Dynamically-feasible elliptical trajectories for fully constrained 3-DOF cable-suspended parallel robots

A cable suspended robot can be moved beyond its static workspace while keeping all cables in tension, by relying on end-effector inertia forces. This allows the robot capabilities to be extended by choosing suitable dynamical trajectories. In this paper, we study 3D elliptical motions, which are the most general case of spatial sinusoidal oscillations, for a robot with a point-mass end-effector and an arbitrary base architecture. We find algebraic conditions that define the range of admissible frequencies for feasible trajectories; furthermore, we show that, under certain conditions, a special frequency exists, which allows arbitrarily large oscillations to be reached. We also study transition trajectories that displace the robot from an initial state of rest (within the static workspace) to the elliptical trajectory, and vice versa.