Coulomb Friction Crawling Model Yields Linear Force-Velocity Profile

[+] Author and Article Information
Ziyou Wu

1506 Gilbert Court S-16 ANN ARBOR, MI 48105 wuziyou@umich.edu

Dan Zhao

3655 GreenBrier Blvd Apt. 141B Ann Arbor, MI 48105 danzhaoy@umich.edu

Shai Revzen

Electrical Engineering and Computer Science Ann Arbor, MI 48109 shrevzen@umich.edu

1Corresponding author.

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 xx xx, xxxx. Assoc. Editor: Ahmet S. Yigit.

ASME doi:10.1115/1.4042696 History: Received December 07, 2018; Accepted January 31, 2019


Conventional wisdom would have it that moving mechanical systems which 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 traveled, 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>0.98) 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 multi-legged locomotion may lead to governing equations more reminiscent of viscous friction than would be immediately obvious.

Copyright © 2019 by ASME
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