The Inverse Kinematics of Cable-Driven Parallel Robot with More Than 6 Sagging Cables Part 1: From Ideal to Sagging Cables

A cable-driven parallel robot (CDPR) has n cables whose lengths are used to control the pose of the platform. We assume here that \(n>6\) and that the cables have elasticity and mass i.e. are sagging cables. In that case the inverse kinematics (IK, i.e. finding the cable lengths to reach a given platform pose) has usually an infinite number of solutions. It is then common to look for an IK solution that satisfies some optimality condition usually related to the cable tensions i.e. solving a very difficult constrained optimization problem as sagging cables leads to highly non linear constraints. To the best of the author knowledge this issue has never been addressed and we propose an algorithm for solving the IK without guaranteeing to obtain the minimum of the optimality criterion. Unfortunately it is time consuming with about 5 to 46 min of solving time for a CDPR with 8 cables.