A unique representation of the kinematic chain and the atlas database

Based on a new topological graph, the perimeter topological graph, many new primary concepts are proposed in this paper for the first time, the synthesis of which creates the synthetic degree-sequence of perimeter topological graphs. Then by labeling vertex coordinates on perimeter topological graphs according to certain rules, the canonical perimeter topological graph is obtained. Its adjacency matrix, the characteristic adjacency matrix, is unique for any kinematic chain. After that, through the combination of the synthetic degree-sequence and the characteristic adjacency matrix, the characteristic representation code is proposed. This code establishes a one-to-one correspondence with a kinematic chain, and has been used in the development of a program which not only sketches topological graphs of kinematic chains automatically, but also creates the atlas database of kinematic chains. Finally, several automatic sketching examples are given, and the functions of the atlas database are introduced.