIC MECHANISM ON THE TEST RIG

A multi-purpose bipedal robot has been designed in order to mimic the behavior of running duck to simulate the dynamics VOLUME 6, 2018

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

FIGURE 2. Three-degree-of-freedom robot on the test rig. (Supplementary video 1).

of a bird from terrestrial running to avian flapping flight. This bionic robot is a three-degree-of-freedom testrig based robot inspired by the performance of duck. The bird-like robot consists of lower limb and forelimb mechanisms composed of running, flapping wings, folding and unfolding the wings and adjustment of angle of attack mechanisms. Each mechanism actuates with an electric motor and the control system of all mechanisms are passive. These mechanisms are assembled together by the main body to make a bipedal robot and mounted on the testrig in order to restrict the movements of the robot. The testrig is composed of treadmill in the bottom and two walls in front and back. The main central axis of the robot has two planar bearings contacting with the walls in order to keep the main axis of the robot in parallel with the testrig. Therefore, planar bearings and the walls make constraints for the motion of the robot. Hence, the robot is only able to move up and down, left and right and roll about its axis (namely the robot can move along the Y- and Z-axes and rotate about the X-axis) (Fig. 2). (see the supplementary material 1 for more details about the bill of material). The twists and constraints of the chains have been analyzed and discussed with reciprocal screw theory for the kinematics of mechanisms. III. METHOD OF RECIPROCAL SCREW THEORY

The kinematic chain analysis and synthesis with reciprocal screw theory are used for leg and wing mechanisms. Screw theory established in 1871 from the investigation of line geometry by Ball [46]. A rigid body’s instantaneous velocity and the force exerting on it can be expressed by screws [47]. Screws are utilized to represent the constraints that a spatial rigid body is subject to and its free motions under these constraints [48]. A screw is completely determined by its axis and pitch in geometry [47], [48]. Therefore, the twist matrix of a kinematic chain demonstrates the free motions of the chain and its reciprocal screws denote a full expression of the terminal constraints [50]–[52]. The reciprocal relationship between the motion screw and wrenches provides a pretty means to analyze and synthesize a spatial mechanism. For a screw system, the principal screws determine the VOLUME 6, 2018

mechanical characteristics of the system and the terminal constraint of a kinematic chain is decided by the maximal independent set of the twists. This method can be widely applied for the kinematic chains of all kinds of bionic mechanisms and complicated robots [46]–[52]. Based on screw theory [53]–[56], the equation $T 1$r = 0 is given,where 0 I3×3 $r is the reciprocal screw of $ and 1 = when I 3×3 0   100 I3×3 =  0 1 0 . The Plücker homogeneous coordinates of 001 a line are used to define the twist as $ = [ l m n p q r ]T which is subjected to l 2 + m2 + n2 = 1 and lp + mq + nr = 0, where l, m and n represent the angular velocity and p, q and r denote the linear velocity of a point in the rigid body corresponding to the origin of the coordinate system. In a similar way, $r , reciprocal screw matrix is expressed by $r = [ l r mr nr pr qr rr ]T where lr , mr and nr represent the resultant force and pr , qr and rr denote the resultant torque about the origin of the coordinate system. Hence, equation $T 1$r = 0 can be rewritten as lpr + mqr + nrr + pl r + qmr + rnr = 0. The physical meaning is that the work done at any instant by the external forces to a stable rigid body should always be zero. The motion and constraints of lower limb and forelimb mechanisms of a bipedal are captured by analyzing the twist matrix of the kinematic chain. IV. WALKING/RUNNING MECHANISM OF LOWER LIMBS

Most of birds have similar anatomy of structure in lower limbs (Fig. 3). In the perspective of mechanics, only linkages are in different sizes but the joints are almost similar [34]. A reconstructed duck leg can contain a universal joint in hip, a linkage in femur, a revolute joint in knee, a linkage in tibiotarsus, a revolute joint in heel, a linkage in tarsometatarsus and a spherical joint in pedal, respectively (Fig. 3). A. KINEMATIC CHAINS OF THE BIPEDAL LOWER LIMB MECHANISM

Kinematic chain of the simple and rough architecture of the duck lower limb has been established (Fig. 4). The biologic 64983

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

The twist of the heel joint (revolute joint C) is $4 = [ 1

0

0

0

−yC ]T

zC

(4)

The twists of the pedal joint (spherical joint D) are $5 = [ 1 $6 = [ 0 $7 = [ 0 Therefore, $ABCD  1 0 0 1  0 0 $ABCD =  0 0  0 0 0 0 FIGURE 3. Bird’s leg structure. (A). Duck leg’s anatomy. (B). Reconstructed duck legs. (C). Right side of the legs of bipedal birds in lateral view, showing single-limb support [34].

kinematic chain of the lower limb of duck is composed of one universal joint in the hip, two revolute joints in the knee and the heel and one spherical joint in the pedal in series. As the analysis results of the kinematic chains with screw theory are independent with the selection of coordinate system, the coordinate system is set on the hip joint (universal joint) in such a way that most of the screw coordinates can have the simplest expressions. We supposed the origin of the coordinate system is superimposed with the center of hip joint (universal joint A), x-axis is parallel to the axis of the knee/heel joint (revolute joint B/C), y -axis is perpendicular to line AB and z-axis is along the line AB. In the defined coordinate system, it is assumed that the coordinates of joint A, B, C and D are A(0 0 0), B(0 0 zB ), C(0 yC zC ) and D(0 yD zD ), individually. The twist matrix, $ABCD , consists of the twists of the universal joint A, revolute joints B and C and spherical joint D. The twists of the hip joint (universal join A) are $1 = [ 1

0

0

0

0

0 ]T

(1)

$2 = [ 0

1

0

0

0

0 ]T

(2)

The twist of the knee joint (revolute joint B) is

64984

0

0

0

zB

0 ]T

1

0 0

0

−yD ]T

zD 0

−zD

(5)

T

0]

(6)

T

(7)

0 1 yD 0 0 ]   = $1 $2 $3 $4 $5 $6 $7 . 1 0 0 0 zB 0

1 0 0 0 zC −yC

1 0 0 0 zD −yD

0 1 0 −zD 0 0

 0 0   1   yD   0  0 (8)

The constraint analysis is given by ($TABCD 1)$rABCD = 0.   0 0 0 1 0 0  0 0 0 0 1 0    0 zB 0 1 0 0  r   0 zC −yC 1 0 0  (9)  $ABCD = 0    0 z −y 1 0 0 D D    −zD 0 0 0 1 0 yD 0 0 0 0 1 Therefore, in general cases, the rank of matrix $ABCD is Rank($ABCD ) = 6 which means the degree of freedom of the end-effector (pedal) is six and the reciprocal screw of the kinematic chain of the duck’s lower limb mechanism proves that there is no constraint for the motion of the end-effector.

FIGURE 4. Kinematic chain of duck lower limb mechanism (URRS).

$3 = [ 1

0

(3)

FIGURE 5. Planar linkage of duck lower limbs.

In order to actuate and control the pedals (end-effectors) some electric motors must be utilized. For the sake of simplicity, a planar linkage has been considered for each leg and the trace path of the end-effector has been analyzed in order to be similar with Jansen’s ideal walking curve. To obtain an acceptable trace path and optimum size of the linkages, all dimensions of the linkages have been analyzed (Fig. 5). VOLUME 6, 2018

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

FIGURE 6. Configurations of lower limb mechanism. (Supplementary Video 2).

FIGURE 7. Kinematic chain synthesis of leg mechanism of a running bipedal.

All joints in the leg mechanism are revolute ones except the pedals that are universal pairs. To keep pedals in parallel with the surface of the testrig, auxiliary mechanism is used (Fig. 6). Walking/running mechanism works by only one electric DC motor and using worm and worm gear as a power transmission system (see the supplementary material 2 for more details about the gears). When the DC motor works, the leg mechanism simulates the motion of a walking duck. In all joints, ball bearings are utilized and the linkages are made of light materials fabricated by 3D printer. The main body which is a chassis or skeleton of the robot is composed of two parts in such a way that it makes a connection between legs and flapping wing mechanism. The material of the main body is also light and manufactured by 3D printer (Fig. 6). Hence, the main body of robot contains lower and upper segments. Lower limb mechanism is attached to the lower segment and flapping wing mechanism is connected to the upper segment. The interface between upper and lower segments is the main central axis and both segments are able to rotate about this axis freely. The rolling of the body is limited by two springs to make flexibility between upper mechanisms and lower mechanism passively. VOLUME 6, 2018

Joints A, I and H are fixed on the main body of the mechanism and the whole mechanism works under the actuation of a DC motor on joint G. Joint A is the origin coordinate of the system (XYZ) and the position of the pedal (x, y, z) that is attached to the end-effector (link DL) is measured in coordinate with respect to the origin. The links BCD and CEF are unified and joints C and E are assembled near the middle, respectively. The linkages IJ, BJ, JK, CK and KL are dedicated to keep the end-effector (DL) in horizon and to be parallel with the testrig (Fig. 7). The kinematic chain of the running leg mechanism is analyzed. Twists of joints G, F and E are as follows $GFE = [ $G

$F

$E ] 0 ]T

$G = [ 0

0

1

0

$F = [ 0

0

1

a sin α

$E = [ 0

0

1

b sin β + YH

0

a cos α

0 ]T

b cos β − XH

0 ]T (10)

where a and b represent the length of links GF and HE, individually (Fig. 7). Based on screw theory, the wrench matrix of kinematic chain GFE is obtained by the reciprocal 64985

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

screw equation ($TGFE 1)$rGFE = 0:  0 0 1 0 $rGFE =  0 0 0 1 0 0 0 0

where c represents the length of link AB (Fig. 7). The wrench matrix $rAB of kinematic chain AB is obtained

T

0 0 1

0 0 0

(11)

Similarly, the twist matrix of kinematic chain HE can be given as $HE = [ $H $H = [ 0 $E = [ 0

$E ] 0 0

1

YH

1

b sin β + YH

−XH

b cos β − XH

0]

$rHE 0 0 0 0   = 0 0  sin β cos β − XH sin β +YH cos β XH sin β +YH cos β 

T 1000 0 1 0 0  0 0 1 0  0001 (13)

The wrench system applied on link FE depends entirely on Equations (11) and (13). Consequently, according to the wrench matrix of link FE again free motion screw of link FEC can be obtained as sin β

0

cos β

0 ]T

(14)

Equation (14) shows that the screw of link FEC is an instantaneous translation along the direction (sin β cos β0)T which is a function of β angle. The linkage BC, tolerates constraints from the kinematic chains FEC and AB. The twist matrix of kinematic chain FEC_B can be expressed as $FEC_B = [ $FEC

$C

The twist matrix of link AB again can be calculated from (18) as $AB = [ 0

0

0

sin β

$C = [ 0

0

1

YC

cos β

$B = [ 0

0

1

c sin θ +YA

0]

c cos θ −XA

0 ]T (15)

The wrench matrix of kinematic chain FEC_B is obtained as  T 0 0 1 0 0 0 $rFEC_B =  0 0 0 1 0 0  (16) 0 0 0 0 1 0

$rAB = [ $r1 $rIJ = [ $r5

$A = [ 0 $B = [ 0

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0 0

YA

1

c sin θ + YA

−XA

0]

c cos θ − XA

$B ] $J ]

(19)

(21)

$r2 $r6

$r3 $r7

$r4 ] $r8 ]

$r1 = [ 0

0

1

0

0

0 ]T

$r2 = [ 0

0

0

1

0

0 ]T

$r3 = [ 0

0

0

0

1

0 ]T

$r4 = [ cos θ

1

0 ]T

(22)

where

$B ] T

cos θ

The free motion of link BJ with respect to the body (link AI) can be obtained by getting the reciprocal screws of links AB and IJ.

The twist matrix of kinematic chain AB can be expressed as $AB = [ $A

sin θ

0

$AB = [ $A $IJ = [ $I

T

0 ]T

−XC

0

The wrench system applied to BC depends completely on Equations (16) and (18). Consequently, according to screw matrices applied on link BCD (i.e. links AB and FEC), free motion screw of link BCD is a combination of (14) and (19). Hence, it can be written as  T 0 0 0 sin θ cos θ 0 $BCD = $BC = (20) 0 0 0 sin β cos β 0 Equation (20) shows that the screws of linkage BCD are instantaneous translations along the directions (sin β cos β0)T and (sin θ cos θ0)T . Namely, motion of linkage BCD is a function of θ and β angles. Therefore, the two screws represented in (20) are not independent but restricted by the actuating parameters, θ and β (see trace path of joints C and D in Fig. 7). To realize the situation of link DL (pedal is attached to link DL), as the performance of links BJ, CK and DL are parallel, the relative motion of link BJ with respect to the body (link AI) is analyzed. Link BJ has two kinematic chains, AB and IJ, hence, the twists of them, are considered individually. For the sake of simplification, joint A is assumed as an origin, hence, for link ABandIJ there are

$B ]

$FEC = [ 0

T 1000 0 1 0 0  0 0 1 0  0001 (18)

T

The wrench matrix of kinematic chain HE ($rHE ) is written as

0

0 0  0 0  = 0 0  sin θ cos θ − XA sin θ + YA cos θ XA sin θ + YA cos θ

0 ]T (12)

$FEC = $FE = [ 0

$rAB 

sin θ

0

0

0

0 ]T

(23)

and T

$r5 = [ 0

0

1

0

0

0 ]T

(17)

$r6 = [ 0

0

0

1

0

0 ]T

0]

VOLUME 6, 2018

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

$r7 = [ 0 0  $r8 = cos θ

0

0

sin θ

0 ]T

1 0

0

XAB sin θ

0

T

(24)

where XAB is the distance between joints A and I. Therefore, the wrenches exerted by the kinematic chains of links AB and IJ to link BJ in matrix form can be expressed as $rBJ = [ $r1

$r2

$r3

$r4

$r8 ]

(25)

The twist matrix of link BJ, $BJ , would be obtained by T using the equation $rBJ 1$BJ = 0 as   0 0 0 0 0 1 1 0 0 0 0 0   0 1 0 0 0 0   $BJ = 0 0 0 0 cos θ sin θ 0  0 0 XAB sin θ cos θ sin θ 0 (26)

FIGURE 8. Changes of center of mass of the pedal and its trace path (footprint) during running. The movement variations of pedal are drawn in x and y directions during running in 5 seconds. Also the final footprint of the pedal in the xy-plane and a cycle is captured.

Therefore,  $BJ = 0

0

0

− sin θ

cos θ

0

T

(27)

Equation (27) illustrates that link BJ instantaneously makes a translational movement along the direction
T − sin θ cos θ 0 which is just perpendicular to the centerline of the crank. Hence, link BJ is always parallel with the base. Therefore, the motion synthesis and wrench matrix of the end-effector (link DL) of the running leg mechanism represents that the constraints are the force along the z-axis and two moments (torques) about the x- and y-axes (roll and yaw). It means link DL only has the motions along the x- and y-directions and a rotation about the z-axis. The pedal is attached to link DL (Fig. 7) in such a way that the rolling angle is restricted passively by using two springs in both sides of the joint although it allows the pedal to rotate about the x-axis (rolling). Pedals have 55 mm displacement in x-direction and 22 mm in y-direction (Fig. 8). The linear velocity and linear acceleration of the pedal change periodically during running (Fig. 9). Also all links of the leg mechanism have their own angular velocities and angular accelerations while the mechanism moves (Fig. 10). As a DC motor at the speed of 300 rpm is assumed for the mechanism, hence, considering the characteristics of the gears (see the supplementary material 2 for more details about the gears), the period of a cycle would be one second. V. WING MECHANISM

A mechanism with the capability of folding and unfolding of the wing has been designed (Fig. 11). Therefore, with respect to the area of the fully extended wings, in order to simulate the duck flapping (downstroke and upstroke), each wing includes three parts. The parts have been connected together by a mechanism which is composed of two spur gears and two linkages (see the supplementary material 2 for more details about the gears). The gears are made of steel and the linkages are made of ABS and fabricated by 3D printer. The folding and unfolding wing mechanism works by a four-bar linkage VOLUME 6, 2018

FIGURE 9. Changes of linear velocity and acceleration of the pedal during running in x- and y-directions within 5 seconds. The values are obtained by using a DC motor for the mechanism which is driven at the speed of 300 rpm (the changes of pedal linear acceleration is captured in supplementary video 3).

(AB, BC and CDF links) acting by a mini servo motor at joint A (Fig. 11). Spur gear F is fixed to link CDF and is able to rotate related to link FH at joint F. Also spur gear G is fixed to link GI and has freely rotation related to link EG at joint G. In a similar way, spur gear I is fixed to link GI and freed to link IK at joint I and spur gear H is freed to link FH and fixed to HJ. When the four-bar linkage employs, motion of joint F excites the mechanism to extend or fold the wing in wingspan direction (Z-direction). The power transmission line is link CDF, gear F, gear G, link GI, gear I, gear H and finally link HJ, respectively. Between the links, airfoils which are made of fiber carbon are utilized in order to simulate a wing from wing root to the tip. They are all parallel to each other during wing motion (Supplementary video 4). 64987

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

Similarly, the twist matrix of kinematic chain EG can be written as $EG = [ $E $G ] $E = [ 0

0

1

0

$G = [ 0

0

1

l1 cos α

0 ]T

−a

−(a + l1 sin α)

0 ]T (32)

where a is the distance between joints D and E, and l1 represents the lengths of links DF and EG, then the wrench matrix of kinematic chain EG ($rEG ) is obtained as  T 0 0 1 0 0 0  0 0 0 1 0 0   $rEG =  (33)  0 0 0 0 1 0  sin α cos α 0 0 0 a cos α The wrenches applied to link FG depends on (29), (31) and (33). Therefore, based on wrench matrix of link FG, the twist of link FG can be obtained as $FG = [ 0

$FH = [ $F

The kinematic chain of the folding and unfolding mechanism of the right wing is analyzed. Twist of joints A, B and C are given as $B

$C ]

$A = [ 0

0

1

YA

−XA

0 ]T

$B = [ 0

0

1

YB

−XB

0 ]T

$C = [ 0

0

1

YC

−XC

0 ]T

(28)

In a similar fashion, the twist matrix of kinematic chain DF can be obtained as $F ]

$D = [ 0

0

1

0

$F = [ 0

0

1

l1 cos α

0

0 ]T −l1 sin α

The wrench matrix of kinematic chain presented by  0 0 1 0 0  0 0 0 1 0 $rDF =   0 0 0 0 1 sin α cos α 0 0 0 64988

0 ]T (30)

DF ($rDF ) is T 0 0  0 0

cos α

− sin α

0 ]T

(34)

$H ]

$F = [ 0

0

1

l1 cos α

$H = [ 0

0

1

(l1 +l2 ) cos α

(31)

−l1 sin α

0 ]T

−(l1 +l2 ) sin α

0 ]T (35)

where l2 is the length of links FH and GI. The wrench matrix of kinematic chain FH ($rFH ) is obtained as 

According to screw theory, the wrench matrix of kinematic chain ABC is acquired by the reciprocal screw equation ($TABC 1)$rABC = 0.  T 0 0 1 0 0 0 r $ABC =  0 0 0 1 0 0  (29) 0 0 0 0 1 0

$DF = [ $D

0

Equation (34) shows that the twist of link FG is an instantaneous translation along the direction (cos α − sin α0)T . The twist matrix of kinematic chain FH can be written as

FIGURE 10. Changes of angular velocity and acceleration of the leg mechanism. The graphs are captured while a DC motor is utilized to enforce the mechanism at the angular velocity of 300 rpm. They are illustrated in 5 seconds.

$ABC = [ $A

0

$rFH

0  0 =  0 sin α

0 0 0 cos α

1 0 0 0

0 1 0 0

0 0 1 0

T 0 0  0 0

(36)

Similarly, the twist matrix of kinematic chain GI can be gained $GI = [ $G $G = [ 0

$I ] 0

1

l1 cos α

−(a + l1 sin α)

0 ]T

$I = [ 0 0 1 (l1 + l2 ) cos α −a − (l1 + l2 ) sin α 0 ]T (37) The wrench matrix of kinematic chain GI ($rGI ) is calculated as  T 0 0 1 0 0 0  0 0 0 1 0 0   (38) $rGI =   0 0 0 0 1 0  sin α cos α 0 0 0 a cos α The wrench system exerted on link HI depends on (36) and (38). Hence, according to the wrench matrix of link HI, its twist can be obtained as $HI = [ 0

0

0

cos α

− sin α

0 ]T

(39)

VOLUME 6, 2018

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

FIGURE 11. Folding and unfolding of the wing mechanism. Linear displacement and the changes of linear velocity in three directions are drawn. The structure of the wing mechanism and the attached airfoils are shown from folded wing to the unfolded one.

Equation (39) shows that the twist of link HI is an instantaneous translation along the direction (cos α − sin α0)T . In the same way, we obtain a similar equation to (34) and (39). It indicates that the third, JK, and second, HI, beams have the same motion as that of the first one, FG and therefore, all of them have the same translational degree of freedom ($FG = $HI = $JK ). VI. FLAPPING MECHANISM

This mechanism is operated by three spur gears and two fourbar linkages by using one DC motor. DC motor is mounted on joint A and coupled to Gear A (Fig. 12). Gear A enforces gears B and C and they both execute two four-bar linkages to create the reciprocal motion of the wing mechanisms. Four-bar linkage of right wing is composed of links BD, DF and FH, and left wing contains links CE, EG and GI while the joints B, H, C and I are fixed on the body. The maximum flapping angle in upstroke is 48◦ and in downstroke is 67◦ . (see the supplementary material 2 for more details about the gears). The kinematic chain of the flapping mechanism only for the right end-effector for the sake of similarity with the left one is given. Hence, the twists of joints B, D and F are VOLUME 6, 2018

calculated as $BDF = [ $B

$D

$F ]

$B = [ 0

0

1

YB

−XB

0 ]T

$D = [ 0

0

1

YD

−XD

0 ]T

$F = [ 0

0

1

YF

−XF

0 ]T

(40)

Based on screw theory, the wrench matrix of kinematic chain BDF is acquired by the reciprocal screw equation ($TBDF 1)$rBDF = 0. 

$rBDF

0 = 0 0

0 0 0

1 0 0

0 1 0

0 0 1

T 0 0 0

(41)

Wing mechanism is mounted on link HF and the movement of the wings are considered during flapping (Fig. 12). Similarly, the twist matrix of kinematic chain HF can be obtained as $HF = [ $H

$F ]

$H = [ 0

0

1

0

$F = [ 0

0

1

l sin β

0

0 ]T −l cos β

0 ]T (42) 64989

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

FIGURE 12. Structure of the four-bar linkages of the flapping mechanism. Maximum flapping angle in upstroke and downstroke, trace path of the wing tip and kinematics of the mechanism are illustrated.

FIGURE 13. Center of mass of the left wing changes during flapping. (the CoM of the left wing changes in Y-direction during flapping is captured in supplementary video 5).

The wrench matrix of kinematic chain gained  0 0 1 0 0  0 0 0 1 0 r $HF =   0 0 0 0 1 cos β sin β 0 0 0

HF ($rHF ) is T 0 0  0 0

(43)

The wrench system applied to link HF (right wing) depends on (41) and (43). It illustrates two pure forces 64990

along the Z-axis and the centerline of crank HF and two moments of couple (torques) around X- and Y-axes. Based on wrench matrix, the free motion screw of link HF again is obtained as $HF = [ 0

0

1

sin β

− cos β

0 ]T

(44)

Equation (44) represents the twist motion of linkage HF. Center of mass of the wings which can change about 215 mm in Z-direction and 37 mm in Y-direction (Fig. 13). VOLUME 6, 2018

Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

FIGURE 14. Adjustment mechanism of angle of attack changing from −20◦ to +45◦ .

VII. ADJUSTMENT MECHANISM OF ANGLE OF ATTACK

In aerodynamics, angle of attack is the angle between the body’s reference line (wing’s chord line) and the oncoming flow. The lift coefficient of wings changes with angle of attack. Increasing angle of attack increases lift coefficient before reaching the stall. The integrated wings and flapping mechanisms are mounted on the upper bracket of the main body and this unified set is able to rotate about the axis (AA0 ) by using a set of worm wheel and worm gear (Fig. 14). A mini-servo motor is dedicated to apply momentum on the worm gear, and by rotating the worm wheel the whole flying complex rotates in order to adjust angle of attack. (Fig. 14). The angle of attack varies from −20◦ to +45◦ relative to the main central axis (see the supplementary material 2 for more details about the gears). VIII. CONCLUSION

In this paper a set of mechanisms have been designed in a unit to simulate a bipedal gait and flying in order to implement supplementary experiments about walking/running and flapping. During this investigation, all mechanical mechanisms are inspired from the performance of a real duck. In lower limb mechanism, the footprint of the pedal represents the movement of legs and trace path of the forelimb mechanism (wing beat mechanism) demonstrate the amplitude of flapping. Depends on the predefined mission of the experiments, both lower (running) and upper (flapping) mechanisms are able to act either simultaneously or individually. Changeability on the angle of attack of the wings is another opportunity for the experiments to simulate takeoff and landing situations. Also flapping in any length of wingspan (from folded to unfolded), depend on the strategy of the experiments (flapping in any wing aspect ratio) is possible. Therefore, to reach these aims, a three-degree-of-freedom robot is designed and quantified. The changes of center of mass of the body (rolling of the body) and the amplitude of the wing flapping angle (caused by passive or active flapping beat) during running can be measured by using accelerometers on the body and the wings. These values would be obtained from lower to higher velocity while the robot flaps in any wing aspect VOLUME 6, 2018

ratio (wingspan) and angle of attack. In order to analyze the effect of forced vibration applied by the running legs to the wings, the wings should be fixed in arbitrary situation (no flapping) and thus the velocities which excite the wings to act probable rigid /flapping modes can be obtained. ACKNOWLEDGMENT

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Y. Saffar Talori, J.-S. Zhao: Robotic Mechanism to Validate the Origin of Avian Flight

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YASER SAFFAR TALORI was born in Tehran, Iran, in 1979. He received the B.S. degree in mechanical engineering from the K. N. Toosi University of Technology in 2003, the M.S. degree in aerospace engineering from Beihang University in 2015, and the Ph.D. degree with the Department of Mechanical Engineering, Tsinghua University, in 2018. From 2003 to 2013, he was involved in design and manufacturing of space structures and mechanisms. His research interests include analysis, design, optimization, and manufacturing of mechanical structures, mechanisms and robots, fast runner bipedal robots, bionic and robotic birds, and flying mechanisms. JING-SHAN ZHAO was born in Shandong, China, in 1974. He received the B.S. degree in mechanical engineering from the University of Science and Technology Beijing in 1998 and the Ph.D. degree from Tsinghua University in 2004. He is currently a Professor of mechanical engineering with Tsinghua University. He actively supervises many students at all level of study, bachelor’s, master’s, and Ph.D. He has authored three books, over 90 articles, and over 50 inventions. His interest of research includes spatial mechanisms, mechanism synthesis, theoretical kinematics, workspace and singularity analysis, robot design, design of bionic robot, design and application of industry robot, mechanical system dynamics and control, structural dynamics, vibration analysis and control, structure strength analysis and optimization, foldable mechanism synthesis, vehicle system engineering, suspension and steering system, and transmission system optimization.

VOLUME 6, 2018