Pitching Moment Generation in an Insect

Corresponding author: Hoon Cheol Park E-mail: [email protected]

Journal of Bionic Engineering 11 (2014) 3651

Pitching Moment Generation in an Insect-Mimicking Flapping-Wing System

Tri Quang Truong1,2, Vu Hoang Phan1,2, Sanjay P. Sane3, Hoon Cheol Park1,2 1. Biomimetics and Intelligent Microsystem Laboratory & Artificial Muscle Research Center, Konkuk University, Seoul 143-701, Korea

2. Department of Advanced Technology Fusion, Konkuk University, Seoul 143-701, Korea 3. National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bangalore, India

Abstract Unlike birds, insects lack control surfaces at the tail and hence most insects modify their wing kinematics to produce

control forces or moments while flapping their wings. Change of the flapping angle range is one of the ways to modify wing kinematics, resulting in relocation of the mean Aerodynamic force Center (mean AC) and finally creating control moments. In an attempt to mimic this feature, we developed a flapping-wing system that generates a desired pitching moment during flap-ping-wing motion. The system comprises a flapping mechanism that creates a large and symmetric flapping motion in a pair of wings, a flapping angle change mechanism that modifies the flapping angle range, artificial wings, and a power source. From the measured wing kinematics, we have found that the flapping-wing system can properly modify the flapping angle ranges. The measured pitching moments show that the flapping-wing system generates a pitching moment in a desired direction by shifting the flapping angle range. We also demonstrated that the system can in practice change the longitudinal attitude by generating a nonzero pitching moment.

Keywords: flapping-wing system, pitching moment, flapping angle, unsteady blade element theory, mean aerodynamic center, center of gravity

Copyright 2014, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(14)60018-4

1 Introduction

Flying insects generate the aerodynamic forces necessary for control flight entirely by modulating their wing kinematics because, unlike birds, most insects have no control surfaces at the tail. Recent studies have un-covered previously unknown unsteady aerodynamic mechanisms of flapping flight in insects. These include the clap and fling[1], leading edge vortex generation[2,3], rotational lift[2,4], and wing-wing interaction[5] mecha-nisms, which help explain the basic principles of un-steady force generation in insect flight. Armed with a clearer picture of the mechanisms of flight force gen-eration, it is possible to focus on mechanisms underlying the stability and dynamics of insect flight.

Among the many approaches used to study this problem include the use of blade element theory and quasi-steady aerodynamics on insects that were teth-ered[6], the use of inverse methods on flapping wings in freely flying or virtual models[7]. In addition to these,

there has been substantial progress in predicting the unsteady force generated by flapping wings. Three-dimensional Computational Fluid Dynamics (CFD) has been successfully applied to solve the Na-vierStokes equations for flapping wings in low Rey-nolds number regimes[8,9]. However, the CFD modeling suffers from strong mesh dependency and requires large computational resources and computational time. As a more effective approach, Unsteady Blade Element Theory (UBET) has been developed to estimate the unsteady flight force with reasonable accuracy[10,11]. In UBET, unsteady forces such as rotational force and added mass force are incorporated with the translational force that is estimated based on quasi-steady aerody-namics. UBET could also be used to make accurate force estimation on three-dimensional wing kinematics[10], and estimate the mean aerodynamic force center[12], which is crucial in assessing the flight stability of a flapping-wing system. Thus, the mathematical tools developed to predict the unsteady force generated by

Truong et al.: Pitching Moment Generation in an Insect-Mimicking Flapping-Wing System 37

flapping wings offer an easy means for rapid estimation of aerodynamic forces and torques.

However, designing mechanisms for control force and moment generation, which should be integrated to a flapping-wing mechanism, remains a nontrivial job. Therefore, it is beneficial to first learn the methods that insects use to generate control forces, and then simplify these methods to design a control mechanism. Across the range of insect taxa, several parameters have been observed to contribute to the generation of control force in typical insect flight[13]. These include the stroke am-plitude (or amplitude of the flapping angle)[14], wing beat frequency (or flapping frequency)[15,16], and the change in posture[17,18], as well as changes in wing stroke plane[19,20]. Mostly, stroke amplitude is regarded as the main control parameter of aerodynamic force generation in fruit flies[13]. Change in the stroke amplitude causes relocation of the mean Aerodynamic force Center (AC). Wing beat frequency is another important parameter in flight force and control force generation, and greatly affects force generation and flight speed. In flies and locusts, the change in body posture, via abdominal flexion[17,18] or changes in wing stroke position[19,20], modifies the location of the Center of Gravity (CG) thereby modifies the relative distance between the mean AC and CG to generate a control moment around the body.

On the robotic front, the above findings provide useful clues for developing control mechanisms in flapping-wing systems that mimic insects and lack tail control surfaces. In Ref. [21], two piezoceramic actua-tors were used for a tiny flapping-wing system: a larger actuator for exciting the wings, and another smaller actuator for stroke amplitude modification. With this design, the stroke amplitudes of the left-hand and right-hand wings could be made approximately 20% different, which may generate a control force. Another design described in the literature is a movable thoracic structure that can create asymmetric flapping angles in a pair of wings[22]. The mechanism can create a difference of 15% to 20% in the stroke amplitudes of the left-hand and right-hand wings. These control devices adopt the basic principles of insect flight, although the inclusion of extra actuators and linkages adds weight to the flapper. A recently demonstrated hummingbird-mimicking flap-ping micro air vehicle displayed steady control of its attitude in flight demonstration[23], using a mechanism

that appears to actively control wing kinematic pa-rameters such as wing rotation, in each half stroke of flight control[24]. This flapping-wing micro air vehicle is a unique system that was able to demonstrate varied controlled flight without the need for control surfaces at the tail.

In a previous paper[12], we showed that the genera-tion of pitch moment can be prevented by adjusting the flapping angle range in our flapping-wing system de-signed to mimic the wing motion of the beetle, Allo-myrina dichotoma[25]. In this case, the system could safely take off from the ground even in absence of con-trol[12]. The observation suggested that alteration in the range of flapping angle relocates the mean AC of the flapping wings, even when the amplitudes of flapping angles of the left-hand and right-hand wings were the same. Thus, changes in the flapping angel range, which cause relocation of the mean AC, may enable a flap-ping-wing system to generate zero or non-zero pitch-up or -down moment.

Here, we test this hypothesis by proposing a simple rack-rocker mechanism to change the flapping angle range in a flapping-wing system. We combined the flapping angle change mechanism with the flap-ping-wing system described in Refs. [12,25,26]. The mechanism is able to shift the flapping angle range while maintaining almost the same amplitude of flapping angle. In the following sections, we explain the design, fabri-cation, and evaluation of the flapping-wing system with the mechanism for pitching moment generation.

2 Design of a flapping-wing system

2.1 Design of a flapping mechanism integrated with a rack-rocker mechanism We used the combination of the Scotch yoke and

slider-crank mechanisms to design a flapping mecha-nism that converts the rotational motion ( ) of the crank Rc into the flapping motion ( ) of wings attached to the output link l2, as shown in Fig. 1[25,26]. The flapping mechanism is symmetric about the vertical column, and only the right-hand side of the flapping mechanism is shown in Fig. 1a for analyzing the relationship between the input motion ( ) and the output angle ( ). The Scotch yoke mechanism converts the rotational motion ( ) of the crank Rc, which is driven by an electromagnetic motor, into linear up and down motions of the horizontal slider. The linear motion of the horizontal slider drives

Journal of Bionic Engineering (2014) Vol.11 No.1 38

the slider-crank mechanism to create a flapping motion of the output link l2 around the hinge O3 through the coupler l1. The location of O3 can be shifted by moving the rack up or down, as shown in Fig. 1c. Shifting the rack triggers rotation of the pinion rocker about the fixed hinge O4, which results in rotation of O3. The rotation of O3 about O4 is defined by the rocker angle , as shown in Fig. 1. The relocation of O3 changes the flapping angle range of the output link l2, which is described in detail at the end of this section.

Based on Fig. 1a, the output angle can be found as follows using the law of cosines

2 2 2 2 21 1 2 3 c 3

2 2 22 3 c 3

[ (1 cos ) ( sin sin ) ]cos ,

2 (1 cos ) ( sin sin )

l l l h R l

l l h R l(1)

where 1 3c 3

(1 cos )tan .

sin sinl

h R l (2)

Based on Fig. 1b, the flapping angle can be expressed as

= 90 . (3)

Fig. 1b shows the normal case of = 0 . When the crank Rc rotates from /2 to /2, the leading edge of a wing, which is attached to the output link l2, sweeps from max to min. These last values represent the end of the upstroke and the end of the downstroke, respectively. The flapping angle range can be expressed as [ min, max],

and the amplitude of the flapping angle can be expressed as max min. For the normal case, we expect that the attached wing flaps symmetrically about the x-axis and the output amplitude of the flapping angle is 100 , which means that min = 50 and max = 50 . Once the distance h and the length l2 are chosen, we can find the length l1 and the required length Rc of the crank using

2 2 2 min min1 c 2 2

2 max min

( sin )sin( ) 4 ,2 (sin sin )

h ll h R l l hh l

(4)

2 max minc

2 max min

(sin sin ).

2 (sin sin )l h

Rh l

(5)

Table 1 lists the dimensions used for the present integrated flapping mechanism. By substituting the known values in Eqs. (4) and (5), we can find l1 and Rc.

To change the flapping angle range, we relocate the moving hinge point O3 by shifting the rack up or down as described above and shown in Fig. 1c. For the di-mensions listed in Table 1, we are able to make the rocker l3 tilt down for an angle of = 10 or tilt up for a rocker angle of = 20 , as shown in Fig. 1c. Because of

Rac

k

Rac

k

Fig. 1 Schematics and CAD model of the flapping mechanism. (a) Schematic drawing of the right-hand side of the mechanism; (b) definitions of angles for = 0 ; (c) front view of the CAD model and flapping angle range for various positions (up or down motion of the rack rotates the pinion rocker, which modifies the position of the output link, where the wings are attached; this changes the flapping angle range, maintaining almost the same amplitude of flapping angle.

Table 1 Dimensions of the parts and linkages in the flapping mechanism

Crank, Rc(mm)

h (mm)

Coupler, l1 (mm)

Output link, l2 (mm)

Rocker, l3 (mm)

3.1 8.0 8.4 4.0 2.0


the tilt of the rocker l3, the flapping angle changes and a pitching moment are generated. Thus, tilting down and tilting up the output link triggers pitch-up and -down motions of the flapping-wing system, respectively. These are explained in more detail in the following sections.

By substituting the values of into Eq. (1), we can find the variation of the flapping angle range over a flapping cycle for the three cases of normal, pitch-up, and pitch-down, as shown in Fig. 2. In Fig. 2, the solid line denotes the normal case, the solid line with hollow circles denotes the pitch-up case, and the dashed line with filled squares denotes the pitch-down case.

The plots show time histories of perfectly sym-metric flapping angles for upstroke and downstroke, because the flapping angles were calculated for a con-stant rotating speed of the motor. If the rotational speed of the motor is not constant, the time histories of the flapping angle shown in Fig. 2 can be altered.

From Fig. 2, we can compare the flapping angle ranges ([ min, max]) for the three cases, which are summarized in Table 2. The table shows that we can modify the flapping angle range by changing the rocker angle . The change in the flapping angle range causes relocation of the mean AC, which modifies the relative location between the mean AC and CG. The mean AC is expected to be located at about the mid-stroke[12]. For the normal case, the pitching moment generation can be prevented by adjusting relative location between the mean AC and CG. Based on the Table 2, we expected that the location of the mean AC is shifted down when the flapping angle range is shifted down, which corre-sponds to the case of = 10 . As a result, a pitching moment is generated to make the flapping-wing system pitch up. Conversely, when the flapping angle range is shifted up, which corresponds to the case of = 20 , the location of the AC is now shifted up. Consequently, a pitch-down moment is generated. Therefore, by chang-ing the flapping angle range, we can manipulate the pitching moment generation in the flapping-wing system. Even though the mechanism was designed such that change in the magnitude of flapping angle by shifting the rack can be minimized, the flapping angles of the three cases were not exactly the same. They became about 10% increased or decreased from the flapping angle of the normal case. Despite of the difference in the mag-nitudes of flapping angles, the tree cases could demon-strate the relocation of the mean aerodynamic center to

produce positive or negative pitching moments, which will be explained in the following sections.

Based on this design, we first produced virtual parts and then virtually assembled them using commercially available three-dimensional CAD software, as shown in Fig. 3. The CAD design was used to guarantee suc-cessful assembly after making actual parts. The parts were built according to the CAD design using CAM system (MM-300S, resolution 10 m, MANIX, Korea). We purchased reduction gears, hinges, motor from markets, and constructed an actual assembly of the in-tegrated flapping mechanism.

( = 0 ) ( = 10 ) ( = 20 )

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Cycles (t/T)

60

40

20

20

40

60

Flap

ping

ang

le

(deg

ree)

0

Downstroke Upstroke

Fig. 2 Variation in the designed flapping angle over a flapping cycle.

Table 2 Effect of the rocker angle on the flapping angle range

Flapping angle range Amplitude of the flapping angle min max

Mid stroke angle( max + min)/2

0 (Normal)

50 50 0

10 (Pitch-up)

66 45 11

20 (Pitch-down)

30 63 17

Fig. 3 Virtual parts and assembly of the integrated flapping mechanism.


2.2 Passive wing rotation mechanism Passive wing rotation mechanisms have been used

for flapping-wing systems by some researchers[12,2832]. In Refs. [12,2830], the wings were passively rotated around a flexible hinge attached to the leading edges without any constraints at the trailing edges, which led to mostly constant wing rotation angle throughout the wingspan during the flapping motion. In another type of passive wing rotation mechanism, the trailing edges near the wing roots were constrained while the wings flapped[31,32]. This type of passive wing rotation mecha-nism creates a negative wing twist along the wingspan such that all the wing sections flap with a positive angle of attack for both downstroke and upstroke motion. In one study[31], a flapping-wing system with wing twist generated a higher thrust (force in the body axis direc-tion), and consumed less power than a system without wing twist. Therefore, we incorporated wing twist into the flapping-wing system described in this study. The actual assembly of the integrated flapping mechanism with artificial wings is shown in Fig. 4. The wing length (Rw), mean chord length ( c ) and wing Aspect Ratio (AR) of one wing are shown in Fig. 4. Details of the fabrica-tion of the artificial wings and the constraints of the trailing edge near the wing roots can be found in Refs. [31,32].

3 Estimation of forces and pitching moment using UBET

3.1 Estimation of forces We used a UBET model presented in Refs.

[10,12,31] to estimate the forces generated by the flap-ping-wing system. In the UBET model, the motion of the wing is decomposed into two motions: flapping around the flapping axis (the z-axis) and rotation around the feather axis (the -axis), as shown in Fig. 5a. The feather axis, which corresponds to the leading edge vein in the present flapping-wing system as shown in Fig. 4, flaps in the x-y plane or the stroke plane. The location of the feather axis is determined by the flapping angle . The wing rotation angle of a wing section, which is the angle between the -axis and the wing section, at a distance r from the wing root, is r as shown in Fig. 5b. In Fig. 5b, the wing section moves to the right-hand side (upstroke), and thus the geometric angle of attack of the wing sec-tion is , which can be determined based on the rotation

angle r[10]. The time histories of the flapping angle and wing rotation were acquired by analyzing images taken by two high-speed cameras. Details of the measurement of the wing kinematics are given in section 4.1.

20 mm2.75

cAR

Fig. 4 Actual assembly of the flapping-wing system with arti-ficial wings.

r

z Flapping axis

Stroke plane

Oy

A wing sectionFeather axis

x

(a)

Leading edge (LE)dFTdL

Feather axis

dFT

dD

Leading edge (TE)

c(r)

xfVT

Vi

Vr

(b)

Fig. 5 (a) Definitions of the wing section[10]; (b) force compo-nents for UBET analysis[10,12,31].


The force generated by a wing section has four components: the translational force, the added mass force, the rotational force, and the inertial force[10,11]. Because the flapping-wing system has two wings flapping sym-metrically through the plane of symmetry (the Y-Z plane in Fig. 6), only the nonzero force components in the y and z directions and the pitching moment about the x-axis were of interest in this study. Because more details on the mathematical expression of each force component can be found in Ref. [10], we briefly summarize the equations used for the force components below. 3.1.1 Translational force

The translational force is decomposed into com-ponents in the y direction dFTy(t) and in the z direction dFTz(t) at an instantaneous time t, which are determined as[10]

T T T Td ( ) d cos and d ( ) d ,y zF t F F t F (6)

where 2 2L D1 1d d , d d ,2 2

L C V S D C V S

T Td d sin d cos , and d d cos d sin .F L D F L D

The symbols , CL, CD, dS, and denote the air density, lift coefficient, drag coefficient, wing section area, and induced angle, respectively. Here, CL and CD were taken from Ref. [5], in which they were verified to be appli-cable for a Reynolds number of the order of 104[10].

3.1.2 Added mass force

The added mass force is decomposed into compo-nents in the y direction dFAy(t) and in the z direction dFAz(t) at an instantaneous time t, which are calculated as[10]

2A r

2A r

d ( ) cos cos d 4 ,

d ( ) sin d4

y n

z n

F t c a r

F t c a r (7)

where c is the wing chord length; and

2r f r r f rsin ( /2 ) cos sin ( /2 )na r c x c x ,

which is the acceleration of the center of the wing sec-tion at an instantaneous time; and xf is the distance be-tween the feather axis and the leading edge[10,12,31]. If the leading edge is collocated with the feather axis as in the present system, then xf = 0.

r

z Flapping axis

Stroke plane

O y

r

Feather axis

c/2

dFTz

dFTydFUy

T

UdFUzRCGZ

CG

X

YdFUj = dFAj + dFRj , j = y, z

T(xT, yT, zT), U(xU, yU, zU), CG(xCG, yCG, zCG), Fig. 6 Force components acting on a wing section for estimation of pitching moment. 3.1.3 Rotational force

The rotational forces in the y direction dFRy(t) and in the z direction dFRz(t) at an instantaneous time t are respectively expressed as

R rot r R rot rd ( ) d sin cos and d ( ) d cos ,y zF t F F t F (8)

where 2rot T rot rd d ,F V c c r which is the force normal to the surface of the wing section[11], and crot is the rota-tional force coefficient, which is a function of non-dimensional rotational velocity and the position of the feather axis xf[11].

3.1.4 Inertial force

The inertial force of a wing section in the y direc-tion dFIy(t) and in the z direction dFIz(t) at an instanta-neous time t are respectively calculated as

I w I wd ( ) (d ) and d ( ) (d ),LE LE

y zTE TEF t m y F t m (9)

where dmw is the mass of a wing section, and ,y z are the accelerations at an instantaneous time of the mass dmw in the y and z directions, respectively[10,12,11].

Finally, the forces in the y and z directions gener-ated by the two wings at an instantaneous time can be obtained by integrating the forces generated by all the wing sections over the wing length Rw and then multi-plying by

w

w

T A R I0

T A R I0

( ) 2 (d d d d ),

( ) 2 (d d d d )

Ry y y y y

R

z z z z z

F t F F F F

F t F F F F (10)


The average forces in the y and z directions gener-ated by the flapping-wing system over a flapping cycle can be estimated as

,ave 0

,ave 0

1 ( )d,

1 ( )d

T

y y

Tz z

F F t tT

F F t tT

(11)

where T is the flapping period of the wings. Because the forces generated by the flapping system keep changing during the flapping motion, the average forces for a flapping cycle were used as apparent forces generated by the flapping system when we analyzed the flight stability of the flapping-wing system[6,33].

3.2 Estimation of pitching moment and mean aero-

dynamic force center To theoretically investigate the effect of change in

the flapping angle range on the pitching moment gen-eration in the flapping-wing system, we have estimated the pitching moment generated by the flapping wings about the CG. Therefore, in addition to the force esti-mation conducted in Ref. [12,31], in the present paper we describe a method to estimate the pitching moment generated by a flapping-wing system about the CG.

Let us consider a wing section shown in Fig. 6. The XYZ coordinate system originates at the CG of the flap-ping-wing system. The XYZ coordinate system can be formed by translating the xyz coordinate system by the vector CGR , as shown in Fig. 6. As described in section 3.1, there are four force components acting on the wing section: the translational force, the added mass force, the rotational force, and the inertial force. To estimate the pitching moment about the X-axis generated by the wing section, we assume that the translational force acts at point T located at 25% chord length behind the leading edge as for a symmetric airfoil in steady aerodynam-ics[34], the added mass force and the rotational force are acting at point U located at 50% chord length[10,11,35], and the inertial force is acting at the center of mass I of the wing section, which is approximately located at 10% chord length behind the leading edge according to the mass distribution of the fabricated wings. The moment coefficient of the wing is assumed to be zero because its contribution to the average pitching moment is mainly zero when the flapping motion is symmetric during up-

stroke and downstroke. Based on these assumptions, the pitching moment around the X-axis generated by a wing section at an instantaneous time t is calculated as

T CG T U CG A R

I CG I T CG T

U CG A R I CG I

d ( ) [( )d ( )(d d )

( )d ] [( )d

( )(d d ) ( )d ],

X z z z

z y

y y y

M t y y F y y F F

y y F z y F

z z F F z z F (12)

where yT and zT are the y and z coordinates of point T, yU and zU are the y and z coordinates of point U, yI and zI are the y and z coordinates of point I, and yCG and zCG are the y and z coordinates of the CG, respectively. In Eq. (12), the component in the first bracket is the moment gener-ated by the vertical force in the z-axis, and the compo-nent in the second bracket is the moment generated by the horizontal force in the y-axis. By integrating Eq. (12) over the wingspan and then multiplying by two, we can obtain the pitching moment generated by the two wings about the X-axis at an instantaneous time t as follows after rearrangement

CG CG( ) ( ) [ ( ) ( )],X x z yM t M t y F t z F t (13)

where Fy(t) and Fz(t) are determined by Eq. (10) and Mx(t) is the pitching moment about the x-axis generated by the wings at an instantaneous time t, which can be expressed as

w

w

T T U A R I I0

T T U A R I I0

( ) 2 d (d d ) d

2 d (d d ) d .

Rx z z z z

Ry y y y

M t y F y F F y F

z F z F F z F (14)

Similar to Eq. (12), in Eq. (14), the first and second terms are the pitching moment about the x-axis due to the vertical force Fz and the horizontal force Fy, respec-tively. Eq. (13) is regarded as the transformation of the pitching moment between the two coordinate systems. Based on Eqs. (13) and (14), the average pitching mo-ment about the CG generated by the flapping-wing sys-tem can be calculated as

,ave CG ,ave CG ,ave( ) ( ) ,X Fz z Fy yM y y F z z F (15)

where the average vertical force Fz,ave and the average horizontal force Fy,ave are determined by Eq. (11) and yFz and zFy are the mean AC of the vertical force and the horizontal force (or the apparent centers of the average vertical force and the average horizontal force), respec-tively. These can be expressed as


w

T T U A R I I ,ave0 0

2 d (d d ) d d / ,T R

Fz z z z z zy y F y F F y F t FT

(16)

w

T T U A R I I ,ave0 0

2 d (d d ) d d / .T R

Fy y y y y yy z F z F F z F t FT

(17)

The results of estimation of the forces and pitching moment about the CG and the location of the AC for the three cases of the rocker angle are presented in section 5.2.

4 Measurement of wing kinematics, force, and pitching moment

4.1 Measurement of wing kinematics To confirm that the flapping angle range was actu-

ally modified as designed in the flapping-wing system, we captured the wing kinematics for three values of the rocker angle . In addition, the measured wing kine-matics was used for estimation of forces and pitching moment by the UBET. The wing kinematics of the flapping wing was determined by tracking marked points placed at three sections of 0.25, 0.50, and 0.75 of the wingspan (Rw) on the wing. The points are shown on the surfaces of the wings in Fig. 4. To track the marked points, we examined sequential images captured by two synchronized high-speed cameras at 2000 frames 1 and analyzed them based on the Direct Linear Transforma-tion (DLT) method[27]. The DLT method allows us to reconstruct a three-dimensional coordinate of a point based on two or more two-dimensional-views of that point. The DLT method has been implemented in MATLAB code provided by Hendrik[27]. More details on how to obtain the wing kinematics are described in Ref. [10].

Based on the tracked coordinates of the marked points during the flapping motions, we could obtain the time histories of the flapping angle and the rotation angle of the wing at the three locations in the spanwise direc-tion. Then, we acquired the mean time histories of the two angles by averaging the measured wing kinematics for three cycles. Finally, they were fitted to a summation of sine and cosine functions based on the least-squares method[36,37]. The function used for the least square fit is given as

0 k k1

cos(2 ) sin(2 ) ,r

k

a a k ft b k f (18)

where is either the flapping angle or the rotation angle, f is the flapping frequency of the wing, and a0, ak, and bk are the coefficients determined based on the least- squares method[37]. The fitted wing kinematics was used for assessing the shift in flapping angle range relative to the change in the rocker angle , and they were used as the input data for estimating the force via UBET. The processed wing kinematics is presented in section 5.1.

4.2 Measurement of force and pitching moment

We used a multi-axis load cell (Nano 17, Stainless steel, ATI Industrial Automation, USA, force resolution of 0.3 gf, moment resolution of 1.6 gfmm) to measure the forces and pitching moment generated by the flap-ping-wing system. The load cell was vertically installed in the assembly of the flapping-wing system through an adapter made of carbon rod with a diameter of 7 mm and acrylic panels as shown in Fig. 7a. The adapter is divided

0.36c

20 mm50 mm

cd

Connected to the

flapping-wing systemAdapter

(upper part)

Slider slot

Bolts and nuts

Connected to the load cell

Adapter(lower part)

(b)

Fig. 7 Test setup for force and pitching moment measurement. (a) Test setup; (b) zoom in at the slider slot connector.


in to two parts: the lower part is connected to the load cell and the upper part is connected to the flapping-wing system. The two parts of the adapter are connected to-gether by a slider slot and two bolts and nuts as shown in Fig. 7b. The slider slot allows us to adjust the relative position between the two axes of the flapping-wing system and the load cell. In this way, the location of the flapping-wing system was adjusted to make the zL axis of the load cell pass through the CG of the flapping-wing system and perpendicular to the stroke plane.

The xyz and XYZ coordinate systems in Fig. 7 are the same coordinate systems defined in Fig. 6. The ori-gin of the xLyLzL coordinate system locates at the center of the top surface of the load cell. The wings symmet-rically flap through the Y-Z plane in Fig. 7, which is identical to the yL-zL plane.

The CG was located at approximately 36% of the mean wing chord ( )c from the leading edge, which means that the z coordinate of the CG in the xyz coor-dinate system (zCG) was 7.2 mm. The flapping-wing system was excited by an external power supply (E3646A, Agilent, Malaysia) at a flapping frequency of approximately 38.5 Hz 0.5 Hz. Whenever we activated the flapping-wing system, a pair of wings were placed at the end of the upstroke or at the beginning of the down-stroke ( max position in Fig. 1c), so that we were able to determine the starting point of each flapping cycle in the acquired signals from the load cell.

Fig. 8 shows a typical signal for the vertical force (Fz) acquired by the load cell. Each measurement batch dataset included approximately 100 flapping cycles. The load cell was activated for approximately 3 s before exciting the wings. For measuring the forces and mo-

ment, the wings were excited for approximately 3 s. Subsequently, the load cell was deactivated for ap-proximately 3 s after the wings stopped flapping. The conditions before and after exciting the wings are called Idle 1 and Idle 2 conditions, respectively, as shown in Fig. 8. When the difference in the average signals of the two idle conditions was less than or equal to 0.1 gf, which was approximately 30% of the resolution of force measurement by the load cell, we deemed that the test setup worked properly to acquire the signal.

The average vertical force (Fz,ave), horizontal force (Fy,ave), and moment about the xL-axis (MxL,ave) were calculated by taking the averages of corresponding sig-nals for each measurement batch dataset of 100 flapping cycles. In this way, we were able to obtain the average forces and moments generated by the flapping-wing system for the three values of rocker angle ( ): normal ( = 0 ), pitching up ( = 10 ), and pitching down ( = 20 ). For each rocker angle, we obtained ten measurement batch datasets. Because the measured moment signal from the load cell is the moment about the xL-axis of the load cell (MxL,ave), we needed one more step to calculate the average pitching moment about the X-axis (moment about the CG, MX,ave) using

L,ave ,ave ,ave ,X x yM M F d (19)

where Fy,ave is the average horizontal force and d is the distance between the load cell to the CG, as shown in Fig. 7. The measured forces and pitching moments about the CG for the three cases of are presented in section 5.2.

5 Result and discussion

5.1 Wing kinematics The measured wing kinematics of the flap-

ping-wing system for the three values of rocker angle are shown in Fig. 9. Each set of wing kinematics was acquired by averaging the time histories of three typical flapping cycles. Fig. 9a shows the time histories of flapping angle ( ) for each case. The amplitudes of flapping angles were approximately 104 , 116 , and 99 for the cases of = 0 (normal), = 10 (pitching up), and = 20 (pitching down), respectively. All flapping angle amplitudes were slightly larger than the design values in section 2.1 because of bending of the leading edge vein of the wing during flapping motion and clearance introduced during fabrication. The results in

0 2000 4000 6000 8000 10000 12000Samples

100

50

50

100

150

Ver

tical

forc

e F z

(gf)

0

Idle 1 Idle 2

About 100 flapping cycles

Fig. 8 Definition of one measurement batch dataset.


Fig. 9a show that depending on the rocker angle , the flapping angle range can be symmetric ([ 52 ,52 ]), shifted down ([ 68 ,48 ]), or shifted up ([ 33 ,66 ]) about the x axis for = 0 , = 10 , and = 20 , re-spectively. This change in the flapping angle range leads to relocation of the mean AC and modifies the relative position between the mean AC and the CG of the flap-ping-wing system. Consequently, a non-zero pitching moment about the CG will be changed. Fig. 9b shows the time histories of the wing rotation angle r, defined in section 3.1, at the three wing locations for three dif-ferent cases. As shown in Fig. 9b, the wing was nega-tively twisted during the downstroke and reversed dur-ing the upstroke. This means that the amount of wing rotation was larger near the wing tip (r = 0.75Rw) than near the wing root (r = 0.25Rw). Consequently, the rota-tional angle was variable from wing root to wing tip. This is qualitatively similar to the rotational angle characteristics of a beetles hind wing[10].

Unlike in the estimated flapping angle history in Fig. 2, the time durations of downstroke for the three cases are slightly shorter than those of upstroke. It is

basically because the rotational speed of the installed motor is not constant. Especially for the case of = 10 , since the amount of wing rotation, therefore the angle of attack of the wing, is slightly smaller during the down-stroke, as shown in Fig. 9b, than in the upstroke. There-fore, smaller aerodynamic forces are possibly generated by the flapping wings and the burden from the wing to the motor is relatively reduced. Finally, the motor can rotate faster than in the upstroke. Therefore, the time history of the flapping angle is shifted to the left. 5.2 Force and pitching moment 5.2.1 Normal case ( = 0 )

In this case, we set the rocker angle = 0 and ac-quired the average vertical force, horizontal force, and pitching moment about the CG for ten measurement batch datasets. Then, we took average of the ten datasets to obtain average forces and pitching moment generated by the flapping-wing system. Table 3 lists the averages and the standard deviations of the ten measurement batch datasets, and the forces and pitching moment es-timated by UBET. The location of the mean AC for each force component is also included in Table 3.

As seen in Table 3, the average measured vertical force (Fz,ave) and horizontal force were 5.1 gf and 0.1 gf , respectively. For the vertical force, the UBET esti-mation was in good agreement with the measured value because the difference between their values was 3.9%. The average horizontal force (Fy,ave) was only approxi-mately 2.0% of the vertical force and was close to the resolution of the load cell (0.3 gf). The small average horizontal force was reasonable because of the sym-metric flapping motion about the feather axis, or x-axis, in the flapping-wing system, even though the accuracy of the measured horizontal force was questionable. The limited accuracy of the measured horizontal force pos-sibly gave rise to a large difference when it was com-pared to that estimated by UBET. Table 3 Average forces and moment obtained by measurement and UBET estimation ( = 0 )

Item Measurement UBET Difference

Average vertical force, Fz,ave (gf) 5.10.16 4.9 3.9%

Average horizontal force, Fy,ave (gf) 0.10.07 0.7 800.0%

Average moment about the CG, MX,ave (gfmm)

4.92.06 0.7 85.7%

Mean AC of Fz,ave, yFz (mm) 0.0

Mean AC of Fy,ave, zFy (mm) 8.2

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ping

ang

le (d

egre

e)

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80 ( = 0 , measured) ( = 10 , measured) ( = 20 , measured) ( = 0 , fitted) ( = 10 , fitted) ( = 20 , fitted)

(a)

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g ro

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ree)

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140 0.25Rw ( = 10 , fitted)0.50Rw ( = 10 , fitted)0.75Rw ( = 10 , fitted)0.25Rw ( = 20 , fitted)0.50Rw ( = 20 , fitted)0.75Rw ( = 20 , fitted)

0.25Rw ( = 0 , fitted)0.50Rw ( = 0 , fitted)0.75Rw ( = 0 , fitted)

(b)

Fig. 9 Wing kinematics at a flapping frequency of 38.5 Hz. (a) Flapping angle; (b) wing rotation angle.


The average measured pitching moment about the CG was 4.9 gfmm , and its magnitude was close to the moment resolution of the load cell (1.6 gfmm ). Thus, we can consider that the flapping-wing system produced insignificant moment for = 0 , even though the accu-racy was again questionable. Because of the low and limited accuracy of the measured pitching moment, the difference between the UBET estimation and the meas-ured value was large.

Typical time histories of the measured vertical force (Fz), horizontal force (Fy), and pitching moment (MX) about the CG are plotted along with those obtained by UBET estimation in Figs. 10a, 10b, and 10c, respec-tively. In these figures, the solid lines with squares rep-resent the averages of the measured data for three flap-ping cycles. The error bars represent the standard de-viation of the three datasets. We can see that the esti-mated time histories show similar tendencies to the measured values, even though there is some difference.

5.2.2 Pitch-up case ( = 10 )

For this case, we set the rocker angle to 10 . Using the same method applied to the normal case, we were able to obtain the average measured forces and moment for ten measurement batch datasets. Table 4 indicates that the average measured vertical force (Fz,ave) and horizontal force (Fy,ave) were 6.2 gf and 0.5 gf, respectively. Because the amplitude of the flapping an-gle in this case was approximately 10% larger than that in the normal case, the average vertical force (Fz,ave) was slightly larger than that in the normal case.

The vertical force estimated by UBET was in good agreement with the measured value because the differ-ence in their values was approximately 6.5%. The aver-age measured horizontal force (Fy,ave) was 0.5 gf, which was only approximately 8.0% of the vertical force. This value was again close to the force resolution of the load cell (0.3 gf). The small average horizontal force was reasonable because of the symmetric flapping motion during the downstroke and upstroke. Because of the limited accuracy of the measured horizontal force, the difference between the UBET estimation and the meas-urement for the horizontal force was large, as shown in Table 4, as it was in the normal case, as shown in Table 3.

The average measured pitching moment was 46.4 gfmm, which was approximately ten times larger

than that in the normal case. The difference between the

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Cycles (t/T)

MX ( = 0 , measured, 4.9 gfmm) MX ( = 0 , UBET, 0.7 gfmm)

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(c)

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Fy ( = 0 , measured, 0.1 gf) Fy ( = 0 , UBET, 0.7 gf)

Downstroke Upstroke

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Downstroke Upstroke

Fz ( = 0 , measured, 5.1 gf)Fz ( = 0 , UBET, 4.9 gf) (a)

Fig. 10 Time histories of the forces and pitching moment in normal case ( = 0 ). (a) Vertical force; (b) horizontal force; (c) pitching moment about the CG.

Table 4 Average forces and moment obtained by measurement and UBET estimation ( = 10 )





46.44.36 33.2 28.4%




UBET estimation for the pitching moment and the measured value was 28.4%. This discrepancy was mainly due to the inaccurate horizontal force and po-tential error in the measured wing kinematics of the flapping-wing system. However, both the UBET esti-mation and the measurement show that the flap-ping-wing system created a significant magnitude of negative pitching moment about the CG. The pitching moment about the CG was negative because the flapping angle range was shifted to the downstroke side, com-pared to that in the normal case, as indicated in Table 2 and Fig. 9a. Consequently, the mean AC of the average vertical force shifted to the downstroke side, i.e., shifted to the left-hand side of the CG. It should be noted that the weight of the rack is only 0.53% the weight of the flap-ping-wing system and the movement of the rack is 0.7 mm in the y-direction for creating a rocker angle of

10 . Thus, the movement of the CG in the y-direction caused by the movement of the rack is 0.0037 mm, which is only 0.07% the shifted location of the mean AC in the y-direction (yFz = 5.5 mm) due to the change in the corresponding flapping angle range. Therefore, the location of the CG during the rack motion is neglected in our further discussion.

Based on the measurement and estimation, we can confirm that the flapping-wing system created a negative pitching moment when the flapping angle range shifted to the downstroke side using the pitch control mechanism and when the rocker angle changed from 0 to 10 .

Typical time histories of the measured vertical force (Fz), horizontal force (Fy), and pitching moment (MX) about the CG for = 10 are plotted along with those estimated by UBET in Figs. 11a, 11b, and 11c, respectively. Again, the estimated time histories show similar tendencies to the measured values, even though there is some discrepancy as explained in section 5.2.1.

5.2.3 Pitch-down case ( = 20 )

For the pitch-down case, we shifted the rocker an-gle from 0 to 20 without changing any other con-figuration in the setup. The forces and pitching moment were measured following the same method described in section 4.2. The average measured vertical force, hori-zontal force, and pitching moment about the CG gener-ated by the flapping-wing system obtained from ten measurement datasets are shown along with the values estimated by UBET in Table 5.

Fz ( = 10 , measured, 6.2 gf) Fz ( = 10 , UBET, 5.8 gf)

Downstroke Upstroke

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10

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tical

forc

e F z

(gf

)

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Pitc

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mom

ent M

X(g

fmm

)

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oriz

onta

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ce F

y (g

f)

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500



(a)

(b)

(c)

Downstroke Upstroke

Downstroke Upstroke

Fig. 11 Time histories of the forces and pitching moment in pitch-up case ( = 10 ). (a) Vertical force; (b) horizontal force; (c) pitching moment about the CG. Table 5 Average forces and moment obtained by measurement and UBET estimation ( = 20 )





36.82.23 39.4 7.1%




For this case, because the amplitude of the flapping angle was slightly smaller than the amplitudes in the normal and pitch-up cases, the flapping-wing system for = 20 generated the smallest vertical force (Fz,ave) of

approximately 4.5 gf among the three cases. The average measured horizontal force (Fy,ave) was approximately 0.1 gf, which was again close to the force resolution of the load cell (0.3 gf). The limited accuracy of the measured horizontal force again caused a large dis-crepancy between the estimated and measured values listed in Table 5.

The average measured pitching moment about the CG (MX,ave) was approximately 36.8 gfmm, which can cause a pitch-down motion of the flapping-wing system. The difference between the measured data and the UBET estimation values for the pitching moment was 7.1%. In this case, the flapping-wing system created a positive average pitching moment about the CG. This was because the flapping angle range shifted up com-pared to that of the normal case, as indicated in Table 2. Consequently, the mean AC of the vertical force shifted to the upstroke side, i.e., shifted in the positive y direc-tion compared to that of the normal case, as indicated in Table 5 (yFz = 9.4 mm).

Typical time histories of the measured vertical force (Fz), horizontal force (Fy), and pitching moment (MX) about the CG for = 20 are plotted along with those obtained by the UBET estimation in Figs. 12a, 12b and 12c, respectively. The measured and estimated time histories show similar tendencies, even though there is some discrepancy as explained in section 5.2.2. One can notice that for all the cases of three rocker angles, the UBET tended to underestimate the measured forces. In the UBET estimation, the wing camber in each wing section is not considered. Instead, the camber chord is approximated by connecting the leading edge and trail-ing edge. In reality, each wing section becomes a cam-bered wing section during flapping motion. Since a flat wing typically produces smaller aerodynamic forces than a camber wing[34], the current UBET typically un-derestimate the force generation.

In all cases explained above, the fluctuations in the measured time histories of horizontal and vertical forces are rather large due to vibratory forces created by flap-ping wings and flapping mechanism. When the system is fixed to the load cell, the vibration is recorded as high frequency signals in the data acquisition system. Even

though we filter them out, some of them are still in-cluded and the signals are not well repeated. However, the average forces over cycles are well reproduced with low standard deviation and well matched with the esti-mated ones as we summarized in Tables 3, 4, and 5.

6 Demonstration of pitching moment generation

We set up an experiment to demonstrate that the flapping-wing system is able to generate a reasonable pitching moment during flapping motion when the rocker angle is shifted from 0 . As shown in Fig. 13,

Fz ( = 20 , measured, 4.5 gf) Fz ( = 20 , UBET, 4.4 gf)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Cycles (t/T)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Cycles (t/T)


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30Downstroke Upstroke

Downstroke Upstroke

Downstroke Upstroke

45

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45


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300

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Cycles (t/T)

(b)

(a)

(c)

Fig. 12 Time histories of the forces and pitching moment in pitch-down case ( = 20 ). (a) Vertical force; (b) horizontal force; (c) pitching moment about the CG.


the flapping-wing system was installed in a test jig such that the system was able to rotate freely around the CG in the y-z plane when nonzero pitching moment was gen-erated. The electric power was then turned on using a

wireless infrared transmitter (ITX2H-V2, 38 KHz) and receiver (IRX262, 38 KHz). The power source was a pair of polylithium batteries (3.7 V, 20 mAh, Fullriver, China) connected in series. More details of the integration of the flapping-wing system are reported in Ref. [32].

Fig. 14 shows sequential images of the flap-ping-wing system during the test; these images were captured by a high-speed camera at 2000 frames 1. The flapping frequency was varied from 38 Hz to 40 Hz depending on the charge state of the installed batteries. These frequencies are close to the flapping frequency used in section 5 and the same as those used in the ver-tical takeoff test[12]. We conducted at least three tests for each rocker angle . The video clips of the current demonstration can be found at Ref. [38].

(a) Normal case ( = 0 )

(b) Pitch-up case ( = 10 )

(c) Pitch-down case ( = 20 )

Fig. 14 Sequential images of experimental pitching moment demonstration.

Fig. 13 Experimental setup for demonstration of pitching mo-ment generation.


Fig. 14a shows the test conducted in the normal

case for 3 seconds, which simulated vertical flight. From the sequential images, we observed that the flap-ping-wing system oscillated slightly about the hinge but was still able to remain in the vertical direction when the wings were excited. This means that the average pitch-ing moment was almost zero for = 0 , as explained in section 5.2.1.

The sequential images in Fig. 14b indicate the pitch-up case when the rocker angle = 10 . In this case, immediately after the wings were excited, the flapping-wing system rotated in the clockwise direction around the hinge until it hit the fixture. This means that a negative or pitch-up moment was generated as explained in section 5.2.2 for the pitch-up case.

As shown in Fig. 14c, for = 20 , the flapping-wing system rotated in the counterclockwise direction imme-diately after the wings were excited. This means that the flapping-wing system generated a positive or pitch- down moment as explained in section 5.2.3 for = 20 .

Based on the demonstration test, we can conclude that a desired pitching moment can be generated by shifting the flapping angle range by changing the rocker angle . Thus, we verified the effectiveness of the flap-ping mechanism integrated with the pitch control mechanism.

7 Conclusion

In this work, we presented a design for a flapping mechanism integrated with a mechanism that is able to change the flapping angle range of the wings. A flap-ping-wing system composed of the integrated flapping mechanism and artificial wings was fabricated and tested to evaluate the design. The forces and pitching moment about the CG generated by the flapping-wing system were determined both by measurement and by estimation using UBET. The measured data and UBET estimation showed that it is possible to modify the rela-tive position between the mean AC of the vertical force and the CG of the flapping-wing system by changing the flapping angle range. Consequently, pitching motion of the flapping-wing system can be triggered by generating a desired pitching moment. This was verified through a demonstration using a flapping-wing system installed in a test jig such that it was able to rotate freely about the CG depending on the direction of pitching moment generated by the flapping wings. The proposed mecha-

nism may be used for longitudinal attitude control of an insect-mimicking flapping-wing system.

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant number: 2013R1A2A2A01067315) and this paper was written as part of Konkuk Universitys research support program for its faculty on sabbatical leave in 2013.

References [1] Weis-Fogh T. Quick estimates of flight fitness in hovering

animals, including novel mechanisms for lift production. Journal of Experimental Biology, 1973, 59, 169230.

[2] Ellington C P. The aerodynamics of hovering flight. IV. Aerodynamic mechanisms. Philosophical Transactions of Royal Society B, 1984, 305, 79113.

[3] Dickinson M H, Gotz K G. Unsteady aerodynamic per-formance of model wings at low Reynolds numbers. Journal of Experimental Biology, 1993,174, 4564.

[4] Dickinson M H. The effects of wing rotation on unsteady aerodynamic performance at low Reynolds numbers. Jour-nal of Experimental Biology, 1994, 192, 179206.

[5] Dickinson M H, Lehmann F, Sane S P. Wing rotation and the aerodynamic basis of insect flight. Science, 1999, 284, 19541960.

[6] Taylor G K, Thomas A L R. Animal flight dynamics II. Longitudinal stability in flapping flight. Journal of Theo-retical Biology, 2002, 214, 351370.

[7] Hedrick T L, Daniel T L. Flight control in the hawkmoth Manduca sexta: The inverse problem of hovering. Journal of Experimental Biology, 2006, 209, 31143130.

[8] Liu H, Aono H. Size effects on insect hovering aerodynam-ics: An integrated computational study. Bioinspiration & Biomimetics, 2009, 4, 015002.

[9] Le T Q, Byun D, Saputra P, Ko J H, Park H C, Kim M J. Numerical investigation of the aerodynamic characteristics of a hovering Coleopteran insect. Journal of Theoretical Biology, 2010, 266, 485495.

[10] Truong Q T, Nguyen Q V, Truong V T, Park H C, Byun D, Goo N S. A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing sys-tem. Bioinspiration & Biomimetics, 2011, 6, 036008.

[11] Sane S P, Dickinson M H. The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. Journal of Experimental Biology, 2002, 205, 10871096.


[12] Phan H V, Nguyen Q V, Truong Q T, Truong V T, Park H C, Byun D, Goo N S, Kim M J. Stable vertical takeoff of an insect-mimicking flapping-wing system without guide im-plementing inherent pitching stability. Journal of Bionic Engineering, 2012, 9, 391401.

[13] Taylor G K. Mechanics and aerodynamics of insect fight control. Biological Reviews of the Cambridge Philosophical Society, 2001, 76, 449471.

[14] Dudley R. The Biomechanics of Insect Flight: Form, Func-tion, Evolution, Princeton University Press, Princeton, NJ, USA, 1999.

[15] Horsmann U, Heinzel H G, Wendler G. The phasic influence of self-generated air current modulations on the locust flight motor. Journal of Comparative Physiology, 1983, 150, 427438.

[16] Lehmann F, Dickinson M H. The control of wing kinematics and flight forces in fruit flies (drosophila spp.). Journal of Experimental Biology, 1998, 201, 385401.

[17] Arbas E A. Control of hindlimb posture by wind-sensitive hairs and antennae during locust flight. Journal of Com-parative Physiology A, 1986, 159, 849857.

[18] Hinterwirth A J, Daniel T L. Antennae in the hawkmoth Manduca sexta (Lepidoptera, Sphingidae) mediate ab-dominal exion in response to mechanical stimuli. Journal of Comparative Physiology A, 2010, 196, 947956.

[19] Blondeau J. Aerodynamic capabilities of flies, as revealed by a new technique. Journal of Experimental Biology, 1981, 92, 155163.

[20] Nachtigall W, Roth W. Correlations between stationary measurable parameters of wing movement and aerodynamic force production in the blow fly (Calliphora vicina R.-D.). Journal of Comparative Physiology A, 1983, 150, 251260.

[21] Finio B M, Wood R J. Distributed power and control actua-tion in the thoracic mechanics of a robotic insect. Bioinspi-ration & Biomimetics, 2010, 5, 045006.

[22] Park J H, Yang E P, Zhang C, Agrawal S K. Kinematic design of an asymmetric in-phase flapping mechanism for MAVs. Proceeding on IEEE International Conference on Robotics and Automation, Saint Paul, Minnesota, USA, 2012, 1418.

[23] http://www.youtube.com/watch?v=NuD1WKHsggs [24] Keennon M T, Klingebiel K R, Andryukov A, Hibbs B D,

Zwaan J P. Air Vehicle Flight Mechanism and Control

Method, US Patent, Pub. No. US 2010/0308160 A1, 2010. [25] Nguyen Q V, Park H C, Goo N S, Byun D. Characteristics of

beetles free flight and a flapping-wing system that mimics beetle flight. Journal of Bionic Engineering, 2010, 7, 7786.

[26] Park H C, Nguyen Q V, Byun D, Goo N S. Flapping Appa-ratus with Large Flapping Angles, US Patent, Registration # 12/571,945, 2011.

[27] Hedrick T. Software techniques for two- and three-dimen-sional kinematic measurements of biological and biomi-metic systems. Bioinspiration & Biomimetics, 2008, 3, 034001.

[28] Truong Q T, Nguyen Q V, Park H C, Goo N S, Byun D. Modification of a four-bar linkage system for a higher op-timal flapping frequency. Journal of Intelligent Material Systems and Structures, 2011, 22, 5966.

[29] Syaifuddin M, Park H C, Yoon K J, Goo N S. Design and evaluation of LIPCA-actuated flapping device. Smart Ma-terials and Structures, 2006, 15, 12251230.

[30] Whitney J P, Wood R J. Aeromechanics of passive rotation in flapping flight. Journal of Fluid Mechanics, 2010, 660, 197220.

[31] Truong T Q, Phan V H, Park H C, Koh J H. Effect of wing twisting on aerodynamic performance of flapping wing system. AIAA Journal, 2013, 51, 16121620.

[32] Phan V H, Truong T Q, Park H C. Assessment of initial pitching moment stability for an uncontrolled free flying flapping-wing micro-air-vehicle. Journal of Aircraft, 2013 (Submitted).

[33] Sun M, Wang J K. Flight stabilization control of a hovering model insect. Journal of Experimental Biology, 2007, 210, 27142722.

[34] Anderson Jr J D. Fundamentals of Aerodynamics, McGraw Hill, New York, USA, 2001.

[35] Lock R J, Vaidyanathan R, Burgess S C, Loveless J. De-velopment of a biologically inspired multi-modal wing model for aerial-aquatic robotic vehicles through empirical and numerical modelling of the common guillemot, Uria aalge. Bioinspiration & Biomimetics, 2010, 5, 046001.

[36] Matlab Users Guide, MathWorks Inc, 2006. [37] Bjorck A. Numerical Methods for Least Squares Problems,

SIAM, Philadelphia, USA, 1996. [38] http://www.youtube.com/watch?v=JUJTjQKO9M4

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Pitching Moment Generation in an Insect

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