Abstract. We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance oﬀered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of ﬁnely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute suﬃciently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail- like crawlers. The frictional case is obtained by assuming that the viscous coeﬃcient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial eﬀects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an eﬀective tool to replicate and study collective bacterial motility.
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