Singularity analysis of 6-DOF manipulators with the analytical representation of the determinant

The determinant of a Jacobian is used as a tool for describing the performance of manipulators. Especially for finding a singularity condition of manipulators, the single algebraic equation, i.e., the determinant of the Jacobian, is one of the simple and exact tools to analyze. For parallel manipulators, singularity analysis is one of the most important step in the design to improve their rigidity and performance. This paper provides a unified method for the expression of the determinant of the Jacobian matrix for 6-DOF manipulators including parallel and serial manipulators.