DUDEK, DM; FULL, RJ: Leg Function in Running Insects: Resilience and Impedance of Legs Linked to a Body

Studies of locomotion have shown that many terrestrial runners have the dynamics of a spring-mass system. Our previous work using isolated, rigidly fixed legs has shown that the cockroach hind limb, with its vertically oriented joint axes, has the potential to act as a passive, exoskeletal leg spring in the sagittal plane. The hind limb, however, is not rigidly fixed during locomotion and has been calculated to absorb energy during the stride. To determine the effects the body-coxa joint may have on spring-like behavior, experiments were performed on intact, euthanized animals with a passive, freely rotating body-coxa joint. We used dynamic oscillations of the hind limb of a cockroach (Blaberus discoidalis) to measure mechanical impedance (the time-dependent resistance of a material to deformation) and resilience. The leg was oscillated in the dorso-ventral direction (orthogonal to the plane of rotation for the joints) and induced forces recorded. The resulting force-displacement relationships were non-linear and hysteretic (γ=0.15 for fixed limb, 0.25 for free limb). Induced forces and impedance were 25% (at small amplitudes) to 50% (large amplitudes) lower for a leg with a freely rotating coxa when compared to a rigidly fixed leg. Less energy can be stored in a free leg. Resilience of the limb ranged from 85% for a fixed limb to 65% for a free limb and was independent of oscillation frequency. A leg with a passive, freely rotating coxa represents a worst case scenario for spring-like behavior, but these data focus our attention on the extent of energy absorption of legs attached to a body. In sagittal plane spring-mass systems, managing energy with respect to perturbations may be as important as energy storage and return. Supported by ONR N00014-98-1-0669