Trajectory Verification in the Workspace for Parallel Manipulators

We present a fast algorithm for solving the problem of the verification of a trajectory for a 6-DOF parallel manipulator with respect to its workspace: i.e., given two different postures for the end-effector, is the straight line joining these two postures in the parameters space fully inside the workspace ? This algorithm is based on the analysis of the algebraic inequalities describing the constraints on the workspace and provides a technique for computing those parts of the trajectory that lie outside the workspace. This method is exact if the orientation of the end-effector is kept constant along the trajectory and approximate if the orientation is allowed to vary.