In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

%B Journal of the Mechanics and Physics of Solids %V 84 %P 254 - 272 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022509615300430 %R https://doi.org/10.1016/j.jmps.2015.07.017 %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2015 %T Motility of a model bristle-bot: A theoretical analysis %A Giancarlo Cicconofri %A Antonio DeSimone %K Bristle-robots %K Crawling motility %K Frictional interactions %XBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

%B International Journal of Non-Linear Mechanics %V 76 %P 233 - 239 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746215000025 %R https://doi.org/10.1016/j.ijnonlinmec.2014.12.010