Trajectory Verification in the Workspace for Parallel Manipulators

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Abstract
We present a fast algorithm for solving the problem of the ver ification 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 al gorithm 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.

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