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Dynamic Modeling for Spatial Revolute Joint with Clearances in Multibody Systems Based on HLCP

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Robotics and Mechatronics (ISRM 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 78))

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Abstract

This paper presents a modeling and simulation method for rigid multibody system (MBS) with clearance-affected spatial revolute joints (SRJ) under the assumption that the clearance is much less than the physical dimension of SRJ. The SRJ is treated as an assembly of a rigid journal undergoing no-impact fixed-point motion in a bearing. A simple formulation for solving non-smooth dynamics of MBS with spatial revolute joints with clearances (SRJC) is developed by employing the complementary condition of the normal contact force. The geometric constraints of the SRJ has been transformed into a set of orthogonal bilateral constraints. The contact state determined by the magnitude and orientation of normal constraint forces in cylindrical pairs is formulated as a horizontal linear complementarity problem (HLCP) which is solved by the first kind of Lagrange’s equation and the Baumgarte stabilization method. A precession gyro is considered as a demonstrative application and the numerical results show some dynamical behaviors of MBS containing SRJC. Particularly, the proposed method can be equally applied to non-smooth dynamics of MBS considering the friction and impact.

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Acknowledgments

This research has been supported by the National Natural Science Foundation of China under Grant 51635002(Key Program), 51605011, the Fundamental Research Funds for the Central Universities (YWF-19-BJ-J-336), and the State Key Laboratory of Robotics and System (HIT). The authors gratefully acknowledge the supporting agencies.

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Authors and Affiliations

  1. Beihang University, Beijing, 100191, China

    Long Li, Shengnan Lyu & Xilun Ding

Authors
  1. Long Li
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  2. Shengnan Lyu
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  3. Xilun Ding
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Corresponding author

Correspondence to Shengnan Lyu .

Editor information

Editors and Affiliations

  1. School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW, Australia

    Chin-Hsing Kuo

  2. Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan

    Pei-Chun Lin

  3. Department of Mechanical Engineering, National Central University, Taoyuan City, Taiwan

    Terence Essomba

  4. Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, New Taipei City, Taiwan

    Guan-Chen Chen

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Li, L., Lyu, S., Ding, X. (2020). Dynamic Modeling for Spatial Revolute Joint with Clearances in Multibody Systems Based on HLCP. In: Kuo, CH., Lin, PC., Essomba, T., Chen, GC. (eds) Robotics and Mechatronics. ISRM 2019. Mechanisms and Machine Science, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-030-30036-4_9

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