Kinematics and Workspace of a Spatial 3-DoF Manipulator with Anti-parallelogram joints

This paper introduces a novel spatial serial manipulator composed of three anti-parallelogram (X) joints arranged in two perpendicular planes and separated by offsets. The position of a point on the terminal link is controlled through the three joint angles. The inverse kinematic problem is solved analytically by decomposing it into two planar sub-problems. It is shown that this problem admits up to thirty-two solutions, and an example with these many solutions is presented. The singularities of this manipulator are derived and interpreted geometrically. Finally, the workspace of this manipulator accounting for the joint limits of each X-joint is visualized.