Orientation angle rotatability of planar serial n-link manipulators

This paper presents a new method of analyzing the orientation angle rotatability of a planar serial n-link manipulator by examining the rotatability of its virtual equivalent mechanism. Workspace orientation boundary region decomposition is proposed based on the polynomial discriminant derived from a serial three-link manipulator. 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, the open-chain kinematic problem is converted into a close-chain mechanism, and the Grashof-type condition is used to examine the rotatability of the end-effector link. The reachable position workspace can be divided into several Grashof intervals and non-Grashof intervals based on the extreme positions and singular configurations of a manipulator. The derived equations in this paper can be used to calculate the variation rule of the orientation angle workspace of any given planar serial n-link manipulator on the basis of its link parameters. The orientation angle rotatability of a seven-link serial manipulator is solved by the proposed method and graphical representations of the orientation angle workspaces are mapped onto a three-dimensional coordinate system. The theoretical approach has practical significance for the design of a highly dexterous serial n-link manipulator with proposed link relations.