On the genesis of directional friction through bristle-like mediating elements

Abstract

We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl-Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

References in corpus (3)

• Liquid Crystal Elastomer Strips as Soft Crawlers
• A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model
• Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler

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• Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction