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Automated generation of Kempe linkage and its complexity

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Abstract

It is a famous result of Kempe that a linkage can be designed to generate any given plane algebraic curve. In this paper, Kempe’s, result is improved to give a precise algorithm for generating Kempe linkage. We proved that for an algebraic plane curve of degreen Kempe linkage uses at mostO(n 4) links. Efforts to implement a program which may generate Kempe linkage and simulation of the generation process of the plane curves are presented in the paper.

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Authors and Affiliations

  1. Institute of Systems Sciences, Chinese Academy of Sciences, 100080, Beijing, P.R. China

    Gao Xiaoshan & Zhu Changcai

Authors
  1. Gao Xiaoshan
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  2. Zhu Changcai
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GAO Xiaoshan received his B.S. degree in computer science from the National University of Defence Science and Technology in 1984, and his Ph.D. degree in mathematics from the Institute of Systems Science, Chinese Academy of Sciences in 1988. His main research interests include automated reasoning, symbolic computation, geometric constraint solving and intelligent CAD, intelligen CAI (computer aided instruction). He has published more than fifty papers and two monographs.

ZHU Changcai received his B.S. degree in mathematics from University of Science & Technology of China in 1997 and his M.S. degree in mathematics from Institute of Systems Science in 1999. Now he is a Ph.D. candidate in Institute of Systems Science. His major research interests are design and analysis of linkage, computational complexity, and satisfiability problem.

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Gao, X., Zhu, C. Automated generation of Kempe linkage and its complexity. J. Comput. Sci. & Technol. 14, 460–467 (1999). https://doi.org/10.1007/BF02948787

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  • DOI: https://doi.org/10.1007/BF02948787

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