A joint–joint matrix representation of planar kinematic chains with multiple joints and isomorphism identification

Abstract

The synthesis of the kinematic chain needs to obtain the information of the kinematic chain accurately and comprehensively. Isomorphism identification is an essential step in kinematic chain synthesis. In this article, a novel isomorphism determination method of planar kinematic chains with multiple joints based on joint–joint matrix description was proposed. First, a joint–joint matrix is presented to describe the kinematic chain, which can uniquely represent the kinematic chain structure. Then links and joints information were extracted from the matrix. And the link code and joint code were introduced to represent the link attributes and joint attributes, respectively. Furthermore, the standardization rules of joint–joint matrix are proposed. Isomorphism of kinematic chain is identified by comparing links, joints, and matrices. And the relationship between the links and the joints corresponding to the isomorphic kinematic chain is determined. Finally, the examples demonstrate that the method is novel and efficient.