Closed-form forward kinematics, singularity, dexterity and workspace analyses of a special class of 3-RRR spherical parallel mechanisms

Abstract

3-RRR spherical parallel mechanisms (SPMs) are capable of producing three-DOF spherical motion, which can find applications in various fields. This paper investigates the kinematics and workspace performance of a particular class of 3-RRR SPMs, characterized by coaxial input-joint axes, coplanar distal-joint axes, and six orthogonal links. First, two novel formulations are proposed for the forward kinematics (FK) of this robot class, both resulting in linear univariate polynomials that significantly streamline the FK formulation and reduce the computational complexity. Moreover, this robot class exhibits minimal and physically interpretable singularity loci in both the orientation workspace and the input joint space, greatly facilitating singularity avoidance and path planning. Furthermore, local and global dexterity indices are employed to analyze the mechanism’s performance, from which the architectural parameters yielding optimal dexterity are identified. Finally, the robot class demonstrates a considerably large tilt-torsion orientation workspace when the architectural parameters and link shapes are appropriately selected, allowing for infinite torsional motion when pointed within almost a hemisphere. The foregoing features make the robot class potentially promising in a wide range of applications.