Abstract: Analyzing the actuator singularity of overactuated parallel robot by differential geometric approach is completed. The cause of the actuator singularity is analyzed by the Riemannian metric projection relation on the configuration manifold and the ambient one. The approach of a framework of tangent space for configuration manifold replacing Jacobian matrix to analyze the actuator singularity is presented further according to the definition of embedding mapping. The concise equivalent form for analyzing actuator singularity is described by some properties related with matrix rank. Comparing with the implicit function theorem, the method could avoid the matrix multiplication manipulation and the repeating calculation for inverse matrix, thereby reducing the complexity of computing. Finally, the example of a planar 2-DOF overactuated parallel robot is given, and it shows that the above principle is feasible and effective.

Key words: Solution vector, Actuator singularity, Embedding, Overactuated parallel robot, Riemannian metric