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First published online January 3, 2006
Journal of Experimental Biology 209, 260-272 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01980
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Dynamics of geckos running vertically

K. Autumn1, S. T. Hsieh2,*, D. M. Dudek2, J. Chen2, C. Chitaphan2 and R. J. Full2,{dagger}

1 Department of Biology, Lewis & Clark College, Portland, OR 97219-7899, USA
2 Department of Integrative Biology, University of California, Berkeley, CA 94720-3140, USA



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  		Fig. 1. Theoretical comparison of dynamics of running on level ground (A) vs climbing using two different models. In the first model (B), legs produce deceleratory fore–aft forces, F–x, as an unavoidable consequence of foot attachment. Thus larger acceleratory forces, F+x, are required to counteract the combined deceleration of the legs and gravity g. In the second model (C), legs do not produce deceleratory forces. Thus, acceleratory forces are reduced since only gravity decelerates the animal, and total mechanical energy (Etot) required to climb approaches potential energy (EP).

 


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  		Fig. 2. (A) Force platform used to measure dynamics of climbing geckos Hemidactylus garnotii. (B) Axis conventions used in this study. Positive fore–aft forces (+x; blue) correspond to wall reaction forces that would accelerate a mass upwards. The force of gravity acts in the –x direction. Positive normal forces (+y; red) correspond to wall reaction forces that would accelerate a mass away from the force plate, whereas negative normal forces (–y) correspond to wall reaction forces that would accelerate a mass towards the force plate. The z axis was the lateral dimension and corresponds to forces directed to the animals right or left. Positive lateral forces (+z; green) correspond to wall reaction forces that would accelerate a mass to the animal's right, whereas negative lateral forces (–z) correspond to wall reaction forces that would accelerate a mass to the animal's left.

 


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  		Fig. 3. Gait, force, velocity and energy of the COM vs time during one stride of a 3.6 g (0.035 N) gecko Hemidactylus garnotii climbing vertically at 0.44 m s-1. (A) Tracing of gecko climbing. Yellow circles represent foot contact. (B) Gait pattern and timing of attachment and release for each foot. The initial striped portion of each box represents the time required for the toe pads to attach to the force plate. The filled portion indicates when toe pads were in contact with the force plate, and the second striped portion represents the time for the toes to detach before the foot was lifted from the force plate. (C) Fore–aft, normal and lateral forces of the COM. The horizontal broken line represents weight (35 mN). Force production decreased nearly to zero at mid-stride, despite the fact that all four feet were in contact with the force plate. (D) Fore–aft velocity calculated by integration of the force recording minus gravity. Velocity attained a minimum at the beginning of each step as forces decreased to zero, indicative of a period of ballistic movement. (E) Fore–aft kinetic, normal kinetic, lateral kinetic energy (EK) and gravitational potential energy (EP) fluctuations of the COM. (F) Total mechanical energy of the COM obtained by summation of the fore–aft kinetic, normal kinetic, lateral kinetic and gravitational potential energy components.

 


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  		Fig. 4. Whole body peak GRF magnitudes and phases. Values are means ± 1 s.e.m. One phase is equal to one complete stride or two steps. (A) Normal force showed two maxima, but was highly variable, representing the cancellation of individual leg forces. (B) Fore–aft force peaked once per step with magnitudes of approximately twice body weight (broken line). (C) Lateral force accelerated the COM to the left followed by an acceleration to the right. Two maxima per step were observed.

 


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  		Fig. 5. Mass-specific mechanical power vs velocity in Hemidactylus garnotii climbing vertically and running on the level. Solid line (circles) is the linear least-squares regression (Power=0.9+9.9v, where v is velocity in m s-1; r2=0.83) for climbing. The broken line represents the product of gravity and velocity, the minimum mechanical power production possible. The solid line (triangles) represents the least-squares linear regression (Power=0.3+1.9v; r2=0.48) of geckos running on level ground (Chen et al., 2006Go).

 


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  		Fig. 6. Mean peak GRFs of single legs in geckos climbing (D–F) and running on level ground (A–C). (A) On a level, normal GRFs were always positive. (B) Geckos running over level ground used the forelegs to produce only deceleratory forces, while hindlegs first produced deceleratory forces during the first part of each step, and then produce acceleratory forces during the second part of each step. (C) All four legs pushed laterally away from the midline of the body such that the left legs produced forces that pushed the gecko to the right, while the right legs produced forces that pushed the gecko to the left. (D) In climbing geckos, forelegs produced forces that pushed the gecko away from the vertical surface, while hindlegs produced forces that pulled the gecko toward the vertical surface. (E) Climbing geckos produced positive fore–aft forces that propelled the gecko upwards. (F) During climbing, all four legs pulled laterally towards the midline of the body such that the left legs produced forces that pulled the gecko to the left, while the right legs produced forces that pulled the gecko to the right. The directions of lateral GRFs during climbing were opposite to those produced during level running.

 


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  		Fig. 7. Direction of single-leg round reaction forces in geckos climbing vertically (B–D) and (A) running on level ground. (A) Single leg GRFs during level running. Circle with a dot in the center represents a vector that points toward the reader. t1 represents the time in the first half-step when the forces shown are generated. t3 represents the time in the second half-step. (B) Single leg GRFs during climbing. Circle with an x in the center represents a vector that points away from the reader. t2 represents the time at mid-step when the forces shown are generated. (C) Lateral view of normal GRFs during climbing. (D) Lateral view of overturning (Mo) and stabilizing (Ms) impulse moments during climbing where Fleg is the mean normal force generated by the forelegs over a stride period ({Delta}t), R is the stabilizing moment arm from the foreleg to the hindleg pivot, the integral of Fleg from 0 to {Delta}t represents the foreleg impulse, g is acceleration due to gravity, Mb equals body mass, and r is the distance of the COM to the wall.

 


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  		Fig. 8. (A) MechoGecko and (B) BullGecko, small (4 cm long), climbing robots designed by iRobot Corp. The designs of the feet and treads of the robots were inspired biologically by the toe-peeling mechanism of gecko toes. MechoGecko used pressure sensitive adhesive (PSA) feet. The spherical foot shape promoted peeling to reduce pull-off force. MechoGecko's trispoke legs caused significant velocity fluctuations during climbing. BullGecko used PSA tracks to peel as it climbed. The track design allowed BullGecko to exert a constant fore–aft force on the COM.

 

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© The Company of Biologists Ltd 2006