Preliminaries of a new approach or the direct kinematics of suspended cable-driven parallel robot with deformable cables

Abstract

Direct kinematics (DK) of parallel robots is most of the time a difficult problem. This is true for cable-driven parallel robots (CDPR) especially if cable deformations are taken into account. If the cable model, whatever it is, is introduced in the kinematic equations we always end up with a square system of equations that is usually very difficult to solve.We first show that with minimal assumptions we are able to give an upper bound on the number of the solutions of the DK whatever is the cable model. We then propose a generic method, based on non-linear continuation, to solve the DK for any cable model, that is illustrated with a practical example of sagging cables.