Singularity analysis for a class of serial manipulators with non-spherical wrists

For a serial manipulator with non-spherical wrist, the kinematics of the wrist´s position and orientation is not decoupled and the singularity analysis is very difficult. In this paper, a method is proposed to analytically identify the singularity configurations for a class of serial manipulators with non-spherical wrist. Firstly, the configuration characteristics of typical serial manipulators are analyzed and a general model is constructed to describe their kinematics in a united manner. Secondly, the kinematics transformation without changing the independence of joint motion is presented to simplify the kinematics equations. Then the main elementary transformation matrices are established. Thirdly, the singularity conditions are isolated and collected in a lower sub-matrix by several times of elementary transformations for the modified Jacobian matrix, which is partitioned into a block-triangle matrix. Finally, for the practical applications, some 6-DOF and 7-DOF manipulators are analyzed. The results obtained show the generality and feasibility of the proposed method.