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Structural Analysis of Parallel Mechanisms Using Conformal Geometric Algebra

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Intelligent Robotics and Applications (ICIRA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9834))

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Abstract

The operable description of parallel mechanisms is the key to automatic derivation of structural analysis and synthesis. Conformal geometric algebra is introduced to describe robot mechanisms in this paper. A group of basis bivectors {e 23, e 31, e 12, e 1∞, e 2∞, e 3∞} is established to express position and orientation characteristics of the joint axis. The union of each joint’s characteristics of serial mechanisms is defined via outer product operation and the intersection of each limb’s characteristics of parallel mechanisms is defined by shuffle product operation, respectively. In this work, a new algebraic symbol algorithm for end-effectors’ characteristics is proposed and proved validity via two case studies of 3-RRR and 4-URU PMs which is suitable for computer-aided derivation of mechanisms position and orientation characteristics.

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Acknowledgement

The authors would like to acknowledge the financial support of the Natural Science Foundation of China under Grant 51475050 and also thank the reviewers for their suggestions and comments, which have helped to improve the quality of this paper.

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Authors and Affiliations

  1. Shanghai University of Engineering Science, Shanghai, 201620, China

    Lubin Hang & Chengwei Shen

  2. Changzhou University, Changzhou, 213016, China

    Tingli Yang

Authors
  1. Lubin Hang
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  2. Chengwei Shen
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  3. Tingli Yang
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Corresponding author

Correspondence to Lubin Hang .

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Editors and Affiliations

  1. Tokyo Metropolitan University , Tokyo, Japan

    Naoyuki Kubota

  2. Kyushu University , Fukuoka, Japan

    Kazuo Kiguchi

  3. University of Portsmouth , Portsmouth, United Kingdom

    Honghai Liu

  4. Tokyo Metropolitan University , Tokyo, Japan

    Takenori Obo

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© 2016 Springer International Publishing Switzerland

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Hang, L., Shen, C., Yang, T. (2016). Structural Analysis of Parallel Mechanisms Using Conformal Geometric Algebra. In: Kubota, N., Kiguchi, K., Liu, H., Obo, T. (eds) Intelligent Robotics and Applications. ICIRA 2016. Lecture Notes in Computer Science(), vol 9834. Springer, Cham. https://doi.org/10.1007/978-3-319-43506-0_14

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  • DOI: https://doi.org/10.1007/978-3-319-43506-0_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43505-3

  • Online ISBN: 978-3-319-43506-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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