An Isomorphism Identification Method Of Kinematic Chain Based On Optimal Arrangement And Comparison Of Branch-Chain Matrix Derived

Mechanism structure analysis is the basic step and important stage of mechanical innovative design.The prerequisite for conducting mechanism topology research is to systematically structure synthesis.The isomorphism identification of mechanism kinematic chains is a key issue that must be solved in the process of mechanism structure synthesis,and is very important for realizing automatic mechanism synthesis based on computers.It occupies most of the analysis and calculation workload in the process of mechanism structure synthesis.Finding an isomorphism identification method with simple rules,scientific feasibility,and less analysis and calculation has always been a research hotspot for mechanism scholars.Based on graph theory,hierarchical clustering algorithm,mechanism topology,and other related theories,the dendrogram in the clustering algorithm is introduced,aiming at the problem of isomorphism identification of mechanism kinematic chains,improving the representation mechanism of structural information of kinematic chains with multiple joints using dendrograms,and proposes dendrogram that can uniquely represent structural information of kinematic chains containing multiple joints.It consists of root node,child node,same-layer connector Bi,multiple joint symbol Ji,and connections between nodes.On this basis,the dendrogram is separated to obtain branch chain array.The branch chain matrix is constructed from the branch chain array.Using the information contained in the branch chain matrix to invertible derive unique and complete structural information of the mechanism kinematic chain as a criterion to carry out isomorphism identification of the mechanism kinematic chain.To further reduce the amount of calculation of this method and reduce the number of matrix row transformations when using branch chain matrix for isomorphism identification.On the basis of branch chain matrix,the concept of repeatability matrix of column elements of branch chain matrix and the intimacy between different rows of branch chain matrix are put forward to obtain the unique branch chain matrix of row ranking.While using the repeatability matrix and intimacy to improve the efficiency of the algorithm,preliminary isomorphic screening can also be performed by comparing whether the repeatability matrices of the two mechanism kinematic chains are the same.It is proved by some cases that this method has obvious advantages such as easy to understand rules,low search and comparison workload,and is easy to design computer programs.It provides a new and powerful tool for automatic isomorphism identification and synthesis of computer mechanism kinematic chain.