Orientation capability of planar serial manipulators using rotatability analysis based on workspace decomposition

This paper presents a new approach for analysing and synthesizing the orientation capability of planar serial manipulators. By relating the end-effector to the base joint of a manipulator using a virtual adjustable link, the paper converts the open-chain kinematic problem into that of an equivalent close-chain mechanism, and characterizes the relationship between the orientation capability of a serial manipulator and the rotatability of the equivalent mechanism. The orientation capability of a manipulator can hence be placed in the realm of mechanism rotatability. The approach is taken further by decomposing the reachable workspace of a manipulator into ranges, based on the extreme and singular positions of a manipulator. In each of the workspace ranges, the rotatability of the equivalent mechanism is examined and results are categorized to indicate the orientation capability of the manipulator. The approach produces a direct correlation between the orientation capability and manipulator parameters and generates a way of examining the orientation capabilities of serial manipulators. The approach is extended to n-link serial manipulators.