Mathematical model of inchworm locomotion

•Inchworm is modeled as inextensible elastica.•Two basic cases of inchworm locomotion are analyzed.•Bending strains obtained should be useful for designing inchworm robots.

Inchworms are caterpillars. Their locomotion, involving arching of much of the central portion of their body length, has not been studied as extensively as the peristaltic locomotion of worms or the crawling locomotion of many other caterpillars. A mathematical model is developed to describe the shapes and bending strains of typical inchworm motions. The inchworm is assumed to travel in a straight line on a rigid horizontal substrate. Two basic types of cycles are considered. In Case I, the inchworm body arches and then reverses that motion in becoming flat again. In Case II, the body arches, then cantilevers upward, and then falls down to a flat shape. A continuum model based on an elastica is adopted. The results may be useful in the development of soft robots exhibiting an inchworm mode of motion.