Rank of loop, constraint degree of path, coupling degree of graph and their application.

Some new concepts (rank of a loop, degree of freedom of a graph, path unit and ordered path arrangement, constraint degree of path, coupling degree of a graph, basic graph, etc.), formulas, and algorithms, are proposed in this paper. Based on these concepts, a new systematic theory and practical method for the design of topological structure, kinematics and dynamics of mechanical systems is established. Some conjectures and problems needed to be researched are also put forward. The concepts, formulae and algorithms presented in this paper will find wide potential applications. [ABSTRACT FROM AUTHOR]