An algorithm is developed to determine the workspace on an arbitrary plane for an n-R robot. The algorithm is based on a linear optimization technique and on small incremental displacements applied to coordinate transformation equations relating the kinematic parameters of the n-R robot. The algorithm provides flexibility to let the user treat the robot hand as a point, a line, or a rigid-body. The revolute pairs of the robot may execute full or partial rotation. The proposed method may be extended to incorporate in a robot the existence of prismatic pairs along with revolute pairs.