Modeling of linear objects considering bend, twist, and extensional deformations

Various deformable objects are manipulated in many manufacturing processes. Deformation of these objects is often utilized in order to manipulate them successfully while the manipulation sometimes fails because of unexpected deformation of the objects. Modeling of deformable objects is thus required so that the shape of the objects can be evaluated on a computer in advance. In this paper, we develop an analytical method to model the shape of a deformable linear object such as cords and tubes. First, a geometric representation to describe the shape of a linear object with bending and torsional deformation is introduced. The potential energy of the object and the geometric constraints imposed on it are then formulated. The shape of the object in the stable state can be derived by minimizing the potential energy under the geometric constraints. Next, procedure to compute the deformed shape is developed by applying a nonlinear programming technique. Finally, some numerical examples are shown in order to demonstrate how deformed shapes of linear objects are computed using the proposed approach.