Loci of singular configurations of a 3-DOF spherical parallel manipulator

In order to evaluate the dexterity and kinematic accuracy of a robot manipulator during the design, trajectory planning and control stages, it is of prime importance to know its singular configurations. In this paper, a systematic method to obtain singularity loci of parallel manipulators exemplified by a 3 DOF spherical parallel manipulator is addressed. Firstly, the inverse position equations are formed, and the velocity equation containing the actuator and the end effector (platform) velocities, and Jacobian matrices is derived. Secondly, the determinants of the manipulator Jacobian matrices are evaluated for a specified set of geometric parameters. Finally, the contours of the determinants at 0.0 plane, which are the singularity loci of the manipulator in Cartesian space, are generated. Two different orientation matrices are chosen to demonstrate that the representation of singularity loci is formulation dependent. The main difference of our work from previously published work is that there is no need of expressing singularity loci mathematically. This saves a considerable amount of computational time. The proposed method allows the user to generate the loci of singular configurations of any kinematics chain whose Jacobian matrices are expressed analytically. The method is a quick tool for the designers to decide whether the singularities are acceptable or not. Further, as the singularity loci indicate the acceptable boundaries of singularities, the designers can make use of it to accurately quantify the manipulator dexterity and kinematic accuracy. (C) 2004 Elsevier B.V. All rights reserved.