S1-3.2 Jan. 5 The Relevance of Resonant Frequency in Running Cockroaches Modeled by a Spring-loaded, Inverted Pendulum DUDEK, DM*; SRINIVASAN, M; ROGALE, K; KUKILLAYA, R; HOLMES, P; FULL, RJ; Univ. of British Columbia; Princeton Univ.; Princeton Univ.; Princeton Univ.; Princeton Univ.; Univ. of California, Berkeley firstname.lastname@example.org
An array of morphologically diverse runners, from insects to large mammals, display the dynamics of a spring-loaded inverted pendulum (SLIP) with the same dimensionless leg stiffness (Blickhan and Full, 1993). Such dynamics have been shown to be passively stable over the parameter and speed range of human locomotion. Our previous results of the stiffness of individual legs to the support tripod during running suggest that, in addition to the benefits of passive stability, cockroaches may benefit from reduced power expenditure by using stride frequencies at or near the resonant frequency of the spring-mass system. We approximated stance phase durations and leg sweep angles for a SLIP model of running animals using the method of Geyer et al. (2005), and compared them with numerical solutions of the full equations of motion. Approximations revealed how gravitational, elastic, and centrifugal forces influence periodic gaits, and showed that, unlike in vertical hopping, it is difficult to define a clear natural frequency for a given SLIP. We computed branches of such gaits with and without flight phases and with double-stance phases. We used stride data from running cockroaches to calculate the stiffness of the support tripod over a range of speeds. Dimensionless tripod stiffness ranged from 3-5.5. We also investigated stability for parameters representative of insects and mammals and showed that insect gaits as modeled by a single-stance leg SLIP are unstable over much of their speed range. This suggests that multi-legged support in stance, as in the double tripod gait of the cockroach, may be critical to insect performance. Funded by NSF FIBR.