FINITE ELEMENT OF NONLINEAR CABLES: APPLICATIONS TO ROBOTICS

Frederic Boyer (France) and Dominique Primault (France)

Abstract

This article presents a numerical model of nonlinear cables devoted to robotics applications. The modeling is based on a nonlinear Euler-Bernoulli theory of thin beams. The model and the numerical solution which follows are said geometrically exact since they assume no simplification on the finite rotations of the cable cross sections. Based on a variational formulation, the numerical method uses a one step implicit integration scheme of the Newmark class. With such a choice, the dynamic problem turns into a nonlinear algebraic one, solved through a Newton algorithm. This algorithm requires computing the Jacobian of the dynamics. This is achieved directly in terms of the continuous fields that are discretized through the finite element method at the end of the computations. Finally, the resolution at each Newton step of the linearized dynamics is followed by an update procedure. Once the algorithm written, it is illustrated on several examples of robotics applications.

Keywords and phrases: geometrically exact, finite notations, nonlinear cables, robotics.