Loop theory and applications to some key problems of kinematic structure of kinematic chains

Abstract

Structure synthesis of mechanisms is a pivotal issue in the field of mechanical innovation and mechanical conceptual design. In this paper, a new loop theory of kinematic chains is proposed. Based on this theory, some key problems that hamper computer-based automatic synthesis of mechanisms are solved. 1) The open problem of isomorphism of kinematic chains that has lasted for more than four decades is successfully solved. 2) A new rigid sub-chain detection method that is especially suitable for complex chains is proposed. 3) The characteristic representation code remains the same even if the drawing modes and labeling ways of a chain are changed, and an atlas database of kinematic chains is established. The multi-value problem for the representation of kinematic chains is solved. The results in this paper will benefit the digitization and computerization of mechanical conceptual design.

Keywords

Loop theory / kinematic chains / isomorphism / atlas database

References

[1] Yang T L. Basic Theory of Mechanical System –Structical Kinematical Dynamics. Beijing: Mechanical Press, 1995 (in Chinese)

[2] Cao W Q. The Analysis and Synthesis of Linkage Mechanism. Beijing: Science Press, 2002 (in Chinese)

[3] Mruthyunjaya T S. Kinematic structure of mechanisms revisited. Mech Mach Theory, 2003, 38(4): 279-320

[4] Yan H S. A methodology for creative mechanism design. Mech Mach Theory, 1992, 27(3): 235-242

[5] Rajesh P S, Linda C S. Reliability and efficiency of the existing spectral methods for isomorphism detection. ASME J Mech Des, 2006, 128(6): 1246-1252

[6] Mruthyunjaya T S, Balasubramanzan H R. In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains. Mech Mach Theory, 1987, 22(2): 131-140

[7] Tang C, Liu T. Degree code: a new mechanism identifier. ASME J Mech Des, 1993, 115(3): 627-630

[8] Rao A C, Varada R D. Application of the hamming number technique to detect isomorphism among kinematic chains and inversion. Mech Mach Theory, 1991, 26(1): 55-75

[9] He P R, Zhang W J, Li Q. Some further development on the eigensystem approach for graph isomorphism detection. Journal of the Franklin Institute, 2005, 342(6): 657-673

[10] Ding H F, Huang Z. The establishment of the canonical perimeter topological graph of kinematic chains and isomorphism identification. ASME J Mech Des, 2007,129(9): 915-923

[11] Hwang W, Hwang Y. An algorithm for the detection of degenerate kinematic chains. Mathematical and Computer Modelling, 1991, 15(11): 9-15

[12] Tuttle E R. Generation of planar kinematic chains. Mech Mach Theory, 1996, 31(6): 729-748

[13] Lee H, Yoon Y. Detection of rigid structure in enumerating basic kinematic chain by sequential removal of binary link string. JSME International Journal, 1992, 35(4): 647-651

[14] Rajesh P S, Linda C S. Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm. Mech Mach Theory, 2006, 41(9): 1021-1030

[15] Ding H F, Huang Z. A unique representation of the kinematic chain and the atlas database. Mech Mach Theory, 2007, 42(6): 637-651

[16] Shin J K, Krishnamurty S. On identification and canonical numbering of pin jointed kinematic chains. ASME J Mech Des, 1994, 116(1): 182-188

[17] Wang D L, Dai J S. Theoretical foundation of metamorphic mechanism and its synthesis. Chinese Journal of Mechanical Engineering, 2007, 43(8): 32-42

[18] McKay B D. Practical graph isomorphism. Congressus Numerantium, 1981, 30(1): 45-87

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg