The Forward Kinematics of Cable-Driven Parallel Robots with Sagging Cables

Solving the forward kinematics (FK) of parallel robots is known to be a difficult task and the problem is even more complex for cable driven parallel robot (CDPR): the system of equations that has to be solved is larger than with rigid legs as first the static equations have to be taken into account and, second because the deformation of the cables because of their elasticity and their mass may play a role, while being described by a relatively non algebraic complex model. We consider in this paper any arbitrary CDPR whose cables may present a significant deformation due to their elasticity and own mass and we present for the first time an interval analysis based generic algorithm that allows to calculate in a guaranteed manner all the FK solutions and illustrate its use for a CDPR with 8 cables.