Non-Jumping Take off Performance in Beetle Flight (Rhinoceros Beetle Trypoxylus dichotomus)

Journal of Bionic Engineering 11 (2014) 61–71

Non-Jumping Take off Performance in Beetle Flight (Rhinoceros Beetle Trypoxylus dichotomus) Tien Van Truong1,2, Tuyen Quang Le3, Hoon Cheol Park4, Kwang Joon Yoon1, Min Jun Kim5, Doyoung Byun6 1. Department of Aerospace and Information Engineering, Konkuk University, Seoul, South Korea 2. Department of Mechanical Engineering, National University of Singapore, Singapore 3. KoreaInstitute of Ocean Science and Technology, PO Box 29, Ansan 425-600, South Korea 4. Department of Advanced Technology Fusion, Konkuk University, Seoul, South Korea 5. Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104, USA 6. Department of Mechanical Engineering, Sungkyunkwan University, Suwon, South Korea

Abstract In recent decades, the take-off mechanisms of flying animals have received much attention in insect flight initiation. Most of previous works have focused on the jumping mechanism, which is the most common take-off mechanism found in flying animals. Here, we presented that the rhinoceros beetle, Trypoxylus dichotomus, takes off without jumping. In this study, we used 3-Dimensional (3D) high-speed video techniques to quantitatively analyze the wings and body kinematics during the initiation periods of flight. The details of the flapping angle, angle of attack of the wings and the roll, pitch and yaw angles of the body were investigated to understand the mechanism of take-off in T. dichotomus. The beetle took off gradually with a small velocity and small acceleration. The body kinematic analyses showed that the beetle exhibited stable take-off. To generate high lift force, the beetle modulated its hind wing to control the angle of attack; the angle of attack was large during the upstroke and small during the downstroke. The legs of beetle did not contract and strongly release like other insects. The hind wing could be considered as a main source of lift for heavy beetle. Keywords: take-off, non-jumping mechanism, rhinoceros beetle, kinematics Copyright © 2014, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(14)60020-2

1 Introduction In nature, flapping flight has evolved in insects, birds, bats and pterosaurs. In order to develop a flapping aero-vehicle which mimics birds and insects, one needs to understand the flapping mechanisms and the geometrical parameters of the wing and body. Researchers have attempted to elaborate flapping mechanisms in hovering flight, forward flight[1,2], and remarkable maneuvering flight[3–6]. However, these issues still have remained something of a mystery for two thirds of the world’s species that use flapping flight[7]. Notably, take-off plays an important role in all flight[8]. Understanding take-off mechanisms has brought attention to insect flight research in recent years. Detailed knowledge of the body kinematics is indisCorresponding author: Doyoung Byun E-mail: [email protected]

pensable for understanding the mechanism of take-off. Jumping, i.e., escaping rapidly from the ground[9], is a common take-off mechanism in flying animals. Most of the previous work on take-off has focused on the jumping mechanisms of creatures such as birds[8,10,11], Drosophila[12,13], cicada[14] and flea-beetles[15]. In contrast, to our knowledge, there have been no reports on the kinematics of non-jumping take-off mechanisms in flying animals. Insects use a diverse range of mechanisms for take-off movement. Most of them gets power from jump through rapid movements of their hind legs[16]. Catapult mechanisms are normally used in take-off for larger body weights. Each mechanism used has its unique mechanics of its hind legs, muscle arrangement and actuation, and motor patterns to generate such take-off[9]. The jumping insects studied include

62

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

fleas (siphonaptera)[17], flea beetles (coleopteran)[15], and flies (diptera)[18]. The high velocity and the power output required for jumping movements could be produced by high stored energy. The power-producing muscles in the hind femora contract slowly and the energy could be stored in the distortions of the cuticle[14,19,20]. Then, the stored energy is suddenly released by the recoil of the cuticular energy stores[21]. Beetles are coleopteran insects which have a large body size and two pairs of wings: elytron (outer wing, fore wing) and hind wings (inner wing). Coleoptera comprise about 40% of all insect species and, thus, about 30% of all living animal species[22,23]. A beetle can typically crawl on or under the ground, and/or swim under the water with folded wings, or fly by flapping its unfolded wings. The body length ranges from 0.55 mm to 170 mm, and the body mass of most beetles is less than 10 g[24]. A beetle has six legs and two pairs of wings for ground locomotion. The hind wings of the beetle are folded. They are also covered and protected by the elytra. When a beetle starts to stroke its wings, the elytra open, the hind wings unfold and then both wings flap in related phases. There is also research on beetle flight by Hass et al. for hind-wing folding, the interlocking mechanism of elytra, and 2-dimensional (2D) kinematics and aerodynamic performance of coleopteran insects in hovering flight[25]. The morphology of the closing and opening of the elytra has been studied with recorded flapping[26]. However, the kinematics of both the elytra and hind wings and characteristics of beetle body movement in free-flight have received less attention, especially the take-off performance. In this study, we investigated the take-off mechanism of the rhinoceros beetle, Trypoxylus dichotomus, commonly found in Japan and Korea. We found that Trypoxylus dichotomus takes off without jumping. In order to understand non-jumping take-off in Trypoxylus dichotomus, we used 3D high-speed cameras to quantitatively analyze the kinematic parameters of wing motion, particularly the wing tip trajectory, and the angle of attack. We also reported the kinematics of the opening of the elytra, body dynamics, and performance during the initial stages of flight.

2 Materials and methods 2.1 Animals The beetles were kept in the laboratory on organic

peat at a humidity of 50% and a temperature of 25 ÛC. The beetles were starved for 24 hours prior to experiments. The female beetle usually shows more flight activity than the male beetle[27]. As a result, ten active female beetles were chosen for study in this experiment. The beetles were placed inside a cubic chamber (50 cm × 50 cm × 50 cm) made of transparent acrylic. The beetles tended to crawl for some distance before preparing for take-off; hence, the take-off would tend to be out of the focus region of the high-speed cameras. Thus, each beetle was trained with a paint brush into the center of the flight chamber, the focus region. The beetles then stopped to take off. The training was repeated with a dozen of successful takeoffs. 2.2 High-speed videography Three 2 mm white dots of non-toxic paint were marked on each hind wing as anatomical landmarks for digitization purposes. The elytra were opened and the hind wings were then extended manually to spot the series of dots on the hind wing. As shown in Fig. 1b, the dots indicate the leading edge and the trailing edge of the hind wing at the middle span and the wing tip (Fig. 1b). Natural markers at the wing root of the hind wing, the wing tip, and the wing base of the elytron provided identifiable points for analysis. To assess the body kinematics, the points between the compound eyes and the end point of the abdomen were digitized. The center of the beetle body mass was roughly estimated as the point along the axis halfway between the head and the end of the abdomen. Three high-speed video cameras (Photron, APX) were used to obtain the 3D kinematics during free flight. The images were recorded at 2000 fps with a pixel resolution of 1024 × 1024. A schematic diagram of the experimental apparatus is shown in Fig. 1a. Two cameras were positioned on the sides of the chamber, and the third was positioned on the front of the chamber. The high-speed cameras were connected to an image processor and personal computer. Three halogen lamps with a power level of 1 kW were placed at appropriate positions to illuminate the focus region. A modified Direct Linear Transformation (DLT) merges seperate 2D camera views into a single 3D coordinate space[28]. The DLT involves a mapping function, which defines the direct transformation of coordinates between the 3D object space and the 2D image planes though the camera[28]. The cameras were cali-

Truong et al.: Non-Jumping Take off Performance in Beetle Flight (Rhinoceros Beetle Trypoxylus dichotomus)

brated with a 64-point calibration frame (measuring 15 cm× 15 cm× 15 cm in x, y, and z coordinates), and the recordings were made at the end of each set of video grammetry trials. The positions of the marked dots on the beetle wing were analyzed with a MATLAB program DLT data viewer[29]. The cameras were triggered manually when the beetle positioned itself in a take-off flight posture. The kinematics data were filtered with a Butterworth filter at a cut-off frequency of 160 Hz, nearly four times of the flapping frequency (37 Hz–41 Hz). Measurements are given as mean standard deviation.

As the hind wings fully unfold in the middle of the down stroke, the first wing beat was defined to be at the beginning of the upstroke in subsequent strokes. The timing of wing and leg events was recorded from each frame following the methods used by Card et al.[13]. The period of each event was presented in the horizontal bar. Take-off was defined when the legs left from the ground. At that moment, the time was set as t = 0 ms. The velocity was calculated as the derivative of positions of the Center of Mass (COM). We captured three take-offs for each beetle. Three right-handed coordinate systems were used to describe the kinematic data. The global coordinate system (xf, yf, zf) is frame-fixed (Fig. 1c). The body coordinate system was located at the COM, and the xb, yb, and zb axes were aligned along the longitudinal, lateral, and gravity directions, respectively (Fig. 1c). The wings coordinate system was located at the root of the wing (xw, yw, zw).The movement of the body coordinate system was transferred to fixed coordinates for each time step by using a series Euler rotation as E

bo f

E

wob

xb Roll

zwr

ywr zf

yb

63

ª BT B\ « « BT A\ «  AT ¬

ª BTw B\ w « « BTw A\ w « ¬«  ATw

AT AI B\  BI A\ AT AI B\  BI A\ AT AI

AIw ATw B\ w  BIw A\ w AIw ATw B\ w  BIw A\ w AIw ATw

AT BI B\  AI A\ º » AT BI B\  AI A\ » , » BT BI ¼

(1)

BIw ATw B\ w  AIw A\ w º » BIw AT w B\ w  AIw A\ w » , (2) » BIw BT w ¼»

where Bș represent cosș, Aș represent sinș; Bȥ respresent cosȥ, Aȥ respresent sinȥ; BI represent cosI, AI represent sinI; Bșw represent cosșw, Așw represent sinșw, Bȥw represent cosȥw, Aȥw represent sinȥw, BIw represent cosIw, AIw represent sinIw, ȥw, șw and Iw are the Euler angles relating coordinate (xw, yw, zw) to (xb, yb, zb) and E ,

Pitch

yf zb

bo f

xwr Yaw

xf

(c)

Fig. 1 (a) Experimental setup: the beetles were placed in a transparent acrylic box and then recorded with a synchronized three high speed cameras. (b) Points spotted on the hind wing for kinematic analysis. (c) The coordinate system: the global coordinate system was fixed to the box frame; the body coordinate related to the global coordinate system was fixed at the COM, the wing coordinates were located at each hind wing base.

E and E are the matrixes of direction cosines.

wo f

w ob

According to the convention in aerodynamics, the rotations around the body center xb, yb, and zb were defined as roll, pitch, and yaw respectively[30]. The wings coordinate system was located at the hind wing base. The wing kinematics were calculated in the local coordinate of each wing as described in previous study[31]. The flapping angle (ij+) was defined as the angle between the projection onto the stroke plane of the line that joins the wing base to the wing tip and the intersection

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

64

line of the stroke plane and the xb, yb plane. The angle of attack, Į, is a geometric angle defined as the angle between the stroke plane and the chord line. The deviation angle, ȕ, was the angle of deviation between the spanwise direction of the wing and the stroke plane. The flapping angle of the elytron, į, was defined by the angle between the lines that connected points from the wing root to the tip at the start and end of the downstroke phase of the elytron.

3 Results Thirty take-offs from ten individuals were analyzed. The adult female Trypoxylus dichotomus used here had a mass of 4.15 g ± 0.5 g, a hind wing length of 42.23 mm ± 1.2 mm and a elytron length of 22.13 mm ± 1.3 mm (N=10, Table 1). Fig. 2 shows a series of photographs taken during the initial flight stages of a female Trypoxylus dichotomus beetle. In preparation for wing beating, the elytra opened first. During this time the hind wings extended (Fig. 3). The middle legs then rose, reaching the full extension so that the hind wings flap down. As shown in Fig. 2, the hind wings unfolded at the middle of the downstroke (t = í61.0 ms) and the first stroke began at í55.0 ms. During the first upstroke, the front leg was lifted (t = í202.5 ms, Fig. 2). The beetle body angle gradually rose while the wings were beating (see also Fig. 6). It can be clearly seen that the beetles do not jump during take-off. The hind wings are between mid-upstroke and the end of upstroke at lift-off on the third cycle wing beat and the beetle comes to the vertical flight posture (t = 0 ms, Fig. 2). The relative timing of take-off events is shown in Fig. 3. In some cases, the middle leg rising precedes the elytra opening. As a consequence, in most cases, the legs had risen by the time the elytra fully elevated (Fig. 2). The beetle completed 2.5 wing beats before beginning the

Fig. 2 Sequential snapshots of a take-off by female Trypoxylus dichotomus captured at 2000 fps. Sequential snapshots recorded from the side view.

Table 1 Body form in Trypoxylus dichotomus. Samples

B1

B2

B3

B4

B5

Body mass (g)

3.96

4.56

4.45

4.61

4.35

Hind wing length (mm)

47.76

45.05

48.23

46.67

48.26

Elytron length (mm)

23.15

22.32

24.21

23.12

23.73

Samples

B6

B7

B8

B9

B10

Body mass (g)

5.25

4.58

5.12

4.86

4.87

Hind wing length (mm)

50.87

49.30

50.11

49.56

49.81

Elytron length (mm)

25.19

24.1

24.98

24.56

24.27

Fig. 3 Timelines of take-off events (N=10). Each timeline represents an event sequence for an individual beetle. The black and grey bands represent the duration of the down stroke and the upstroke respectively.

Truong et al.: Non-Jumping Take off Performance in Beetle Flight (Rhinoceros Beetle Trypoxylus dichotomus)

seemed to be unchanged. On subsequent strokes the body angle began increasing stroke by stroke. From the second strokes, the body angle during downstroke did not decrease as much as it did in the first stroke. At the end of the fourth stroke, the body angle was 61.94Û±3.31Û. Table 2 Timing of take-off events. Event

Mean value

Right elytron open (ms)

12.29±5.82

Left elytron open (ms)

13.37±6.89

Right middle leg elevation (ms)

9.76±2.54

Left middle leg elevation (ms)

9.65±3.79

Right hind wing extension (ms)

4.28±1.87

Left hind wing extension (ms)

7.26±3.48

Lift-off (ms)

45.69±10.21

Wing beat frequency (Hz)

first stroke. The flapping down of the hind wing occurred in both cases at the time when the middle legs rose. All the legs left the ground during the downtroke on the third beating cycle. The periods of the take-off events are presented in Table 2. The entire lift-off takes 45.69 ms ± 10.21 ms (N=10) (Table 2). In general, the extension of the hind wing occurs during the elytra opening. The duration of the elytron opening was not much different between the left and the right wings. However, there was a considerable difference in the duration of the hind wing unfolding between the left and right wings. The beetle typically did not unfold the left and right hind wings in unison (right = 4.28 ms ± 1.87 ms, left =7.26 ms ± 3.48 ms, N=10). The first wing beat frequency was 41.63 Hz ± 1.62 Hz (N=10) and reduced in subsequent strokes (Fig. 4). The first stroke was defined as the stroke in which the hind wing unfolded fully, and it is to start from the upstroke. It should be noted that aerodynamic forces are proportional to the wing tip velocity, wing beat frequency, and wing length[32]. Thus, the beetle takes off with a high frequency to achieve the high lift forces. Fig. 5 illustrates the typical trajectory of the tip of the elytra during opening. The forward movement of the pronotum and depression of the metathorax with respect to the mesothorax unlock he elytra[26]. The elytra opened to the side then upward and forward to create a free space below for the hind wings’ unfolding and beating. The duration of a full elytra opening is 110 ms. The opening tip path is seen in the sequence and almost symmetric for elytra. The swept angle of the elytra opening, which is defined as the angle between the beginning of release and full elevation, was 75.30Û for the left wing and 67.49Û for the right wing. The elytra were released, rotated forward, and the time required to complete elytra opening was 110 ms. The angle between the two elytra is 38.84Û at full elevation. The setting angle of the elytra with the body plane was 20.45Û for the left wing and 19.34Û for the right wing. At the beginning of the first stroke, the body angle was 34.81Û±3.83Û (N=10) (Fig. 6). The body angle vacillated during each wing beat, as it increased during upstroke and decreased during downstroke. The mean variation from the beginning to the end of the upstroke on the first stroke was 5.62Û±3.21Û. After the wings finished beating on the first cycle, the body angle

65

Fig. 4 Wing beat frequency (Hz) during the fist and the 4th wing beat in the take-off (N=10); error bars represent the standard deviations.

Wing bases

15 10 5 0 í5 í15 í10 í20 í25 (a)

í20

í10 0 Y (m)

10

30

10 20 X (m)

0

Fig. 5 Kinematics of the opening elytra of T. dichotomus. (a) 3D trajectories of the tip of the elytra during opening. Opened dots, right elytron; filled dots, left elytron. The lines connecting the wing bases and wing tips represent the span-wise direction of the elytra. (b) Real images of elytra during opening.

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

66 80 70 60 50 40 30 20 10 0

0

0.025

0.05 Time (s)

0.075

0.1

Fig. 6 Body angle of the beetle during take-off. Top figures indicate the end of the upstroke and lower figures indicate the end of the downstroke. The shaded region around those lines displays the instantaneous standard deviation. t=0 indicates the beginning of the first stroke.

Fig. 7 shows the hind wing tip path during a typical take-off process. It can be seen that the motion of the hind wings varied throughout the strokes and was

asymmetric. The wing tip paths of the upstroke and downstroke almost overlapped at the beginning of the downstroke, but it had diverged significantly towards the end of the downstroke. A figure-eight pattern was shown by the right hind wing during the first three strokes and by the left wing during the fourth stroke. In the first stroke, the motion of the left wing was wide and became narrow in subsequent strokes. In addition, we can see clearly how the stroke plane angle changed in each stroke. The stroke plane reduced the tilt while the beetle moved up. The angle between the stroke plane and horizontal plane of the first stroke, second stroke, third stroke, and fourth stroke were 21.35Û, 21.28Û, 13.68Û, 5.01Û for the right hind wing, and 24.27Û, 19.03Û, 11.84Û, 3.04Û for the left hind wing, respectively. The stroke plane angle did not change much during the first two strokes. However, it can be seen that after lift-off, the stroke plane angle reduced dramatically and came to the horizontal posture.

60

Stroke 4

0 í50 50

0 y (mm) í50 í50

0 x (mm)

50

í40 í60 60 40

0

í50 50

í20

20 0 í20

í40

í40

í60 60

í60 60 40

í50

0 x (mm)

50

40 20 0

50 0 í50 50

0 y (mm)

í50 í50

0 x (mm)

50

50 Stroke 1

í40 í60 60 40 20

0

0 y (mm) í50

Stroke 2

0 í20

í20

50 Stroke 3

60 40 20

40 20 0

50

0 í50 50

0 y (mm)

í50 í50

0 x (mm)

50

í20

20 0 í20

í40 í60 60

í40 í60 60

40 20

40 20

0 í20

0 í20

í40

í40

í60 í60 í40 í20

0 20 x (mm)

40

60

í60 í60 í40 í20

0 20 x (mm)

40

60

Fig. 7 3D kinematics of the first four strokes of the beetle take-off. The first column indicates the trajectories of the tip of the hind wings in the global coordinate system. The second column shows the lateral view of the hind wing tip’s path. The hind wing bases are indicated by black crosses. The third column illustrates the top view of the hind wing’s tip. The Center Of Mass (COM) indicated by the black dots. The crosses indicate the hind wing base. The continuous lines represent the left hind wing and the dashed lines represent the right hind wing, respectively.

Truong et al.: Non-Jumping Take off Performance in Beetle Flight (Rhinoceros Beetle Trypoxylus dichotomus)

Before take-off, the beetles crawled randomly in the flight chamber. Because the hind wing is a flexible membrane, it was difficult to capture the wing kinematics of the beetle inside the optimum focus region of the three cameras. Beetles B2 (see Table 1) and B4 were eager to take off. When beetle B2 and B4 were placed in the focus region, they immediately took off. We could record three good resolution movies from five recorded take-offs for beetles B2 and B4. The wing kinematics of B2 and B4 were analyzed. The measured data of these kinematics were taken from three in focus take-offs for B2 and B4. Fig. 8 illustrates the variation of the flapping angle of the elytra and the flapping angle, deviation angles, and the angle of attack of the hind wings. We analyzed a total of 24 stroke sequences. The dimensionless time (t/T) is 0 to 0.5 for the upstroke and 0.5 to 1 for the downstroke. The ratio of downstroke to upstroke for the flapping motion was around 1. It has been reported that the ratio was around 1 due to the asynchronous muscle of a beetle[33]. The flapping angle of the elytron was found to be asymmetric between the left wing and the right wing and varied with time, approximately as a sinusoidal function. In the first stroke, the difference in flapping angle is very small between the left and right elytron. In the downstroke of the subsequent stroke, the flapping angle of the right is higher than the left elytron. The average flapping angles were measured to be 38.8Û±1.82Û for the left elytron and 43.72Û±2.32Û for the right elytron. Similar to elytra, the variation of stroke position angle with respect to time approximately followed a Sine function. During the second stroke, there is a significant difference between the left (143.48Û±6.63Û) and right hind wings (173Û±4.14Û). This asymmetry persists in the third stroke and then the hind wings come back to synchronization. The angle variation was almost symmetric for the upstroke and downstroke in the fourth stroke. The wings display a narrow motion, indicated by the small deviation angle (less than 15Û). In particular, the change in deviation angle through strokes is very different between the left and the right hind wings. The right wing shows a much weaker variation in deviation angle during strokes than the left wing. On the second stroke, the right wing moved near and roughly parallel to the stroke plane. At that time, the flapping angle also reduced. In the fourth row of Fig. 8, the angle of attack of the hind wing is shown in 0.5R sections along the span di-

67

rection. R is the hind wing length. The amplitude of the angle varied from 25.32Û±3.87Û to 158.06Û±6.01Û for the left hind wing and 10.09Û±4.06Û to 157.83Û±6.35Û for the right hind wing. It can be seen that on the fourth stroke, the stroke planes were nearly horizontal. The period of the hind wing rotational and translational motions was demonstrated. The durations of supination and pronation were approximately equal and the total rotation duration occupied 27.45% of the stroke period. The angle of attack reduced from 140.15Û±5.42Û to 53.99Û±4.46Û in pronation (t=0.01 s to 0.0145 s) for the left wing (153.81Û±7.1Û to 53.49Û±10.72Û for the right wing) and increased from 30.23Û±4.38Û to 118.11Û±5.38Û for the left wing (20.89Û±4.3Û to 108.99Û±10.69Û for the right wing) in supination (t = 0.023 s to 0.0265 s). The pattern of the angle of attack on the first stroke and second stroke of each wing was similar. The variation of the angle of attack was approximately symmetrical. On the right wing, the angle of attack was nearly constant from the beginning to the middle of the upstroke translation period on the first and second strokes, and then the angle of attack increased to the maximum at the beginning of supination. Meanwhile, at the left wing, the angle of attack decreased and then increased in the upstroke translation period. The beetle pitched upward over the first stroke to lift off the middle legs and gradually elevate the whole body during the second stroke. However, the angle of attack pattern changed during the third 50 0 í50 100 0 í100 20 0 í20 150 100 50 0 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Time (s)

Fig. 8 Variation of the flapping angle of the elytra and the flapping angle, the deviation angle and the angle of attack of the hind wings. The shaded region around those lines displays the instantaneous standard deviation. Shaded bar corresponds to the downstroke period. The right wing is indicated by the red lines and the left wing by the blue lines. The shaded areas represent the duration of each downtroke. t=0 indicates the begging of the firs stroke.

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

similar and slightly increased after lift-off. The angular acceleration fluctuated in the first upstroke and then maintained a value close to zero.

4 Discussion In this work, we sought to understand the take-off mechanism in the rhinoceros beetle (Trypoxylus dichotomus). Our findings show that Trypoxylus dichotomus takes off without jumping, in contrast with the most common mechanism in flying animals. We characterized the non-jumping take-off mechanism of Trypoxylus dichotomus. We found that the elytra elevated,

30

Horizontal

20

Vertical

10 0 0.4 0.3 0.2 0.1 0 150 100 50 0 í50

0

0.02

Angle (deg)

(a)

Angular velocity (deg·sí1)

stroke in which the beetles lift off. The left wing rotated dramatically down, generating the body pitch angle and afterward rotated reversely to the middle of translation. In contrast, the angle of attack pattern of the right wing seems to be reverse of the left wing during translation. The angle of attack of the right wing decreased at the middle of translation and then peaked. This change is maintained for one stroke, indicating that the beetle can agilely modulate the wing to lift off. During the first three cycles, the angle of attack of the right wing reduced during the downstroke, and the two wings flapped asymmetrically. After lift-off, the pattern of wing motion became nearly symmetric during the fourth stroke. After the wings began beating, the beetles gradually changed their COM in both horizontal and vertical directions throughout the wing strokes (Fig. 9a). During take-off, the horizontal and vertical COM was nearly equal. The beetle continuously increased its horizontal and vertical velocity. The peak vertical velocity was 0.31 m·sí1 ± 0.02 m·sí1 (N=10) at the middle of the first stroke. During the first upstroke, the horizontal velocity increased rapidly and then gradually. From the second stroke to the end of the upstroke of the third stroke, the ratio of horizontal to vertical velocities was nearly 1. After the beetle lifted off from the ground, the vertical velocity was less than the horizontal velocity. Generally, the horizontal acceleration component was shallow and nearly constant during take-off, indicating that the beetle consistently launched itself into the air in the horizontal direction. The vertical acceleration increased during upstroke and reduced during upstroke coinciding with the change of body angle. Regarding the rotational body kinematics, the slope of the pitch and yaw angles was small from the beginning to the middle of the upstroke during the third stroke, which is the lift-off point. The mean pitch and yaw angles were 8.36Û±1.39Û and 7.48Û±1.67Û, respectively. Later, the pitch angle increased to 38.06Û±1.5Û at the middle of the downstroke during the fourth stroke and remained constant. The yaw angle increased, reaching a peak of 37.12Û ± 1.51Û around that time, and then decreased. This resulted from the wings beating symmetrically after the third cycle. The slope of the roll angle was small, and the roll angle was less than 20Û. In contrast, the pitch angular velocity decreased from the first upstroke (450.94Û±72.45Û per second). From the first upstroke, the yaw and pitch angular velocities were

Angular acceleration (×106deg·sí2)

68

(b)

0.04 0.06

0.08 0.1

Time (s)

Pitch Yaw

40 30 20 10 0

Roll

1500 1000 500 0 3 2 1 0 0

0.02

0.04 0.06 0.08 0.1 Time (s)

Fig. 9 (a) Translational body kinematic. (b) Rotational body kinematic. The shaded region around those lines displays the instantaneous standard deviation. Shaded bar corresponds to the downstroke period. The position, velocity and acceleration plotted are the value of the COM. Those initial values were calculated at beginning of the first stroke.

Truong et al.: Non-Jumping Take off Performance in Beetle Flight (Rhinoceros Beetle Trypoxylus dichotomus)

the hind wings extended, and the hind legs rose, thus, creating the space for the wing-beating of the hind wing. The hind wings unfolded when they were flapping. The full hind wings flapped, and the beetle gradually lifted off from the ground. For all of the observed beetles, the legs lost contact with the ground during the upstroke of the third wing-beating cycle. The beetles launched slowly into flight in both horizontal and vertical directions. The beetle varied its body angle in each stroke and transitioned into vertical flight. The beetles showed stable take-off, indicated by the slender rotation angle about all three of its body axes. In addition, the acceleration of the three rotation angles was small. Because of the non-jumping mechanism of the rhinoceros beetle, there are no rapid escapes from the ground. Moreover, we could not see any movement of the legs in the beetle during take-off. The legs of a jumping insect push the ground similar to spring mechanism that was observed in many insects such as locusts[21,34] , shore bugs[9] or in bird flight[8,10]. It was noted that the legs provide a large thrust for jumping[19,35] in jumping take-off mechanisms. The take-off acceleration could range from 15 to 270 times gravity in a flea beetle[15] and around 10 to 160 times gravity in flea bugs[20]. In contrast, the vertical acceleration of the beetle does not seem to change throughout strokes, it just increases during upstroke and decreases during downstroke in each stroke. Most of insects use strong force from the leg in jumping mechanism to initiate the take-off flight. Without the wings, the insect are able to launch into the air by only jumping[13,15]. The force production by the two legs corresponds approximately to 20 times of the weight of fly[36]. The force relative to body mass and acceleration generated at take-off is 414 times[17] of their body in the largest jumps in froghoppers[14] and 135 times in fleas[14]. Meanwhile, the force from the leg is minor during flight initiation of the beetle because the absolute value of acceleration seems to be zero throughout strokes. A jumping insect uses the legs, which contract then suddenly expand to accelerate its body to a high position in the air before the wings unfold and flap. The beetle C. auta presents two different strategies of jumping: the body spins through air in wingless jumping and the wings open before take-off[15]. In the second strategy, the body is stable and against the spinning[15]. The stability during take-off is also improved from opening wings in

69

shore bugs[9]. By using wings during jumping, the fly launches into the air and is slower but more stable. However, during wingless jumping, the fly translates faster but also rotates rapidly about all three of its body axis[13]. In voluntary take-off (using wings), the fly beats their wings for about one stroke before lift-off and then the legs depress downward[13]. Meanwhile, in non-jumping take-off of the beetle Trypoxylus dichotomus, the wings flap around 2.5 strokes before lift-off without any movement of the legs. The force balance produced by the hind wing makes the body of the beetle stable. It can be clearly seen that the body exhibits stable take-off with a small velocity and acceleration of rotation angle (Fig. 9b). After the small tumbling in the first upstroke, the beetle achieved steady take-off. The stability of the beetle Trypoxylus dichotomus during the take-off was established by the non-jumping mechanism where the force was generated by the hind wing.

5 Conclusion In present study, we revealed that the Rhinoceros Beetle, Trypoxylus dichotomus, takes off without jumping. In order to understand non-jumping take-off in Trypoxylus dichotomus, we used 3D high-speed cameras to quantitatively analyze the kinematic parameters of wing motion, particularly the wing tip trajectory, and the angle of attack. In contrast to other jumping insects, the beetle Trypoxylus dichotomus could achieve stability in vertical take-off. The take-off mechanism in the beetle Trypoxylus dichotomus may give additional information for non-jumping take-off mechanism in other insect.

Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant number: 2010-0015174).

References [1]

Willmott A P, Ellington C P. The mechanics of flight in the hawkmoth Manduca sexta. I. Kinematics of hovering and forward flight. Journal of Experimental Biology, 1997, 200, 2705–2722.

[2]

Hedrick T L, Daniel T L. Flight control in the hawkmoth manduca sexta: the inverse problem of hovering. Journal of

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

70

heights. Nature, 2003, 424, 509–509.

Experimental Biology, 2006, 209, 3114–3130. [3]

[4]

Fry S N, Sayaman R, Dickinson M H. The aerodynamics of

[18] Ennos A R. The Kinematics an Daerodynamics of the Free

free-flight maneuvers in drosophila. Science, 2003, 300,

Flight of some Diptera. Journal of Experimental Biology,

495–498.

1989, 142, 49–85.

Iriarte-Diaz J, Swartz S M. Kinematics of slow turn maneuvering in the fruit bat cynopterus brachyotis. Journal of Experimental Biology, 2008, 211, 3478–3489.

[5]

[6]

measurement of honeybee bilateral wings using four virtual

[21] Sutton G, Burrows M. The mechanics of elevation control in

structured-light sensors. Journal of Sensors and Actuators A:

locust jumping. Journal of Comparative Physiology A:

Physical, 2008, 148, 19–27.

Neuroethology, Sensory, Neural, and Behavioral Physiology,

Wang H, Zeng L, Liu H, Yin C. Measuring wing kinematics,

2008, 194, 557–563. [22] Grimald D, Engel M S. Evolution of the Insects. Cambridge: Cambridge University Press, Cambridge, UK, 2005. [23] El Jundi B, Huetteroth W, Kurylas A E, Schachtner J.

Biology, 2003, 206, 757.

[9]

[20] Sutton G P, Burrows M. Biomechanics of jumping in the flea. Journal of Experimental Biology, 2011, 214, 836–847.

turning maneuvers in dragonflies. Journal of Experimental

[8]

Journal of Experimental Biology, 2006, 209, 4607–4621.

Zhang G, Sun J, Chen D, Wang Y, Flapping motion

flight trajectory and body attitude during forward flight and

[7]

[19] Burrows M. Jumping performance of froghopper insects.

Shyy W, Lian Y, Tang J, Viieru D, Liu H. Aerodynamics of

Anisometric brain dimorphism revisited: implementation of

Low Reynold Number Flyers. Cambridge University Press,

a volumetric 3D standard brain in Manduca sexta. Journal of

Cambridge, UK, 2011.

Comparative Neurology, 2009, 517, 210–225.

Earls K. Kinematics and mechanics of ground take-off in the

[24] Van Truong T, Le Q T, Tran H T, Park H C, Yooh K J, Byun

starling sturnis vulgaris and the quail coturnix coturnix.

D. Flow visualization of rhinoceros beetle (Trypoxylus

Journal of Experimental Biology, 2000, 203, 725–739.

dichotomus) in free flight. Journal of Bionic Engineering,

Burrows M. Jumping strategies and performance in shore

2012, 9, 304–314.

bugs (Hemiptera, Heteroptera, Saldidae). Journal of Experimental Biology, 2009, 212, 106–115.

[25] Haas F, Gorb S, Blickhan R. The function of resilin in beetle wings. Proceedings of the Royal Society of London. Series B:

[10] Tobalske B W, Altshuler D L, Powers D R. Take-off mechanics in hummingbirds (Trochilidae). Journal of Experimental Biology, 2004, 207, 1345–1352.

Biological Sciences, 2000, 26, 1375–1381. [26] Le T Q, Byun D, Saputra P, Ko J H, Park H C, Kim M. Numerical investigation of the aerodynamic characteristics

[11] Berg A M, Biewener A A. Wing and body kinematics of takeoff and landing flight in the pigeon (Columba livia). Journal of Experiemetal Biology, 2010, 213, 1651–1658.

of a hovering Coleopteran insect. Journal of Theoretical, Biology, 2010, 266, 485–495. [27] Frantsevich L, Dai Z, Wang W Y, Zhang Y. Geometry of

[12] Fontaine E I, Zabala F, Dickinson M H, Burdick J W. Wing

elytra opening and closing in some beetles (Coleoptera,

and body motion during flight initiation in Drosophila

Polyphaga). Journal of Experimental Biology, 2005, 208,

revealed by automated visual tracking. Journal of Experimental Biology, 2009, 212, 1307–1323.

3145–3158. [28] Hongo

Y.

Appraising

behaviour

during

male-male

[13] Card G, Dickinson M H. Performance trade-offs in the flight

interaction in the Japanese horned beetle trypoxylus

initiation of Drosophila. Journal of Experimental Biology,

dichotomus septentrionalis (Kono). Behaviour, 2003, 140, 501–517.

2008, 211, 341–353. [14] Burrows M. Kinematics of jumping in leafhopper insects

[29] Hatze H. High-precision three-dimensional photogram-

(Hemiptera, Auchenorrhyncha, Cicadellidae). Journal of

metric calibration and object space reconstruction using a

Experimental Biology, 2007, 210, 3579–3589.

modified DLT-approach. Journal of Biomechanics, 1988, 21,

[15] Brackenbury J, Wang R. Ballistics and visual targeting in flea-beetles (Alticinae). Journal of Experimental Biology,

dimensional kinematic measurements of biological and

1995, 198, 1931–1942. [16] Burrows M, Picker M D. Jumping mechanisms and performance

of

pygmy

533–538. [30] Hedrick T S. Software techniques for two- and three-

mole

crickets

(Orthoptera,

Tridactylidae). Journal of Experimental Biology, 2010, 213, 2386–2398. [17] Burrows M. Biomechanics: Froghopper insects leap to new

biomimetic systems. Bioinspiration & Biomimetics, 2008, 3, 034001. [31] Phillips W F. Mechanics of Flight, John Wiley & Sons Inc, New York, USA, 2004. [32] Van Truong T, Le T Q, Byun D, Park H C, Kim M. Flexible

Truong et al.: Non-Jumping Take off Performance in Beetle Flight (Rhinoceros Beetle Trypoxylus dichotomus)

71

wing kinematics of a free-flying beetle (rhinoceros beetle

[35] Cofer D, Cymbalyuk G, Heitler W J, Edwards D H.

trypoxylus dichotomus). Journal of Bionic Engineering,

Neuromechanical simulation of the locust jump. Journal of

2012, 9, 177–184.

Experimental Biology, 2010, 213, 1060–1068.

[33] Altshuler D L, Dickson W B, Vance J T, Roberts S P,

[36] Sutton G P, Burrows M. The mechanics of azimuth control

Dickinson M H. Short-amplitude high-frequency wing

in jumping by froghopper insects. Journal of Experimental

strokes determine the aerodynamics of honeybee flight. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102, 18213–18218. [34] Josephson R K, Malamud J G, Stokes D R. Power output by an asynchronous flight muscle from a beetle. Journal of Experimental Biology, 2000, 203, 2667–2689.

Biology, 2010, 213, 1406–1416. [37] Zumstein N, Forman O, Nongthomba U, Sparrow J C, Elliott C J. Distance and force production during jumping in wild-type and mutant Drosophila melanogaster. Journal of Experimental Biology, 2004, 207, 3515–3522.