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A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

Author

Listed:
  • Ying Zhang
  • Xin Liu
  • Shimin Wei
  • Yaobing Wang
  • Xiaodong Zhang
  • Pei Zhang
  • Changchun Liang

Abstract

A geometric modeling and solution procedure for direct kinematic analysis of 6-4 Stewart platforms with any link parameters is proposed based on conformal geometric algebra (CGA). Firstly, the positions of the two single spherical joints on the moving platform are formulated by the intersection, dissection, and dual of the basic entities under the frame of CGA. Secondly, a coordinate-invariant equation is derived via CGA operation in the positions of the other two pairwise spherical joints. Thirdly, the other five equations are formulated in terms of geometric constraints. Fourthly, a 32-degree univariate polynomial equation is reduced from a constructed 7 by 7 matrix which is relatively small in size by using a Gröbner-Sylvester hybrid method. Finally, a numerical example is employed to verify the solution procedure. The novelty of the paper lies in that the formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA and the size of the resultant matrix is smaller than those existed.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:6245341
    DOI: 10.1155/2018/6245341
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    Cited by:

    1. 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.

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