On Singularity of a Planar Parallel Manipulator with and without Actuation Redundancy

To start with, three kinds of singularities of a two-degree-of-freedom planar parallel manipulator with and without actuation redundancy are studied respectively. Then analytical relationships between the link lengths of the two manipulators and characteristic shapes and distribution of the singularities are derived. Based on Jacobian matrix of the kinematic transformation, equations of the singularity curves are developed. Further the corresponding loci are drawn in terms of some nondimensional structural parameters. A comparison shows that the second kind of singularity loci of the general parallel manipulator will degenerate into several singular points when redundancy is applied to, which demonstrates its availability on eliminating singularities. The results have reference value in the singularity-free trajectory planning and control.