Conventional wisdom would have it that moving mechanical systems that dissipate energy by Coulomb friction have no relationship between force and average speed. One could argue that the work done by friction is constant per unit of distance travelled, and if propulsion forces exceed friction, the net work is positive, and the system accumulates kinetic energy without bound. We present a minimalistic model for legged propulsion with slipping under Coulomb friction, scaled to parameters representative of single kilogram robots and animals. Our model, amenable to exact solutions, exhibits nearly linear (R2 > 0.96) relationships between actuator force and average speed over its entire range of parameters, and in both motion regimes, it supports. This suggests that the interactions inherent in multilegged locomotion may lead to governing equations more reminiscent of viscous friction than would be immediately obvious.
Coulomb Friction Crawling Model Yields Linear Force–Velocity Profile
Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received December 7, 2018; final manuscript received January 31, 2019; published online March 5, 2019. Assoc. Editor: Ahmet S. Yigit.
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Wu, Z., Zhao, D., and Revzen, S. (March 5, 2019). "Coulomb Friction Crawling Model Yields Linear Force–Velocity Profile." ASME. J. Appl. Mech. May 2019; 86(5): 054501. https://doi.org/10.1115/1.4042696
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