DUDEK, D.M.; FULL, R.J.; Univ. of California, Berkeley: Mechanical Properties of the Support Tripod in Running Insects

Terrestrial runners produce ground reaction forces that can be modeled as a spring-mass system. Two beneficial consequences of bouncing while running include: 1) the ability to use springs to store and return elastic strain energy and 2) passive self-stabilization resulting from a well tuned musculo-skeletal system. Running cockroaches, Blaberus discoidalis, have been modeled as a spring-mass system in both the horizontal and sagittal planes. They self-stabilize in the horizontal plane (Kubow and Full, 1999) and recover from large lateral perturbations without a step transition (Jindrich and Full, 2002). It remains to be seen whether preflexes of running cockroaches are tuned in the sagittal plane to simplify control of locomotion via dynamic self-stabilization. We determined mechanical impedance and damping ratio (&zeta) of the support tripod of running cockroaches by tethering them above a Styrofoam ball floating on an air bearing. A servomotor imposed sinusoidal force oscillations in the sagittal plane and recorded the induced displacements. Impedance varied with the magnitude of the imposed force and was 2-4 times that of a single, ablated limb. The dimensionless stiffness of 14.03�1.56 was close to the 16.7 estimated from force plate data (Blickhan and Full,1993). The support tripod is underdamped (&zeta = 0.63�0.15) during low frequency perturbations corresponding to stride frequencies used in running. An underdamped tripod can store and return energy. High frequency perturbations were overdamped (&zeta = 1.59�0.57). Despite reducing efficiency, damping improves dynamic stability and simplifies control by removing unwanted energy to achieve quick settle times with little overshoot. Supported by ONR N00014-98-1-0669