Study On The New Definition Of Basic Loop Set Of Kinematic Chain And Its Generation Method

Loops are an inherent feature of the kinematic chain structure,and existing studies have dealt with basic loops.However,there is a lack of theoretical studies related to shortest loops and basic loop sets,so there should be more rigorous and operable definition and generation methods for basic loop sets.This will help to analyze a large number of kinematic chain topologies with corresponding structural theories,and lay the theoretical foundation for the subsequent kinematic chain isomorphism discriminations,rigid sub-chain discriminations and their active sub-selection and the establishment of topological graph atlas libraries.Firstly,the graph theory and basic knowledge of kinematic chains are introduced.The loop structure information of kinematic chains is analyzed in depth,based on the basic concepts and characteristics of existing basic loop sets,so as to propose a more rigorous definition of basic loop sets.Then,the new definitions of main and branch chains are obtained based on the different connection relationships between the root and child nodes.For better data processing,the method of obtaining the information table of the layered structure of the links is proposed.Then,according to the data structure characteristics of the link layered structure information table,the representation method of the tree structure diagram and the method to determine the type of links and multiple joints are proposed.It also rearranges the placement order of the links in the tree structure diagram,which can more specifically and intuitively express the information of non-cross-connection between the links of the kinematic chain topology diagram.Finally,a new method of defining and obtaining the branch chain matrix is proposed based on the tree structure diagram and layered structure information table,and then the branch chain matrix is initially optimized.The basic loop set extraction rules are proposed based on the data relationship between rows and columns of the branch link matrix.After analyzing the basic conditions of the basic loop set definition,the problem that the number of loops in the loop set is smaller than the number of independent loops is solved.The correctness and effectiveness of the method are fully demonstrated through the analysis of examples of separable kinematic chains,non-separable combinatorial kinematic chains and kinematic chains with large symmetry.In the article,a new definition of basic loop set is proposed,combined with branch chains to express the connection relationship between links,the theory of tree structure expression of kinematic chains and related branch matrix,as well as the extraction method of basic loop set based on this.The above method has simple rules and is easy to be implemented programmatically by computer.The basic loop sets of motion chains with complex structures can be obtained quickly.The correctness and validity of the above theory are proved by examples.