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A Novel Geometric Modeling and Calculation Method for Forward Displacement Analysis of 6-3 Stewart Platforms

Author

Listed:
  • Ganmin Zhu

    (School of Modern Post, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Shimin Wei

    (School of Modern Post, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Ying Zhang

    (School of Modern Post, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Qizheng Liao

    (School of Modern Post, Beijing University of Posts and Telecommunications, Beijing 100876, China)

Abstract

A novel geometric modeling and calculation method for forward displacement analysis of the 6-3 Stewart platforms is proposed by using the conformal geometric algebra (CGA) framework. Firstly, two formulas between 2-blade and 1-blade are formulated. Secondly, the expressions for two spherical joints of the moving platform are given via CGA operation. Thirdly, a coordinate-invariant geometric constraint equation is deduced. Fourthly, a 16-degree univariate polynomial equation without algebraic elimination by using the Euler angle substitution is presented. Fifthly, the coordinates of three spherical joints on the moving platform are calculated without judging the radical symbols. Finally, two numerical examples are used to verify the method. The highlight of this paper is that a new geometric modeling and calculation method without algebraic elimination is obtained by using the determinant form of the CGA inner product algorithm, which provides a new idea to solve a more complex spatial parallel mechanism in the future.

Suggested Citation

  • Ganmin Zhu & Shimin Wei & Ying Zhang & Qizheng Liao, 2021. "A Novel Geometric Modeling and Calculation Method for Forward Displacement Analysis of 6-3 Stewart Platforms," Mathematics, MDPI, vol. 9(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:442-:d:504240
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    References listed on IDEAS

    as
    1. Feng Wei & Shimin Wei & Ying Zhang & Qizheng Liao, 2017. "Forward Displacement Analysis of a General 6-3 Stewart Platform Using Conformal Geometric Algebra," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-9, February.
    2. Ying Zhang & Xin Liu & Shimin Wei & Yaobing Wang & Xiaodong Zhang & Pei Zhang & Changchun Liang, 2018. "A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-9, February.
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