Coulomb Friction Crawling Model Yields Linear Force–Velocity Profile

Ziyou Wu, Dan Zhao, Shai Revzen

J Applied Mechanics, vol. 86, no. 5, 2019

Abstract

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.

BibTeX

@article{wu2019coulomb,
  author = {Wu, Ziyou and Zhao, Dan and Revzen, Shai},
  title = {Coulomb Friction Crawling Model Yields Linear Force--Velocity Profile},
  journal = {J Applied Mechanics},
  year = {2019},
  volume = {86},
  number = {5},
  doi = {10.1115/1.4042696},
  publisher = {American Society of Mechanical Engineers Digital Collection},
  cvtopic = {ddmodel}
}