Trajectory verification of parallel manipulators in the workspace

We present a fast algorithm for solving the problem of determining if the straight line between two different postures of a parallel manipulator lie fully inside its workspace. This algorithm is based on the analysis of the algebraic inequalities describing the constraints on the workspace (link lengths range, mechanical limits on the joints, interference between the links) and enables to compute which part of the trajectory is outside the workspace. This method is exact if the orientation of the end-effector is kept constant along the trajectory and approximate in the opposite case