Number synthesis of kinematic chains based on permutation groups

A systematic and precise approach is developed for enumerating non-isomorphic kinematic chains based on the theory of permutation groups. First, we define contracted link adjacency matrices of kinematic chains, and elements in the matrices are separated into four sets. We then propose an algorithm for assigning values to elements of these sets to generate non-isomorphic configurations according to their permutation groups. As a result, the numbers of simple kinematic chains with up to twelve links and seven degrees of freedom are listed.

[1]  T. S. Mruthyunjaya.  A computerized methodology for structural synthesis of kinematic chains: Part 2— Application to several fully or partially known cases , 1984 .

[2]  T. S. Mruthyunjaya.  Structural synthesis by transformation of binary chains , 1979 .

[3]  A. Raicu.  Matrices associated with kinematic chains with from 3 to 5 members , 1974 .

[4]  N. Manolescu,et al.  A method based on Baranov Trusses, and using graph theory to find the set of planar jointed kinematic chains and mechanisms , 1973 .

[5]  Hong-Sen Yan,et al.  Linkage Characteristic Polynomials: Definitions, Coefficients by Inspection , 1980 .

[6]  Hong-Sen Yan,et al.  Linkage path code , 1984 .

[7]  F. Freudenstein,et al.  The Development of an Atlas of the Kinematic Structures of Mechanisms , 1984 .

[8]  F. Freudenstein,et al.  On a theory for the type synthesis of mechanisms , 1966 .

[9]  L. S. Woo,et al.  Type Synthesis of Plane Linkages , 1967 .

[10]  V. Agrawal,et al.  Canonical numbering of kinematic chains and isomorphism problem: min code , 1987 .

[11]  T. S. Mruthyunjaya.  A computerized methodology for structural synthesis of kinematic chains: Part 1— Formulation , 1984 .

[12]  J. Uicker,et al.  A method for the identification and recognition of equivalence of kinematic chains , 1975 .

[13]  T. S. Mruthyunjaya.  A computerized methodology for structural synthesis of kinematic chains: Part 3— application to the new case of 10-link, three- freedom chains , 1984 .

[14]  H.-S. Yan,et al.  METHOD FOR THE IDENTIFICATION OF PLANAR LINKAGE CHAINS. , 1982 .

[15]  Ferdinand Freudenstein,et al.  Some Applications of Graph Theory to the Structural Analysis of Mechanisms , 1967 .

[16]  F. R. E. Crossley.  A Contribution to Gruebler’s Theory in the Number Synthesis of Plane Mechanisms , 1964 .

[17]  George I. Davida,et al.  Optimum Featurs and Graph Isomorphism , 1974, IEEE Trans. Syst. Man Cybern..

[18]  T. S. Mruthyunjaya,et al.  In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains , 1987 .

[19]  A. H. Soni,et al.  Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains , 1973 .

[20]  Frank Erskine Crossley.  On an unpublished work of Alt , 1966 .

[21]  Trevor H. Davies,et al.  Structural analysis of plane linkages by Franke's condensed notation , 1966 .

[22]  E. R. Maki,et al.  The Creation of Mechanisms According to Kinematic Structure and Function , 1979 .

[23]  A. H. Soni.  Structural Analysis of Two General Constraint Kinematic Chains and Their Practical Application , 1971 .

[24]  Frank Harary,et al.  Graph Theory , 2016 .