Workspace and Cuspidality Analysis of a 2-X Planar Manipulator

摘要

This paper analyzes the workspace of a planar 2-X manipulator, i.e. made of two crossed four-bar mechanisms in series. This architecture has some advantages over classical 2-R manipulators such as its ability to be driven with tendons, but its kinematics is more challenging because of a variable instantaneous center of rotation of the X-mechanisms. The workspace boundaries are determined algebraically and its accessibility is analyzed. In the absence of joint limits, the workspace has regions with two and four inverse kinematic solutions. Depending on the values of its geometric parameters, the manipulator at hand may be cuspidal, i.e. it can change its posture without meeting a singularity. A necessary and sufficient condition is stated for the manipulator to be cuspidal. The effect of joint limits is analyzed and the accessibility regions are further classified according to the reachable configurations of each X-mechanism in these regions.