A new theory for the topological structure analysis of kinematic chains and its applications

Based on the array representation of loops in topological graphs of kinematic chains, this paper proposes two basic loop operations, “Θ” and “⊕”, for the first time. The existent conditions and properties of “⊕” operation are researched and four laws about the operation are presented. Furthermore, after the important concepts of the independent loop set and its selection theorem are proposed, the loop relationship of kinematic chains is revealed; thus an original theory of loop analysis is established. Finally, some applications are given under the basic theory above, such as the isomorphism identification, the detection of rigid sub-chains, and the freedom type analysis of kinematic chains.