Modeling of shape bifurcation phenomena in manipulations of deformable string objects

Abstract

A systematic approach to the modeling of deformable string objects is presented. Various string objects such as cords and wires are manipulated in many manufacturing processes. In such processes, it is important for successful manipulation to evaluate their shapes on a computer in advance because their shapes can be changed easily even under the same conditions. We refer to the situation that a shape can be changed into another shape even under the same constraints as shape bifurcation. In this paper, we will develop an analytical model of the shape of string objects including shape bifurcation. First, we will investigate the mechanism of the shape bifurcation phenomena based on the potential energy. Then, we will propose a hypothesis on the mechanism of shape bifurcation based on local minima of the potential energy. Second, the potential energy of a string object and the geometric constraints imposed on it are formulated. The shape of the object can be derived by minimizing the potential energy under the geometric constraints. Thirdly, a procedure to compute the shape of a deformed string object is developed considering the local minima of the energy. Finally, we show some numerical examples with shape bifurcation using our proposed method. From the results, we conclude that our proposed method accurately describes deformed shapes of string objects including shape bifurcation.