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The kinematics of cable-driven parallel robots with sagging cables: preliminary results

We consider in this paper cable driven parallel robot (CDPR) with m catenary cables that present a significant deformation due to their elasticity and own mass and we address the kinematics of such a robot under the assumption of static state. We show that the inverse kinematics (IK) requires to solve a square system of equations if the robot has up to 6 cables and an underconstrained system if m > 6. We first show that usual methods for solving the IK of CDPR with other cable model cannot be used and we propose an algorithm that allows one to determine all possible solutions. We then address the forward kinematics (FK) that is known to be usually a difficult task for parallel robots. We show that solving the FK always amounts to solve a square system of equations and that the problem is even more complex than solving the FK of parallel robots with rigid legs as the system is non algebraic and has a larger number of equations. We then propose a generic algorithm for solving the FK for any number of cables. We illustrate the use of the IK and FK solver on a CDPR with 8 cables.