Bending and Torsional Deformation Analysis of a Twisted Wire

Abstract

A modeling method to represent bending/torsional deformation of an electric wire is proposed based on the differential geometry. A twisted wire called a robot cable is used in a prismatic/rotational joint of an industrial robot to transmit signals or electric power. It is composed of a twisted bunch of several strands of many copper wires. The copper wire may be cracked by repeated bending/torsional deformation associated with the movement of a joint and such crack leads to wiring disconnection. To predict the life-cycle of the wires and to prevent such wiring disconnection, it is required to estimate deformation of not only the strands but also the copper wires when the wire is bent/twisted. In this paper, the deformed shape of a wire, which corresponds to a twisted bunch of n strands, is described by 3+2n independent variables and can be derived by minimizing the potential energy of each strand under various constraints. As the relationship between copper wires and their strand is similar with that between strands and their twisted bunch, the deformed shape of each copper wire can be also derived with the same method.