Kinematics-chain isomorphism determination method based on number matrices

Abstract

The invention relates to the field of mechanism kinematics chains, and discloses a kinematics-chain isomorphism determination method based on number matrices. Components and kinematic pairs of kinematics chains are numbered, and the number matrices are generated; then kinematics-chain information is extracted; the number matrices are standardized, and the kinematic pairs and the components are renumbered; standardized number matrices are obtained, then respective standardized composite-hinge information and standardized kinematic-pair information of the kinematics chains are extracted, the standardized composite-hinge information, component information and the standardized kinematic-pair information are sequentially compared, if all thereof are the same, the kinematics chains are isomorphic, and otherwise, the kinematics chains are isomeric. According to the kinematics-chain isomorphism determination method based on the number matrices of the invention, both reliability and number labeling ability of determination are considered, calculation is simple, a calculation amount is less, and determination of correspondence relationships of components and kinematic pairs of isomorphic kinematics chains is realized at the same time.

Description

technical field [0001] The invention relates to the field of mechanism kinematic chains, in particular to a kinematic chain isomorphism judging method based on a numbering matrix. Background technique [0002] The kinematic chain isomorphism judgment is of great significance to the structure type synthesis and optimal structure type of the mechanism. At present, there are many methods for the isomorphism judgment of the mechanism. The methods for giving the bijection of graph nodes and edges are: [0003] 1. Based on the eigenvalue and eigenvector calculation method of the adjacency matrix or correlation matrix, and the eigenvalue method based on the component connectivity matrix, when there are many identical eigenvalues, the calculation amount of the isomorphism judgment will increase sharply, or even fail; [0004] 2. Mechanism isomorphism determination based on genetic algorithm, but genetic algorithm is essentially a probabilistic search method, which has the defects of...

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Problems solved by technology

[0004] 2. Mechanism isomorphism determination based on genetic algorithm, but genetic algorithm is essentially a probabilistic search method, which has the defects of being premature and easy to fall into local solutions, and the calculation amount of isomorphism determination with genetic algorithm has not yet been given theoretically. make more accurate forecasts;

[0005] 3. According to the successive product matrix of the correlation matrix and its transpose matrix, the prime number representation of the adjacency matrix of the kinematic chain of the mechanism is established through the corresponding relationship between the rows of the product matrix and the array, and the isomorphic bijection of the isomorphism determination is not given by this method. The upper limit of the number of times of matrix multiplication, and the judgment is still more complicated when there are many identical values ​​in the row and the array

[0009] At present, the main problem of mechanism isomorphism determination is that the existing methods cannot take into account the reliability and labelability of the determination at the same time, the calculation is complicated and the calculation amount is large, and the corresponding relationship between the components and the kinematic pairs of the isomorphic kinematic chain cannot be obtained. judgment, so it needs to be further studied

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