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

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Acknowledgements

This research was sponsored by the National Natural Science Foundation of China (Grant No. 50575197), the China Postdoctoral Science Foundation Funded Project (Nos. 200801271, 20080430122), and the Postdoctoral Funded Project by Yanshan University.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg