On the determination of the workspace of complex planar robotic manipulators

A new method for the determination of the workspace of complex planar robotic manipulators is described in this paper. The method is based on the use of joint limits to obtain equations describing limiting curves. These limiting curves are then segmented at their mutual intersections and validated The resulting sets of portions of curves form the envelope of the workspace. The algorithm is completely general and can be applied to any three-degree-of-freedom planar manipulator-serial, parallel or hybrid-with or without joint limits. Examples of the application of the method to a serial three-degree-of-freedom manipulator, to a hybrid three-degree-of-freedom manipulator and to a parallel three-degree-of-freedom manipulator are given.