The Systemic Research on Loop Characteristics of Planar Kinematic Chains and Its Applications

Based on the array representation of loop in topological graph of kinematic chains, this paper proposes two basic loop operations. Their existent conditions and properties of the two operations are also researched. In further loop analysis we discuss the important concepts including the independent loop, canonical degree-sequence and perimeter topological graph. Two Theorems deal with the relationship of loops. Based on above basic theory some important applications are given, such as the isomorphism identification based on the loop set concept, the detection of the rigid sub-chains in a kinematic chain and the type analysis of freedom of kinematic chains.