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Analysis of dynamic modeling and solution of 3-RPS parallel mechanism based on conformal geometric algebra

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Abstract

In this paper, the dynamic modeling and generalized force analysis of three-(rotation pair)-(prismatic pair)-spherical pair (3-RPS) parallel mechanism were carried out for the first time based on the five-dimensional geometric algebra space—(4,0,1) conformal geometric. Compared with the traditional homogeneous matrix method, the maximum error values of generalized force of the three branch chains are \(1.90 \times 10^{ - 4} \,{\text{N}}\),\(1.39 \times 10^{ - 4} \,{\text{N}}\) and \({6}{\text{.0}} \times {10}^{{ - {5}}} \;{\text{N}}\),respectively. The results are basically consistent with the homogeneous matrix method. For composite rigid body transformation of two rotational motions, the rotation matrix method needs 27 times of multiplication and 18 times of addition, while the conformal geometric method only needs 16 times of multiplication and 15 times of addition. The computational efficiency of this method can be improved. In five-dimensional space, derivative operation can be linearly mapped to multiplication operation in three-dimensional space, so that dynamic equation has no derivative term. The dynamic model can separate variables of known and unknown, and realize parallel computation. This method provides a new idea for dynamic modeling and solving of parallel mechanism.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51975277).

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Zhicheng Song, Bai Chen, Lingyu Wang & Hongtao Wu

  2. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Surong Jiang

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  1. Zhicheng Song
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Correspondence to Surong Jiang or Hongtao Wu.

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Song, Z., Jiang, S., Chen, B. et al. Analysis of dynamic modeling and solution of 3-RPS parallel mechanism based on conformal geometric algebra. Meccanica 57, 1443–1455 (2022). https://doi.org/10.1007/s11012-022-01472-1

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