LAUSR

Abstract This paper presents a trajectory formulation that connects an initial point at rest to a final point to be reached with zero velocity but nonzero acceleration for planar two-dof and spatial three-dof cable-suspended mechanisms with point-mass end-effectors. The trajectory is designed to reach the first of a sequence of target points that can be located outside of the static workspace of the mechanisms. The proposed motion consists of oscillations of progressively increasing amplitude centred at the initial point, whereby an upper bound for the minimum feasible number of oscillations is determined by ensuring positive tension in all cables throughout the trajectory. It is shown that this number of oscillations can be found for any trajectory that is entirely located below the spools. The paper provides novel insight into the dynamics of the three-dof mechanism, and highlights the similarities and differences between the planar and spatial motions. Simulation results of example trajectories are included in order to illustrate the approach, along with a video demonstration of an experimental validation performed using a three-dof prototype.