The establishment of edge-based loop algebra theory of kinematic chains and its applications

Based on the edge-based array representation of loops in the topological graphs of kinematic chains, this paper first proposes three arithmetic operations of loops. Then the concept of the independent loop set as well as its determination rules is introduced, and a new structure decomposition algorithm of kinematic chains is presented. Based on the algorithm, an automatic and efficient method for rigid sub-chain detection and driving pair selection of kinematic chains is proposed. Finally, an index is proposed to assess computation complexity of kinematic analysis with respect to different driving pair selections.