Passive mechanical properties of legs from running insects

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Abstract
While the dynamics of running arthropods have been modeled as a spring-mass system, no such structures have been discovered that store and return energy during bouncing. The hindleg of the cockroach Blaberus discoidalis is a good candidate for a passive, vertical leg spring because its vertically oriented joint axes of rotation limit the possibility of active movements and contributions of muscle properties. We oscillated passive legs while measuring force to determine the leg's dynamic, mechanical properties. The relative dimensionless stiffness of an individual cockroach leg was equal to that estimated for a single leg of a biped or quadruped. Leg resilience ranged from 60 to 75%, affording the possibility that the leg could function as a spring to store and return the mechanical energy required to lift and accelerate the center of mass. Because hysteresis was independent of oscillation frequency, we rejected the use of a Voigt model – a simple spring in parallel with a viscous damper. A hysteretic damping model fit the cockroach leg force–displacement data over a wide range of frequencies and displacement using just two parameters. Rather than simply acting as a spring to minimize energy, we hypothesize that legs must manage both energy storage and absorption for rapid running to be most effective.