Meijer, K*; Libby, T.M.; Full, R.J.: Passive stability provided by the musculo-skeletal properties of an insect leg.

Cockroaches have an amazing ability to run over rough terrain. It has been hypothesized that their ability to perform stable locomotion in unstructured environments is facilitated by the mechanical properties of their muscles and exoskeleton. To investigate the passive stabilizing properties of individual legs, we measured the mechanical impedance of the metathoracic limb of tethered cockroaches (Blaberus discoidalis). The hind limb of the cockroach was attached to a muscle lever system with a stainless steel rod. Sinusoidal length oscillations (2-25 Hz, 1-5 mm) were imposed on the hind limb in the plane of leg movement when muscles were relaxed. The resulting angular changes of the coxa-femur and femur-tibia joints amounted to 10-40 % of their natural range of motion. We found that the peak leg forces in response to the length oscillations ranged from 2.8 – 8 mN, which is within the range reported for single leg forces of freely running cockroaches (Full et al., 1991). Analysis of the displacement- force data indicated that the leg behaves as a spring-damper system. The magnitude of impedance (Dforce/Dlength) ranged from 5-15 mN/mm and showed no effect of oscillation frequency. These values are substantially lower than those found for out of plane oscillations. It suggests that in a relaxed animal the response is slower for planar vs. non-planar perturbations. The tangent of the phase angle increased with frequency from 0.2 – 0.9, indicating that a significant part of the energy introduced by perturbations is dissipated in the leg. Our next step is to use a model of the cockroach leg to determine the muscle and exoskeleton contributions to the measured leg impedance. Supported by ONR N00014-98-1-0669.