Collision and Geometric Mechanics of Three Rope Tangles

Abstract

Due to the geometric feature and information, increasing investigations have been focused on tangled systems with rich mechanics behaviors. But most of them are limited to single physical intertwining or mathematical knot, which makes it difficult to illustrate the interaction between mechanics and geometry. This work proposes different kinds of elastic tangles with three ropes, in which the mechanics components and geometric properties are obtained. Five topological parameters are derived to show the relation between tangle type and mechanics characteristic. Based on the geometry knot theory, the strength and stability of tangles can be predicted by geometry rules. Moreover, numerical calculation and experiment are performed to support the theoretical prediction. This work wishes to provide guidance for the design and control of systems with complex entanglements and further inspire geometric mechanics of slender flexible elastomers.