Dynamically Feasible Trajectories for Three-DOF Planar Cable-Suspended Parallel Robots

This paper proposes a trajectory planning technique for planar three-degree-of-freedom cable-suspended parallel robots. Based on the kinematic and dynamic modelling of the architecture, force constraints that can guarantee that cables remain under tension are obtained. Periodic parametric trajectories that extend beyond the static workspace are designed. The trajectories involve combined translations and rotations. Substituting the trajectories into the force constraints, interval arithmetics is used to search for global conditions on the trajectory parameters which ensure that the trajectories are feasible. Special frequencies related to combined rotational and translational motions are exposed which can be used to better exploit cable-suspended robots. Moreover, it is observed that the special frequencies related to the translation are akin to the natural frequency of pendulum-like systems. The proposed trajectory planning approach can be used to plan combined rotational and translational dynamic trajectories that can extend beyond the static workspace of the mechanism, thereby opening novel applications and possibilities for cable-suspended robots.