Extreme reaches and reachable workspace analysis of general parallel robotic manipulators

This article presents a systematic numerical method for analyzing the extreme reaches and the reachable workspace of general parallel robotic manipulators. In this method, finding the extreme reach is formulated as an optimization problem. The closed loops of the robot are virtually disconnected into open kinematic chains. Violations of the loop closure constraints and the position error of the end-effector are included in the objective function as penalty terms. This formulation not only is conceptually straightforward, but also can effectively reduce the problem size. The problem is solved by using a two-stage sequential unconstrained minimization algorithm. A procedure for determining the boundary surfaces of the reachable workspace is also presented. (C) 1998 John Wiley & Sons, Inc.