Locomotion behavior and dynamics of geckos freely moving on the ceiling

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Bionic Engineering October 2010 Vol.55 No.29: 3356–3362

doi: 10.1007/s11434-010-3079-6

Locomotion behavior and dynamics of geckos freely moving on the ceiling

WANG ZhouYi1,2, WANG JinTong1,2, JI AiHong1 & DAI ZhenDong1*

1 Institute of Bio-inspired Structure and Surface Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2 College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received May 26, 2009; accepted December 23, 2009

To understand the mechanical interactions when geckos move on ceiling and to obtain an inspiration on the controlling strategy of gecko-like robot, we measured the ceiling reaction force (CRF) of freely moving geckos on ceiling substrate by a 3-dimensional force measuring array and simultaneously recorded the locomotion behaviors by a high speed camera. CRF and the preload force (FP) generated by the geckos were obtained and the functions and the differences between forces generated by fore- and hind- feet were discussed. The results showed that the speed of gecko moving on the ceiling was 0.17–0.48 m/s, all of the fore- and hind-legs pulled toward the body center. When geckos attached on the ceiling incipiently, the feet generated a very small incipient FP and this fine FP could bring about enough adhesive normal force and tangential force to make the gecko moving on ceiling safely .The FP of the fore-feet is larger than that of the hind-feet. The lateral CRF of the fore-feet is almost the same as that of the hind-feet’s. The fore-aft CRF generated by the fore-feet directed to the motion direction and drove their locomotion, but the force generated by the hind-feet directed against the motion direction. The normal CRF of fore- and hind-feet accounted for 73.4% and 60.6% of the body weight respectively. Measurements show that the fore-aft CRF is obviously lager than the lateral and normal CRF and plays a major role in promoting the fore-feet, while the hind-feet of the main role are to provide a smooth movement. The results indicate that due to the differences of the locomotion function of each foot between different surfaces, the gecko can freely move on ceiling surfaces, which inspires the structure designing, gait planning and control developing for gecko-like robot.

3-dimensional locomotion reaction force, dynamics, ceiling, 3-dimensional force measuring array, gecko

Citation: Wang Z Y, Wang J T, Ji A H, et al. Locomotion behavior and dynamics of geckos freely moving on the ceiling. Chinese Sci Bull, 2010, 55: 3356–3362, doi: 10.1007/s11434-010-3079-6

Robotics is one of the major application areas of modern bionics [1]. Robots, which are used in un-structured cir-cumstance, especially the robots with TDOF (Three Dimen-sional-terrains Obstacle Free–such as running on floors, climbing on walls and moving on ceilings) locomotion abil-ity are the most challenged high technology and become a mark of the level of technology and the comprehensive na-tional strength. To learn from and obtain the inspiration from nature has become a valuable means in developing new robots. Scientists would like to discover how animals have done in TDOF moving and what mechanism and key technique could be transferred from nature to technology to *Corresponding author (email: [email protected])

develop the TDOF robots. During the past years, Autumn, Bharat, Bergmann have carried out a lot of researches on the structure and micro-structure of gecko feet [2–4], mechanisms of adhesion [3,5] and adhesive strength [4,6–8]. Damme et al. focused on the locomotion kinematics of gecko moving on the horizontal and vertical surfaces [9–14]; Losos et al. studied the morphology [15–17]. On the other hand, the artificial seta array was developed by micro-mold injection [18, 19], electron-beam etching [20], and carbon nano-tubes [21]. However, we know little about the loco-motion behaviors and the interaction force between the feet and ceiling when geckos move on up-side down surface.

Here we report the experimental results on the locomo-tion behavior and dynamics when geckos freely move on

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the ceilings by a locomotion behaviors and reaction force measuring system (LBRFMS) [22,23] which was developed by the IBSS (Institute of Bio-inspired Structure and Surface Engineering) of NUAA (Nanjing University of Aeronautics and Astronautics). We are looking forward to being inspired by the research in order to develop better gecko-like robots.

1 Materials and methods

(i) Animal. Five geckos from Guangxi Zhuangzu Zizhiqu, China, were used in this experiment (body weight: 64.5±2.4 g, body length: 136.6±12.4 mm, mean ± S.D.). The geckos were hosted in two cages which were connected by an aisle to train the gecko to move through the aisle of LBRFMS and feed with mealworms, cricket, vitamin and water. They were kept under natural light cycle, the temperature at 25±2°C, humidity at 60%–70%. To make the description easy, we defined each foot as LF, LH, RF and RH (Figure 1).

(ii) Experiment setup. The facility is made up of a sen-sor array as the bottom of an aisle to measure the reaction force between the foot and the substrate (sensor), which was covered with transparence Plexiglas to limit the motion of the gecko straightly on the sensor array, and two mirrors with 45° to the sensor array plane to record the 3-dimensional locomotion behavior of the gecko motion. The sensor array was made up of 16 (2×8) sensors, each sensor could meas-ure 3-dimensional interaction force. The end of the aisle is a dark plastic box to lure the gecko to move into it (Figure 2(a)).

(iii) Force measurements and acquisitions. The 3-dimen- sional reaction force (Figure 2(b)), namely, lateral, fore-aft and normal forces, when geckos freely moved along the

Figure 1 Gekko Gecko photo.

ceiling, were measured and collected by the experimental facility described above. The reaction forces were measured by the 3-dimensional sensors with resolution to micro- Newton (Figure 2(c)), the strains were regulated by a signal processing system (SCXI-1520 NI, USA), and digitized by an acquisition card (PCI-6052E, NI, USA). The collected data were filtered at a cut-off frequency of 100 Hz. The software of measuring system was developed by our labo-ratory on LabVIEW platform.

(iv) Kinematics observation. The locomotion behavior was recorded by a high speed camera at 215 fps (Mikrotron, MC1311, Germany) and was synchronized with reaction force by light a LED in the view of the camera. Around 2000 images were obtained for each trial and the locomo-

Figure 2 (a) Force platform used to measure dynamics of moving Gekko Gecko on the ceiling; (b) Directional definition of CRFs in this research; (c) Sin-gle three-dimensional sensor’s construction; (d) Transformation between sensor’s coordinate and body’s coordinate; (e) Relationship with CRFs, driving angle and support angle.

3358 WANG ZhouYi, et al. Chinese Sci Bull October (2010) Vol.55 No.29

tion behavior was present by the two points on the gecko’s vertebrae (Figure 2(a)), the points were read out frame by frame and were used to calculate the transient deflection angle ϕ and mean speed during the locomotion.

(v) Data regulation. When geckos moved along the aisle, the relative position between the geckos and sensors was always varying, so it is needed to transfer the force from sensor’s coordinate system (X1 Y1 Z1) to body’s coor-dinate system (X2 Y2 Z2). The force measured by sensor (FX FY FZ) could be converted into body coordinate system (FL FF FN) by eq. (1):

cos sin 0sin cos 0

0 0 1

L X

F Y

N Z

F FF FF F

ϕ ϕϕ ϕ

−⎡ ⎤ ⎡ ⎤⎛ ⎞⎢ ⎥ ⎜ ⎟ ⎢ ⎥=⎢ ⎥ ⎜ ⎟ ⎢ ⎥

⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠⎣ ⎦ ⎣ ⎦

, (1)

where ϕ is the deflection angle (Figure 2(d))．The driving angle α and the support angle β are calculated by

2 2

arctan( / ) (0,180 ).

arctan( / ) ( 90 ,90 )L F

N L F

F F

F F F

α α

β β

= ∈ °⎧⎪⎨

= + ∈ − ° °⎪⎩ (2)

(vi) Data processing. The valid contact of the gecko foot to the sensor, that is all parts of a foot contacted with one sensor, selected from the high speed recording, and the correspondent reaction forces were selected out, the maxi-mum preload force FP during the incipient contact phase, the maximum lateral force FL, fore-aft force FF, normal

force FN, shear force FS(2 2

S L FF F F= + )and reaction force

FT ( 2 2 2T L F NF F F F= + + ) were selected out. The driving

angle α and the support angle β are calculated by eq. (2) at the movement of maximum shear force FS and reaction force FT respectively.

(vii) Statistics. Animals’ reaction force might be influ-enced by many factors, such as body weight, stringent state, locomotion behavior and environmental condition, so the

statistical analysis must be introduced to reveal the role of locomotion mechanics. We compared the difference of the data between groups by t-test and set critical P value as 0.05 (SPSS Inc., Chicago, USA), and all of the tested data were presented by means ± standard deviation (mean ± S.D.).

2 Results

2.1 Locomotion behaviors and gait

Geckos moved on ceiling using the tripod gait at the speed from 0.17 to 0.48 m/s (Figure 3(a)) and stride frequencies 3.4±1.3 Hz (N=18). Unexpectedly, the speed does not relate to the stride frequencies (ANOVA, F=22.49, df =1,13, P=0.051), but relate to the stride length (Stride length=0.068+0.082V; R2 =0.59; P<0.001) . The average of the duty factor of all four limbs is 0.84±0.09 and is not ef-fected by speed (P=0.302>0.05). Geckos extend or crimp their toes (when peeling from the terminal end) to attach on or detach from the substrate when geckos make the trans-formation from stance phase to swing phase. The mean at-taching time is 19±3 ms (N=18), which is 4.3%±3.2% of the mean stride time and 5.4%±2.6% of the mean stance time. The time needed for attaching is not significantly affected by speed (ANOVA, F=0.518, df =1, 17, P=0.481). The mean detaching time is 31±13 ms (N=18), which is 6.4%±4% of the mean stride time and 8%±3.2% of the mean stance time. This time is not significantly affected by speed (ANOVA, F=3.782, df =1, 17, P=0.069) (Figure 3(b)).

2.2 Ceiling reaction force generated by each foot

The groups compared by t-test show no significant differ-ence (P>0.05) between the reaction force generated by the left and right feet, which may result from the fact of sym-metry body structure of the gecko. When geckos moving on ceiling, the maximum of the preload force is FP; the maxi-mum forces in the three directions are FL ,FF ,FN; the driving

Figure 3 The gait vs. time during one stride of a 63.0 g gekko gecko moving on the ceiling. (a) Tracing of gecko moving, circles represent foot contact; (b) Gait pattern and timing of attachment and release for each foot.

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angle α and the support anger β, as shown in Table 1. (1) Lateral force FL. In the lateral direction each foot

pulled towards the midline of the body such that the left feet generated a lateral force to the right while the right feet generated a lateral force to the left because of the presence of gravity. Lateral forces were 1.2 times the normal force. The lateral force of the fore- and hind-feet were not signifi-cantly affected by speed (ANOVA, fore-foot: R2=0.051, F=0.963, d f =1, 18, P=0.339; hind-foot: R2=0.051, F=1.027, d f =1, 19, P=0.324).

(2) Fore-aft force FF. The fore-aft force of the fore-feet directs to the same direction of locomotion, and drives the locomotion. Correspondingly, the fore-aft force of the hind- feet direct to the opposite direction of the locomotion. The fore-aft force’s absolute values of the fore-feet were greater than the hind-feet and were 1.5 times the normal force. The fore-aft force of each foot was not significantly affected by speed (ANOVA, fore-foot: R2=0.088, F=1.731, df =1, 18, P=0.205; hind-foot: R2=0.159, F=3.585, df =1,19, P=0.074).

(3) Normal force FN. When geckos move on ceiling, the sole seta and ceiling surfaces contact with each other completely because of the fine preload force FP at incipient contact phase, which generated sufficient adhesion to bal-ance the gravity. The preload force FP of the fore-feet was significantly affected by speed (ANOVA, R2=0.338, F=9.188, df =1, 19, P=0.007), and FP of the hind-feet is less than that of the fore-feet, which was not significantly af-fected by speed (ANOVA, R2=0.167, F=3.811, df =1, 18, P=0.066). The normal forces maximum of fore- and hind-feet were the largest at the middle of stance time, they were 73.4% and 60.6% of the body weight respectively. The stance feet provided the necessary adhesion to ensure the stability and safety. The normal force of the fore-feet was significantly affected by velocity (ANOVA, R2=0.285, F=7.186, df =1, 18, P=0.015), but the hind-feet were not significantly affected by speed (ANOVA, R2=0.004, F=0.074, df =1, 19, P=0.789).

(4) Driving angle α. The driving angle of the fore-feet

is basicly stable after incipient phase, namely, the direction of the foot’s shear force remains the same. The driving an-gle of each foot was not significantly affected by speed (ANOVA, fore-foot: R2=0.021, F=0.379, df =1, 18, P=0.546; hind-foot: R2=0.011, F=0.211, df =1, 19, P=0.652). However, the driving angle of the hind-feet had larger fluctuation in locomotion.

(5) Support angle β. The support angle’s change range of fore- and hind-feet were very little at stable phase, their mean is less than 30°. The support angle of fore-foot was significantly affected by velocity (ANOVA, R2=0.036, F=0.663, df =1, 18, P=0.426), but the support angle of hind-foot was not significantly affected by speed (ANOVA, R2=0.176, F=4.050, df =1, 18, P=0.059).

2.3 Single foot impulse

The impulse Ii of the three components of the reaction forces and gravity was calculated by integrating the reaction force (Fi) during the stance phase (ts). There were no sig-nificant differences among the mean impulse in the lateral direction for the four limbs, which resulted in very little acceleration of the mass center of a gecko in lateral direc-tion. The impulses caused by the fore-aft force and normal force of the fore-feet were larger than the correspondent value of the hind-feet. For tripod gait locomotion, the total normal impulses generated by the three feet under stance phase approximately equal to that by gravity, which made the mass center of the gecko do not change in the normal direction during the stance phase (Table 2).

0d , , , .

st

i i isI Ft F t i L F N G= = =∫ (3)

3 Discussion

3.1 Differential foot function

Measured results, when geckos moved on the ceiling sur-

Table 1 Mean maximum CRFs, driving angle and support angle of single foot in geckos moving on ceiling

Foot N Lateral force Fl (mN) Fore-aft force FF (mN)

LF 10 –522.6 ±107.0 818.9±202.4

RF 10 434.5 ±128.3 478.5±123.5, P=0.113

655.9±163.3 737.4±197.6, P=0.063

LH 11 –448.6 ±164.9 –610.8±199.6

RH 10 565.5 ±168.4 504.3±173.0, P=0.125

–588.3±220.3 –600.1±204.7, P=0.808

Foot N Normal force FN (mN)

LF 10 221.8 ±86.7 –509.7±111.1

RF 10 170.6 ±80.0 191.6± 85.3, P=0.244

–430.7±106.3 –470.2±113.3, P=0.122

LH 11 91.93 ±85.5 –380.2±100.4

RH 10 109.0 ±52.0 100.1±70.3, P=0.142

–354.7±89.4 –388.1± 93.8, P=0.549

Foot N Driving angle α (°) Support angle β (°)

LF RF LH RH

10 10 11 10

30.98 27.36

145.21 137.67

±16.49 ±13.19 ±29.64 ±23.36

29.17±14.65, P=0.595 141.61±26.41, P=0.526

–28.27–27.09–22.49–27.08

±5.36 ±9.34 ±8.99 ±10.44

–27.68–24.68

±7.43, P=0.734 ± 9.75, P=0.293

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Table 2 Single foot impulse for stance period

Foot N Lateral impulse (mN

s) Fore-aft impulse

(mN s) Normal impulse

(mN s) Gravity impulse

(mN s) Ratio of normal impulse to gravity

impulse (%) LF LH RF RH

10 11 10 10

–167.24±79.16 –85.62±48.65 137.06±87.18 113.13±37.81

196.46–80.68164.04

–144.42

±100.61 ±47.55 ±99.04 ±69.88

–154.23±62.40 –65.30±37.42

–112.18±67.13 –76.92±44.83

351.13±153.94 259.51±113.46 352.90±173.29 278.38±147.31

44.9±6.4 28.2±11.1 33.5±13.1 28.9±12.0

face, show that the fore-aft force generated by the gecko’s fore-feet takes the same direction of the movement, but that by the hind-feet is the opposite. The former is 30% larger than the force generated by the hind-feet. The fore-feet drive the motion of the gecko but the reversed direction of the fore-aft and lateral force makes the gecko hold on the up-side-down surface. All feet pulled towards the center of the body mass because of gravity in locomotion, thus the lateral CRF of each foot pushed away the midline of the body, meanwhile in fore-aft direction, the fore-aft force directions of fore- and hind-feet were the opposite. In a word, the shear force of each foot pushed away the body, which made the center of the body mass move close to the ceiling surface, and maintained the motion position.

The most important perturbation in locomotion was the shock brought by the change of the velocity of the center mass, which was induced by alternation between the foot’s stance period and swing period, and this shock was greatly relieved by the negative fore-aft force of the hind-feet. Ac-celeration and deceleration of the gecko locomotion were controlled by the difference value between fore-aft forces of the fore- and the hind-feet. The hind-feet was important for balancing locomotion shock. This locomotion method driven by the fore-feet and balanced by the hind-feet may slacks down the effect of single foot, while improves

safety of whole moving (Figure 4(a) and (c)). When geckos moved on ceiling, the body weight was

balanced by the normal CRF of the stance foot. The maxi-mum normal CRF of the fore- and hind-feet accounted for 73.4% and 60.6% of the body weight respectively. The gecko should firstly balance its gravity to guarantee the safety of the locomotion, and then the energy consumption is considered. Also, the normal CRF of the fore-feet was used to balance overturning torque in locomotion (Figure 4(b) and (c)).

The anatomy of the gecko’s nerve system showed that the cervical and lumbar parts of gecko’s spinal cord were obviously intumescent and the central nerve tract dominat-ing the locomotion of the fore-feet was thicker than that of the hind-feet [25–27], thus the flexibility of the fore-feet may be better than that of the hind-feet. Some directional reaction force of the fore-feet was significantly affected by speed; on the contrary, the hind-feet’s almost was not. Geckos may pay attention to the active control of the fore- feet; the hind-feet are mainly for the passive balance, which is in a subordinate position.

3.2 Lateral and fore-aft CRF

The direction of the lateral and fore-aft CRF generated

Figure 4 A phase diagram of feet CRFs on ceiling. (a) A phase diagram of lateral to fore-aft components of CRFs; (b) A phase diagram of shear to normal components of CRFs; (c) Single foot CRFs during moving on ceiling. ⊗ represents a vector that points away from the reader.

WANG ZhouYi, et al. Chinese Sci Bull October (2010) Vol.55 No.29 3361

when steadily moving on the ceiling was opposite to the corresponding force generated when running on the ground. Geckos running on the ground push away from the center of the body mass. The formalization of the leg spring template well explained how lateral and fore-aft forces were com-bined in order to increase the stability and controllability in locomotion [13]. However, for geckos moving on the ceil-ing, safety is primary. That is, geckos must adhere to the ceiling stably to guarantee safety.

Animals can cling to objects using friction if they can grasp by producing an adduction force at a sufficient central angle [12, 28]. Adhesion in nature [28–30] requires both the legs and the claws to pull toward the midline [28, 31]. The results show that when moving on the ceiling, geckos’ feet pull toward the midline, and all lateral and fore-aft CRF push away the center of the body mass (Figure 4(a) and (c)). This action not only helps the foot to interlock but also the seta to adhere, generating the larger shear force.

3.3 Foot adhesion

Gecko’s foot palm is bare, each foot possess millions of setae on the toes. The main adhesive forces as well as the tangential force are supported by the setae contacting with the movement surface. The seta’s adhering to the substrate results in attachment, and it separates from the substrate which results in detachment. The process of geckos attach-ing to moving surface could be divided into the following parts: first, sole contact to the substrate; second, the toes adducted and preload the seta array. During the gradual contact; then the toes achieve adhesion. Gecko foot’s reac-tion force curve clearly reflects the preload of the feet when geckos moved on the ceiling. When geckos incipiently con-tact to the ceiling, the preload force was measured during time TP, then the feet attach to the movement surface stead-ily, providing the necessary reaction force for locomotion. The reaction force curve could not reflect the detachment process clearly (Figure 5(a)).

When geckos move on the ceiling, the pre-stress of the fore-feet is obviously higher than the hind-feet, and the contact time of the fore-feet is less than that of the hind-feet. It implies that the CRF of the fore-feet is lager than that of the hind-feet when the feet attached on the moving surface, obviously the efficiency of the fore-feet is higher than that of the hind-feet; the pre-stress has a good linear relationship with the speed of the fore-feet. It suggests that geckos con-trol the fore-feet more carefully than the hind-feet, which also consistent with the previous suppose that the fore-feet play a more significant role than the hind-feet.

The results show that there is no significant difference in the incipient phase TP between the fore-feet and the hind-feet when geckos moving on the ceiling surface; and there is a good exponential relationship between the veloc-ity and the TP of the four feet (v=25.15×TP

–0.85, R2=0.588). It suggests that there is a close relationship between TP and

Figure 5 (a) Reaction force vs time in geckos moving on the ceiling TP is incipient contact time; (b) Velocity vs incipient contact time in geckos moving on the ceiling.

the speed. Accompanied with the reduction of TP, the speed increased, but the increase is limited. This is consistent with the assumptions of Autumn et al. [12] (Figure 5(b)).

This work was supported by the National High Technology Research and Development Program of China (2007AA04Z201) and National Natural Science Foundation of China (60535020, 50635030, 30770285 and 30700068).

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