How does a woodpecker work? An impact dynamics approach

Transcription

1 Acta Mech Sin (205 3(2:8 90 DOI 0.007/s RESEARCH PAPER How does a woodpecker work? An impact dynamics approach Yuzhe Liu Xinming Qiu Tongxi Yu 2,3 Jiawei Tao Ze Cheng Received: 2 October 204 / Revised: February 205 / Accepted: February 205 / Published online: 2 May 205 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 205 Abstract To understand how a woodpecker is able accelerate its head to such a high velocity in a short amount of time, a multi-rigid-segment model of a woodpecker s body is established in this study. Based on the skeletal specimen of the woodpecker and several videos of woodpeckers pecking, the parameters of a three-degree-of-freedom system are determined. The high velocity of the head is found to be the result of a whipping effect, which could be affected by muscle torque and tendon stiffness. The mechanism of whipping is analyzed by comparing the response of a hinged rod to that of a rigid rod. Depending on the parameters, the dynamic behavior of a hinged rod is classified into three response modes. Of these, a high free-end velocity could be achieved in mode II. The model is then generalized to a multihinge condition, and the free-end velocity is found to increase with hinge number, which explains the high free-end velocity resulting from whipping. Furthermore, the effects of some other factors, such as damping and mass distribution, on the velocity are also discussed. Keywords Woodpecker Muscle torque High impact velocity Whipping Hinged rod B Xinming Qiu qxm@tsinghua.edu.cn Department of Engineering Mechanics, Tsinghua University, Beijing 00084, China 2 Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 3 Ningbo University, Ningbo 352, China Introduction Pecking is very important in a woodpecker s daily life. Woodpeckers peck on tree trunks to forage for food and to break the bark and wood to catch worms. Pecking is also done to make loud sounds to stake claims on territory and attract mates. As reported in some studies, a woodpecker will peck more than 2000 times a day, and the frequency of the pecking could reach around 20 Hz. The maximum impact velocity of pecking is 6 7 m/s, and the deceleration of a woodpecker s head is more than 000 g. To explain those phenomena, several studies have been conducted to examine how woodpeckers are able to avoid brain injury in such conditions [ 5]. In addition, how a woodpecker is able to accelerate its head at such high velocities in a short amount of time is also of interest, but few works about this have been reported, except for a simple rigid-body model of a woodpecker proposed by Vincent [6] and based on a comparison of the natural frequency of the system and pecking frequency observed. It was concluded in Ref. [6] that the system of the woodpecker body resonated during pecking, which would save the input energy. By analyzing several videos of pecking woodpeckers, we found that woodpeckers pecking frequency and pecking strength different depending on the purpose for pecking. For example, a woodpecker pecks tree trunks rapidly and lightly when foraging for food. The pecking frequency is approximately 20 Hz, and the swing of the body is very small, which leads to a lower impact velocity. But when a woodpecker aims to break tree bark and wood to catch worms, the strikes are much harder. The pecking frequency is less than 0 Hz, and the swing of the body is larger, enabling the creature to attain a high impact velocity. The present study aims to determine how the different parts of a woodpecker s body work to strike in low-frequency and high-impact-velocity conditions.

2 82 Y. Liu et al. Based on the skeletal specimen of a woodpecker and several videos of pecking woodpeckers, a multi-rigid-segment model of a woodpecker body will be established first. By determining the parameters of a three-degree-of-freedom (DOF system, the impact velocity is found to be affected by and tendon stiffness. In addition, a high impact velocity is produced by the relative rotations between different rigid segments, which is similar to the whipping of rope. The mechanism of rope whipping is analyzed by comparing the responses of a hinged rod to that of a rigid rod. The dynamic behavior of a hinged rod is classified into three response modes depending on the parameters. Of these parameters, a high free-end velocity could be achieved in the case of mode II responses. The analysis is then generalized to multihinge rod conditions, and the factors that affect the free-end velocity, such as hinge number, damping, and mass distribution, are analyzed. 2 Woodpeckers pecking process Under conditions of hard strikes, one cycle of a woodpecker s pecking is shown in Fig., including (a backward leaning, (b farthest position, (c forward movement, and (d strike position. When a woodpecker starts pecking, it moves its body and head backward slowly, as shown in Fig. a. This action occurs at a large distance from the trunk and enables the storage of elastic energy in the muscles and tendons connecting the joints. At the farthest position from the trunk, as shown in Fig. b, it is observed that the angle between the body line and the trunk is θ = 24, and the angle between the head shoulder line and the body line is θ 2 = 70. In different cycles of pecking, θ and θ 2, which significantly affect the impact velocity of the head, may vary slightly. Then the woodpecker moves forward (Fig. c significantly faster than it leans back. By counting the frames of video in different cycles, the duration of the backward lean is determined to be approximately 3 5 times that of the forward movement. In this stage, the elastic energy stored is released to accelerate the head. Here, muscles and tendons work together. As reported in the literature [7], when a muscle contracts, the force provided and the contracting velocity are in negative relation, which means the high contracting velocity will lead to low force. But tendons do not have this limitation. Therefore, it is estimated that the effect of tendon contraction is more significant than that of muscle contraction. As reported in Ref. [8], fleas can take advantage of this mechanism to jump higher. Finally, the woodpecker strikes the trunk (Fig. d. At this moment, the body line and the head bottom line are almost Fig. One cycle of woodpecker pecking. (The video is from the Internet Bird Collection, a Backward lean. b Farthest position. c Forward movement. d Strike position parallel to the trunk. In this video, the frequency of pecking is determined to be approximately 6 8 Hz. As found in previous studies [3,5,6], the tail feather of the woodpecker is very hard and is used to maintain the balance of the body when it strikes the trunk. In the videos, the tail is observed to make contact with the trunk consistently. Furthermore, the tail and the tarsometatarsus (paws and connected bones are found to be kept stationary in all cycles of pecking. 3 Multi-rigid-segment model of a woodpecker To reveal the mechanism by which a woodpecker effectively attains such a high impact velocity and the roles of muscles and tendons during this process, a multi-rigid-segment model of the woodpecker is established. 3. Model simplifications Based on the foregoing description of the pecking process and observation of the skeletal specimen of a woodpecker, a multi-rigid-segment model, consisting of ten rods and one ball, is established (Fig. 2. In the model, the tail, tar-

3 How does a woodpecker work? An impact dynamics approach 83 the skeletal specimen, and rigid bodies are assumed to be homogeneous. Based on observations of the videos, some simplifications are adopted in the multi-rigid-segment model, as follows: ( Beak orientation adjustment is omitted. Before a woodpecker s head hits the trunk, the orientation of the beak can be adjusted by itself. Since we will focus on velocity and acceleration, this orientation adjustment is omitted in the model. Hereafter, the beak striking the trunk is simplified as the impact between ball K and block L. Here, the mass of ball K, including that of the beak, and the length of block L is equal to that of the beak. (2 Rods A and B are fixed. As mentioned earlier, the videos show that the tarsometatarsus and the tail hardly moved during the pecking process, so rods A and B are fixed in the model. Since the strike position can be adjusted by varying the directions of rods A and B, it is reasonable to assume that the ball K always strikes block L at its maximum velocity. Fig. 2 Multi-rigid-segment model of woodpecker. A Tail. B Tarsometatarsus. C Tibia. D Femur. E Lower torso. F Upper torso. G Neck. H Neck2. I Neck3. J Neck4. K Head. M Trunk. L Position where impact happens Table Geometry and mass of woodpecker multi-rigid-segment model [4] Part Truss/ball Length/radius (mm Mass (g Tail A 90 7 Tarsometatarsus B 27 3 Tibia C 34 5 Femur D Lower torso E 25 5 Upper torso F Neck G, H, I, J Head K sometatarsus (paws and connected bones, tibia (leg, and femur (thigh are represented by rods A, B, C, and D, respectively. The torso is represented by rods E and F. The rotation between rods E and F represents the bending of the vertebrae. The long neck is represented by rods G, H, I, and J. These ten rods are connected to their neighbors by hinges. The head is represented by a ball, K, fixed on top of the neck, J. Table lists the geometry and mass of different rigid bodies in the model. The length of the rods is determined by measuring (3 Uniform rotation of neck. The rotation angles between different rods in the neck are assumed to be the same, i.e., the angles between rods F and G, G and H, H and I, and I and J are equal to each other. Since these rigid segments are connected by the same muscles, this assumption should be acceptable. Eventually, the multi-rigid-segment model is simplified as a four-bar linkage (C, D, E connected by hinges with a multisegment bar (F, G, H, I, J. The total degrees of freedom of this system is three, which can be represented by the generalized coordinates that correspond to the rotation between tibia and femur/torso, the bending of the torso, and the rotation of the neck. 3.2 Muscle torque, tendon stiffness During pecking by a woodpecker, muscles provide action force and input energy, tendons store and release energy to amplify the input rate of work, and other soft tissues, including noncontracting muscles, play a role such as in damping. When the woodpecker s body moves backward, the muscles on one side stretch the tendons, and the tendons store elastic deformation energy. Then, as muscles on the opposite side contract, the body moves forward and the tendon torques perform positive work to accelerate the head. Corresponding to the three generalized coordinates, the torques of muscles, tendons, and damping at joint (between rods C and D, joint

4 84 Y. Liu et al. 2 (between rods E and F, and joint 3 (between rods F and G should be analyzed. Muscle torque is determined by the muscle mass of the joint. Muscle torque per unit mass, M, is estimated using Eq. (: M = F l b m = σ S l b ρ S l m = α σ ρ, ( where F is the force exerted by a fascicle of muscle, l b is the arm of the muscle force, m is the muscle mass, ρ, S, l m are the density, cross-sectional area, and length of the muscle fascicle, respectively, and σ is the maximum stress that the skeletal muscle can exert. Here the parameter α is defined as α = l b /l m and assumed to be α = According to [7,9], σ 300 MPa and ρ 30.4 kg/m 3 ; henceforth M 2.68 N m/kg. The muscle masses at joints and 2 are assumed to be the total mass of their nearby rods. The mass of joint 3 is assumed to be g, which represents the total mass of the neck muscle and a small part of the shoulder muscle. Since muscles can only contract in one direction, the mass of muscle contracting forward is assumed to be twice that of muscle contracting backward. Tendon torques are determined by the rotational stiffness and the equilibrium positions. To attain a high impact velocity, the equilibrium position should be the strike position. The rotational stiffness of the tendons are determined by two factors, the duration of pecking and the maximum angles of θ and θ 2 at the farthest position. The video reveals that θ = 24,θ 2 = 70, and a pecking frequency of 7 Hz are adopted. In one pecking cycle, the muscles initially contract backward to store energy and then contract forward to strike. The time at which the muscles contract forward is chosen to be the same as the time when the body moves forward so that the s are always doing positive work. The damping torques are proportional to the angular velocities at the joints. The damping coefficients are chosen so as to attain a higher impact velocity. The aforementioned method is used to determine all system parameters, as listed in Table 2. Using these parameters, the maximum impact velocity obtained is 4.57 m/s at 45.3 ms, as shown in Fig. 3, while the corresponding angles are θ = 24.9 and θ 2 = 68.8, respectively. Therefore, the impact velocity, the time duration, and the pose of the pecking process obtained by this model agree with the observations. During the pecking process, the peak force exerted on the tail is approximately 5.9 N, which shows the importance of the woodpecker s hard tail feather. The effect of the parameters variations on the results are also considered, as listed in Table 3. In each row, only one parameter varies by a small amount. The following observations can be made from Table 3. Table 2 Muscle torques, rotational stiffness of tendons, damping coefficients, and instants when muscles contract in opposite directions Backward muscle torque (N m Forward (N m Rotational stiffness (N m Damping coefficient (N m/s Joint Joint 2 Joint Time (ms Fig. 3 Velocity of centroid of head, neck, and torso. Red solid line: time of maximum head velocity ( The backward is more influential than the forward one. The backward at the neck is the most influential, but the forward at the neck hardly influences the maximum velocity. (2 The maximum velocity is in negative correlation with the rotational stiffness. This is because when the load is constant, the stored energy is higher with lower stiffness. And the rotational stiffness in the neck is most influential. (3 The maximum velocity increases when both θ and θ 2 increase, except if the rotational stiffness at joint 3 changes, when these two angles are mainly dominated by the interaction between neck and torso instead of the movement of the body. Here, the velocity histories of different rigid segments should be noted. From the velocity time curves shown in Fig. 3, the velocities of neck I, neck H, neck G, and torso F will all reach their peak values earlier than that of head K. This implies that when head K reaches its maximum velocity, the velocities of the other segments are already decreasing. This velocity distribution helps the head to attain a higher impact

5 How does a woodpecker work? An impact dynamics approach 85 Table 3 Effects of and rotational stiffness of tendons on maximum velocities, θ,andθ 2 Parameter Variation (N m Maximum velocity (m/s θ ( θ 2 ( Joint backward Joint forward Joint 2 backward Joint 2 forward Joint 3 backward Joint 3 forward Joint rotational stiffness of tendon Joint 2 rotational stiffness of tendon Joint 3 rotational stiffness of tendon The number in the table is the variations from that maximum velocity is 4.57 m/s, θ is 24.9 and θ 2 is 68.8 velocity. Since the torso and long neck of the woodpecker are hinged individually, the global movement of system is similar to the whipping of a rope. Therefore, the mechanism of this so-called rope-whipping phenomenon will be discussed in more detail. Fig. 4 a Hinged rod. b Rigid rod hinge of the hinged rod. β and β 2 are the angles between the segments and the horizontal line. Suppose rotational springs G and G 2 exist at hinges P and P 3, respectively. β i is the angle of the rod relative to the horizontal line. At t = 0, β = 0, β 2 = 0, and the preloads at G and G 2 are β 0 and 0, respectively. Then both rods are released from their respective stationary positions, and the equations of the hinged rod are as follows: ( ( J c ml2 ( 2 ml 2 cos (β β 2 β ( 2 ml2 cos (β β 2 Jc + 4 β ml2 2 ( ml 2 sin (β β 2 β 2 2 G (β 0 β + G 2 (β β 2 2 ml2 sin (β β 2 β 2 G =0, 2 (β β 2 (2 where m and l are the mass and length of rod P P 3 or P 2 P 3. J c is the moment inertia of P P 3 or P 2 P 3 relative to their respective centroids. Then, if we define 4 Whipping mechanism 4. Analyzed model To understand the rope-whipping phenomenon, the movements of a hinged rod are compared with those of a rigid rod, as shown in Fig. 4, in which P is the fixed end that is hinged on the ground, P 2 is the free end, and P 3 is the middle = ml2 G, k 2 = G 2 G, (3 Eq. (2 can be rewritten as ( cos (β β 2 2 cos (β β 2 3 ( 2 sin (β β 2 β β 0 = ( β β 2 +k 2 β + k 2 β 2 2 sin (β β 2 β 2 + k 2 (β β 2. (4

6 86 Y. Liu et al. Fig. 6 Velocity and x-andy-coordinates of P 2. Red dash line:timeof maximum velocity ( =.00, k 2 = 0.25, β 0 =.60, l = 0.2 m Fig. 5 Effect on ratio of maximum velocity r. (β 0 = π /2 a Effect of and k 2. b Effect of k 2 and β 0 Thus, the motion of the hinged rod is determined by, k 2, and β 0, while the velocity of P 2 is V = l β 2 + β cos (β β 2 β β 2. (5 For the rigid rod, the velocity of P 2 can be directly found as ( V 3 3 = β 0 l sin t. (6 2 8 The ratio of the maximum free-end velocity of the hinged rodtotherigidrodisr = V/V. This ratio r only depends on the parameters, k 2, and β 0. Figure 5a, 5b shows the effects of these three parameters on r. Obviously, r is independent of, and usually r > except for small regions where k 2 is very small. The maximum value r max =.509 occurs at k 2 = 0.25 and β 0 =.60 rad. For l = 0.20 m, during the response of the hinged rod, the velocity reaches its maximum Fig. 7 Three modes of response of hinged rod. a Mode I. b Mode II. c Model III of m/s at time t = 2.36 s, at position x = 0.04 m and y = m (Fig Modes of whipping process When the hinged rods with different k 2 and β 0 are released, the responses can be classified into three modes (see Fig. 7, where the arrows indicate the directions of the angular velocities. Mode I occurs under a relatively large k 2, that is, the hinged rod behaves like a rigid rod apart from a slight vibra-

7 How does a woodpecker work? An impact dynamics approach 87 Fig. 9 Mode II responses of β,β 2, β, β 2, β, β 2 of hinged rod. Red dash line: time of maximum velocity ( =.00, k 2 = 0.25, β 0 =.60 Fig. 8 Mode I responses of rigid rod and hinged rod ( =.00, k 2 = 2.00, β 0 = π /2, l = 0.2m. a β,β 2, β, β 2 of hinged rod and β, β of rigid rod. b Velocity and x- andy-coordinates of P 2 tion between two segments. Mode II occurs under a relatively small k 2 ; a peak and a valley exist in the responses of β and β 2, respectively. The maximum velocity ratio r is achieved by this mode. Mode III occurs if both k 2 and β 0 are very small, which will result in the two segments making contact with each other Mode I If k 2 is relatively large, such as k 2 = 2.00, the response of the hinged rod follows mode I. In this case, the maximum velocity ratio r =.20 occurs when β 0 = π /2. The rotation of the rod is depicted in Fig. 8: the time histories of β,β 2, β, β 2 are plotted in Fig. 8a, while the responses of the x- and y-coordinates and the velocity of P 2 are plotted in Fig. 8b. As k 2 increases, the vibration decreases, and thus the response of the hinged rod will be closer to that of the rigid rod; that is, r will tend to Mode II The ratio r reaches its maximum when k 2 = 0.25 and β 0 =.60 rad, while the response can be classified as mode II, as shown in Fig. 7b. The angle between two segments, i.e., β β 2, first decreases and then increases owing to the inertial force and spring G 2. At a certain time before the rod becomes straight again, the rod reaches a state where 0 <β β 2 < π /2, β < 0, and β 2 > 0, then the absolute values of β and β 2 rise rapidly, as shown in Fig. 9. This is because in this situation, the dominating terms in Eq. (4 are β 2 and β 2 2,so Eq. (4 can be simplified to ( β β 2 = sin (β β 2 4/9 /4 cos (β β 2 2 ( 6 β cos (β β 2 β 2 4 cos (β β 2 β β 2. (7 Based on Eq. (7, β is negative and β 2 is positive, so β decreases and β 2 increases. Since β < 0 and β 2 > 0, both β 2 and β 2 2 increase, which causes β to decrease and β 2 increase further. Therefore, the absolute values of angular velocities and the angular accelerations grow even faster until β 2 = β. Then sin(β β 2 becomes negative, so the angular acceleration is reversed and the angular velocities fall. The response of the rod in this mode corresponds to the whipping phenomenon. The square of the velocity of the free-end P 2 (Eq. (5 is derived as V 2 l 2 = 2 ( β β + β 2 β cos (β β 2 ( β β 2 + β β 2 2sin(β β 2 β β 2 ( β β 2. (8 According to Eq. (7, when β = β 2, β and β 2 are almost zero. Therefore, by Eq. (8, the free-end velocity will approach its maximum at this time. Because of this mech-

8 88 Y. Liu et al. Table 4 Free-end velocity ratios for various parameters. (β 0 = π /2 n = 2 n = 3 n = 4 n = 5 Fig. 0 Mode III responses of β,β 2, β, β 2, β, β 2 of hinged rod. Red dash line: time at which the two halves of the rod make contact ( =.00, k 2 = 0.00, β 0 = π /5 r t(s k k k k β (rad β 2 (rad β 3 (rad β 4 (rad β 5 (rad.6 5 Multihinge rod and other factors In this section, the responses of the rod with more hinges are discussed, while the effects of other factors, such as the damping effect, the position of the hinge, and the concentrated mass at the free end, are also considered. 5. Multihinge rod Assuming the hinges are located equidistantly, the equations of hinged rod are as follows: ( [J c + ml 2 n j + ] β j 4 Fig. Map of modes of responses ( =.00 anism, the maximum velocity of the free-end P 2 becomes considerably higher owing to the existence of the middle hinge Mode III If both k 2 and β 0 are very small, then the two segments of the rod may come into contact with each other, as shown in Fig. 7c. In this mode, β 2 decreases monotonically because spring G 2 cannot draw it back, as shown in Fig. 0. A map of the modes is shown in Fig.. The boundary between Modes I and II is at k 2., and the value will vary slightly for different β 0. Mode III only exists in a very small area in the bottom left corner of the map, so its boundary is not plotted. + 2 ml2 n i= j+ + j 2 ml2 i= + 2 ml2 n i=t+ j 2 ml2 i= β i cos ( β j β i [2 (n i + ] β i cos ( β i β j [2 (n j + ] β 2 i sin ( β j β i [2 (n i + ] β 2 i sin ( β i β j [2 (n j + ] ( ( G j β j β j + G j+ β j β j+ = 0. j =, 2,...n, (9 where n is the number of segments of the rod divided by the number of hinges. m, l, and J c are the mass, length, and moment inertia of each segment, respectively. β i is the angle of segment i relative to the horizontal line, and i = refers to the part that is hinged on the ground. G j is the modulus of the rotational stiffness of hinge j, and j = refers to the hinge at the ground. As in the earlier discussion, define = ml 2 /G

9 How does a woodpecker work? An impact dynamics approach 89 Fig. 2 Effects of parameters on ratio of maximum velocity r ( =, β 0 = π /2: a k 2 and m 0. b k 2 and h. c k 2 and c. d k 2 and c 2 and k j = G j /G.Att = 0, all β i and β i are zero. By solving Eq. (9, the velocity ratio r is still irrelevant to regardless of n. Assuming β 0 = π /2, the parameters corresponding to the maximum r are listed in Table 4. As is suggested, when the velocity of the free end reaches its maximum, the angles of all segments are close to each other, so the rod will become almost straight at that moment. Furthermore, r and n are found to be in approximately linear relation, as shown by Eq. (0. This explains why the woodpecker s long neck helps it to attain a high impact velocity: 5.2 Other factors Now we return to the rod with two segments. To investigate the influences of the damping effect, the position of the middle hinge, and the concentrated mass at the free end on the ratio r, more parameters are discussed. Define m 0 as the proportion of the concentrated mass at the free end in the whole mass of the rod. Define h = P P 2 /(2l, and by c and c 2 denote the damping coefficients at P and P 3 divided by G. Henceforth, Eq. (4 can be rewritten as: r = 0.325n (0 ( 8 3 (3 2h + 2m 0h h 2 ( 4 ( + m 0 h + m 0 h h ( h cos (β β 2 β 8 4 ( + m 0 h + m 0 h h ( h cos (β β 2 3 ( + 2m 0 h + m 0 h( h 2 β 2 = 4 ( + m 0 h + m 0 h h ( h sin (β β 2 β β 0 +k 2 β + k 2 β 2 c +c 2 β + c 2 β 2 4 ( + m 0 h + m 0 h h ( h sin (β β 2 β 2 +. ( k 2 (β β 2 + c 2 ( β β 2

10 90 Y. Liu et al. Taking β 0 = π /2 and =.00, the effects of m 0, h, c, and c 2 with different k 2 are calculated individually. As shown in Fig. 2a, r decreases when m 0 increases, and when m 0 gets larger, r is less than. In Fig. 2b, r is close to a radiating distribution, the center is k 2 = 0.20 and h = 0.73, and the maximum of r is.769, implying that the position of the hinge should be slightly farther away than the middle. Since c works both in the hinged rod and the rigid rod, and c 2 only works in the hinged rod, r in Fig. 2c is bigger than in Fig. 2d in most situations. A sharp boundary near the line k 2 = 0.8 can be observed in Fig. 2a, c, and d. This may be attributed to the different peaks at which the velocity of the free end reaches its maximum. 6 Conclusions In the present study, first, one cycle of a woodpecker s pecking process is simplified into a 3-DOF multi-rigid-segment model. The geometrical and mechanical parameters of the model are determined by the skeletal specimen and several videos of woodpeckers pecking. The effects of these parameters on the impact velocity are analyzed. It is found that the relative rotations among connecting rigid segments, which resemble whipping, are the main reason for the high impact velocity of the woodpecker s head. Then the mechanism of whipping is studied by analyzing a hinged-rod model. Depending on the parameters, the motions of this hinged rod are classified into three response modes, of which mode II exhibits the whipping process. Then the hinged-rod model is generalized into a multihinge configuration, for which the free-end velocity of the hinged rod is found to increase with the number of hinges. This explains the high free-end velocity achieved by whipping. Furthermore, the effects of other factors, such as damping and mass distribution, on the velocity are also discussed. Acknowledgments The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NSFC (Grant and the National Fundamental Research Program of China (Grant 20CB The third author (T.X. Yu gratefully acknowledges the support of the NSFC Key Project References. Gibson, L.: Woodpecker pecking: How woodpeckers avoid brain injury. J. Zool. 270, ( Wang, L., Cheung, J.T.-M., Pu, F., et al.: Why do woodpeckers resist head impact injury: a biomechanical investigation. PLoS One 6, e26490 (20 3. Yoon, S.-H., Park, S.: A mechanical analysis of woodpecker drumming and its application to shock-absorbing systems. Bioinspiration Biomim. 6, (20 4. Zhu, Z., Zhang, W., Wu, C.: Energy conversion in woodpecker on successive peckings and its role on anti-shock protection of brain. Sci. China: Technol. Sci. 57, ( Oda, J., Sakamoto, J., Sakano, K.: Mechanical evaluation of the skeletal structure and tissue of the woodpecker and its shock absorbing system. JSME Int. J., Ser. A. 49, ( Vincent, J., Sahinkaya, M., O Shea, W.: A woodpecker hammer. Proc. Inst. Mech. Eng., Part C. 22, 4 47 ( McNeill Alexander, R.: Tendon elasticity and muscle function. Comp. Biochem. Physiol., Part A: Mol. Integr. Physiol. 33, 00 0 ( Bennet-Clark, H., Lucey, E.: The jump of the flea: a study of the energetics and a model of the mechanism. J. Exp. Biol. 47, ( Kelley, D.E., Slasky, B.S., Janosky, J.: Skeletal muscle density: effects of obesity and non-insulin-dependent diabetes mellitus. Am. J. Clin. Nutr. 54, (99