The structure design is the most crucial and innovative one in the process of mechanism system design, and attention is constantly given to them. Although the various methods of structural synthesis are presented, more study due to faultiness of them are essential. All of available configurations of the single joint kinematic chain are gotten by replacing its pairs. On the basis of symbolization of pairs, the authors put forward the mathematic approach of permutation and combination by which all of configurations of the kinematic chain can be obtained, structure graph is used to judge the type of same fabric of the kinematic chain. Finally their application examples in engineering are given.