Orientation angle workspaces of planar serial three-link manipulators

This paper presents a classification on the workspaces of planar serial three-link manipulators, that is, position workspace and orientation angle workspace. Position workspace indicates the region reached by the reference point on the end-effector. Orientation angle workspace indicates a set of angle ranges by which the end-effector can reach with certain orientation for every point in the reachable position workspace. By introducing a virtual equivalent mechanism, reachable position workspace can be di- vided into several Grashof intervals and non-Grashof intervals. The calculation equations of orientation angle workspace are deduced in three situations according to the relationships among four link lengths in the virtual four-bar chain. Three examples are given for three kinds of relationship of link lengths. The orientation angle workspace of extended groups, that is, two of the three link lengths equal, and the orientation angle workspace when the reference point on the end-effector moves along a non-radial direction are also discussed. A program is developed to calculate orientation angle workspaces and output variation curves of orientation angle workspace and key data within the position workspace. The approach and program in this paper can be used for fast calculation and identification of the variation rule of the orientation angle workspace of any given planar serial three-link manipulator on the basis of its link parameters, and for the design of a highly dexterous serial manipulator with proposed link rela- tions.