Skip to Main Content
This paper presents two trajectory-planning approaches for the point-to-point motion of planar two-degree-of-freedom (dof) cable-suspended parallel mechanisms. The proposed techniques can be used to plan trajectories that extend beyond the static workspace of the mechanism. Trajectories are specified as a list of target points that must be reached in sequence, with a zero velocity at each of the target points. In the first technnique, polynomial trajectories are designed to connect the target points, while the second approach uses trigonometric functions. Both techniques ensure continuity of the accelerations. Based on the dynamic model of the robot, algebraic inequalities are obtained that represent the constraints on cable tensions. These inequalities are used to determine the feasibility of the planned trajectories. Polynomial trajectories must be discretized in order to verify feasibility, while trajectories that are based on trigonometric functions can be verified globally, based on a set of simple algebraic equations. Example trajectories are given in order to illustrate the approach. An experimental validation is also presented using a two-dof prototype, and two video extensions are provided to demonstrate the results.