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The establishment of edge-based loop algebra theory of kinematic chains and its applications

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Abstract

Based on the edge-based array representation of loops in the topological graphs of kinematic chains, this paper first proposes three arithmetic operations of loops. Then the concept of the independent loop set as well as its determination rules is introduced, and a new structure decomposition algorithm of kinematic chains is presented. Based on the algorithm, an automatic and efficient method for rigid sub-chain detection and driving pair selection of kinematic chains is proposed. Finally, an index is proposed to assess computation complexity of kinematic analysis with respect to different driving pair selections.

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Acknowledgments

This research is sponsored by the NSFC (Grant No. 50905155), the China Postdoctoral Science Foundation Funded Project (Grant No. 200801271 and No. 20080430122), and the Hebei Nature Science Foundation under Grant E2008000808.

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Authors and Affiliations

  1. Robotics Research Center, Yanshan University, 066004, Qinhuangdao, China

    Huafeng Ding & Zhen Huang

  2. Key Lab of Industrial Computer Control Engineering of Hebei Province, 066004, Qinhuangdao, China

    Huafeng Ding & Jing Zhao

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  1. Huafeng Ding
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  2. Jing Zhao
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  3. Zhen Huang
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Correspondence to Huafeng Ding.

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Ding, H., Zhao, J. & Huang, Z. The establishment of edge-based loop algebra theory of kinematic chains and its applications. Engineering with Computers 26, 119–127 (2010). https://doi.org/10.1007/s00366-009-0141-6

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  • DOI: https://doi.org/10.1007/s00366-009-0141-6

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