By analyzing the characteristics of the topological structure of the Assur groups, an extended adjacency matrix for Assur groups is constructed based on the adjacency matrix describing the kinematic chain. In the new matrix, the columns of multiple jionts and external motion pair are added. It can not only represent the connection information between components, but also can indicate the connection between components, multiple jionts, and external movements. The information of components, reaming and external motion pairs, and their connection relations are contained in the extended adjacency ...