A new rigid sub-chain identification and elimination method of kinematic chains with multiple joints

Abstract

It is a very important process to determine whether there is a rigid sub-chain in the type synthesis for kinematic chains. In this paper, a new method for identifying and eliminating rigid sub-chains of kinematic chains with multiple joints is proposed. Firstly, the properties of the mesh loop set and independent loop set in loop combination were introduced. Properties determine that testing the degrees of freedom (DOF) of all independent loop sets and the combined loops can verify the existence of a rigid sub-chain. Secondly, representation methods and properties of the joint-joint adjacent matrix and loop matrix were explained and the operation method of the loop matrix was explained. A method of obtaining some loop matrices, which represents an independent loop set, by joint-joint adjacency matrix is proposed. Then, the DOF of all independent loop sets and the combined loops of independent loop sets were obtained by the operation method of loop matrix to identify and eliminate the rigid sub-chain. Finally, a large number of cases have proved the feasibility and effectiveness of this method.