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First published online January 3, 2006
Journal of Experimental Biology 209, 249-259 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01979

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Differential leg function in a sprawled-posture quadrupedal trotter

J. J. Chen¹, A. M. Peattie¹, K. Autumn² and R. J. Full^1,*

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

View larger version (24K): [in a new window]   Fig. 1. Horizontal plane GRFs in upright- and sprawled-posture trotters during a step when running at a constant average speed. (A) Upright-posture quadruped running with similar leg function. Fore- and hindlegs first (t1) both generate decelerating fore–aft forces (arrows) followed by an accelerating force later in the step (t3). No lateral GRFs are present. (B) Sprawled-posture hexapod running with differential leg function. Fore- and middle legs first (t1) both generate decelerating forces, while the hindleg generates an accelerating force (Full et al., 1991). All legs develop large lateral forces directed toward the midline. At midstep (t2) forelegs continue to generate decelerating forces and the hindleg an accelerating force. The middle leg only develops a lateral force. At the end of the step (t3), the foreleg generates a decelerating force. Hind- and middle legs both generate accelerating forces. (C) Hypothetical sprawled-posture quadruped running with similar leg function resulting from adding opposing lateral forces to the upright posture pattern in A. Fore- and hindlegs first (t1) both generate decelerating forces followed by an accelerating force later in the step (t3). Lateral GRFs were added assuming sprawled-posture animals tend to produce them. Horizontal forces sum to produce a clockwise yaw throughout the step. (D) Sprawled-posture quadruped running with differential leg function. GRFs approximate those measured in the present study on geckos. The foreleg first (t1) generates the majority of fore–aft decelerating force. At midstep (t2), fore- and hindlegs only generate lateral forces directed toward the midline. Later in the step (t3) hindlegs generate all of the fore–aft accelerating force. The major decelerating force by the foreleg (t1) and accelerating force by the hindleg (t3) are directed to the animal's COM, reducing yaw, and are aligned axially along the leg, reducing joint moments.

View larger version (17K): [in a new window]   Fig. 2. Stride frequency and stride length as a function of velocity. Solid circles represent stride frequency and open circles represent stride length (N=5). Both stride frequency and stride length increased as velocity increased. Stride frequency is represented the solid line and stride length by the broken regression line. For regression equations, see text.

View larger version (17K): [in a new window]   Fig. 3. Limb phase vs velocity. A phase of 1 indicates that limbs hit the ground synchronously; a phase of 0.5 indicates that limbs are in antiphase. Diagonal limbs were in phase whereas ipsilateral (left and right) limbs and contralateral (same side fore- and hind-) limbs were in antiphase. (Ipsilateral and contralateral limbs=0.93+0.01v; r2=0.001. Diagonal limbs=0.47+0.14v; r2=0.55).

View larger version (22K): [in a new window]   Fig. 4. Gait, lateral bending, force, velocity and energy of the COM over one stride (two steps) of a 2.3 g (0.023 N)Hemidactylus garnotii running on the level at 0.50 m s-1. (A) Tracing of gecko running where a solid black foot represents a foot in contact with the substrate. Minimum lateral trunk bending occurred at midstep. (B) Footfall patterns indicated a trotting gait where a fore- and hindleg couplet hit the ground simultaneously followed by the opposite fore- and hindleg couplet. Solid areas in the bars represent toes down whereas striped bars show the time it takes to attach and detach feet. (C) Whole body GRFs of one stride from the force platform. Red lines, normal forces; blue lines, fore–aft forces. Normal forces fluctuate around body weight. A brief aerial phase was observed midstride. Fore–aft forces decelerate and accelerate the COM in each step similar to that of a forward-bouncing, spring-loaded, inverted pendulum. (D) Integration of fore–aft force yields fore–aft velocity of the COM. Velocity dropped to a minimum during midstep and was at a maximum during midstride. Despite the fluctuating velocity, the gecko maintained a constant average velocity of ±10%. (E) Fore–aft kinetic energy and gravitational potential energy of the COM fluctuated in phase. (F) Total energy of COM.

View larger version (15K): [in a new window]   Fig. 5. 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 peaked at approximately twice body weight (broken line). (B) Peak fore–aft forces decelerated and then accelerated the COM at each step with forces about 40% of the normal forces. (C) Lateral force accelerated the COM to the right followed by an acceleration to the left.

View larger version (9K): [in a new window]   Fig. 6. Phase shift between peak gravitation potential energy and fore–aft kinetic energy vs velocity. A phase shift of zero means the fluctuations are in phase, whereas phase shifts of 0.5 shows that fluctuations are in antiphase.

View larger version (20K): [in a new window]   Fig. 7. Single leg peak GRFs of one step measured when only one foot was on the force platform. Red lines and bars represent normal forces, whereas blue lines and bars represent fore–aft forces. Values are means ± s.e.m. (A) Forefoot GRF tracing from a single individual. (B) Hindfoot GRF tracing from a single individual. (C) Mean peak forefoot GRF magnitudes and phases (N=10). (D) Mean peak hindfoot GRF magnitudes and phases (N=14). Fore- and hindfeet both produce positive normal forces, showing geckos did not exert any detachment force.

View larger version (25K): [in a new window]   Fig. 8. Single leg GRFs compared with the hypothesized templates for whole body dynamics. (A) Lateral or sagittal view. Individual leg GRFs represented by red arrows at the beginning of the step (t1) and toward its end (t3). Below is the corresponding spring-loaded inverted pendulum representing the COM dynamics. (B) Anterior view. Peak forces are represented by red vectors at midstep (t2). To the right is a simple mass on top of a spring that represents the summed action of both legs as the animal's bounces down and to its left. (C) Dorsal view. Individual leg GRFs represented by red arrows at the beginning of the step (t1) and toward its end (t3). To the right is the corresponding lateral spring representing the COM dynamics.