Representations & Isomorphism Identification of Planar Kinematic Chains with Multiple Joints Based on the Converted Adjacent Matrix

Handling multiple-joint and isomorphism identification of planar kinematic chains with multiple-joints is a hard work in the analysis and synthesis of mechanisms.A new approach is suggested to convert the multiple-joints to some parallel simple-joints by using a Pin-link to adjoin all the links on a multiple-joint.The converted adjacent matrix is defined to represent the kinematic chains with multiple-joints.According to some characteristic parameters of the converted adjacent matrix,a new method for isomorphism identification of planar kinematic chains is proposed.Some application examples show that the converted adjacent matrix can conveniently represent planar kinematic chains with multiple-joints,and the Eigen values and eigenvectors of the converted adjacent matrix can be used to identify the isomorphism of planar kinematic chains effectively and efficiently.A new way is provided to the analysis and synthesis of mechanisms with multiple-joints.