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Accuracy analysis of spatial multi-loop mechanism effected by paired bearings support joint clearance

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Abstract

The primary objective of this work is to present a three-dimensional (3D) clearance model of the paired bearings support joint (PBS-joint) and address the influence of PBS-joint clearance on the accuracy of the spatial multi-loop mechanism. Through the synthetic use of the vector and homogeneous coordinate transformation methods, the 3D clearance model of the PBS-joint is obtained on the basis of the static balance condition. When clearance is equated as a spatial virtual link, the error space solution models of serial mechanism and single-loop mechanism are developed respectively according to the Denavit-Hartenberg method and the geometric closure condition. The error space standardization solution model of the multi-loop mechanism is then presented through improving the low-layer loop sequence description method of the topological structure relations. Finally, the application in the basic loop mechanism is demonstrated to discuss the procedures adopted in this work and the influence of the PBS-joint clearance. Results show that the PBS-joint clearance may cause the error on the point with a 3D deviation transmission path to deviate the normal distribution. Moreover, the plane-joint clearance model may not yield an accurate analysis of the spatial mechanism.

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Abbreviations

PBS-joint:

Paired bearings support joint

Plane-Joint:

Plane revolute joint

3D:

Three-dimensional

BUD:

Basic unit on the directrix

MBUG:

Main basic unit on the generatrix

ABUG:

Assistant basic unit on the generatrix

CRF:

Characteristic reference frames

PCRF:

Pose characterization reference frame

G r :

Radial clearance of bearing

r eb :

Vector from a to b in O′j - x′jy′jz′j

\(r_{ab}^k\) :

The k direction component of rab

μ :

Mean value

σ :

Standard deviation

j T i :

Homogeneous transformation matrix from Oj - xjyjzj to Oi - xiyizi

j A i :

Homogeneous transformation matrix from Oj - xjyjzj to Oi - xiyizi after Oi - xiyizi being deviated

Rot :

Rotation operators

Trans :

Translation operators

R :

Rotation matrix

P :

Position vector

P e :

Position deviation

φ e :

Attitude deviation

Θ:

Error space

Г:

Error space set

///:

Rank of single loop

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Acknowledgments

This work was supported by the National Natural Science Foundation of the People’s Republic of China (Grant number 51675264) and the Natural Science Foundation of Jiangsu Province (Grant number BK20180437).

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Authors and Affiliations

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

    Fei Lin, Chuanzhi Chen & Jinbao Chen

  2. Aerospace Systems Engineering Shanghai, Shanghai, 201108, China

    Meng Chen

Authors
  1. Fei Lin
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  2. Chuanzhi Chen
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  3. Jinbao Chen
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  4. Meng Chen
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Corresponding author

Correspondence to Chuanzhi Chen.

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Recommended by Editor No-cheol Park

Fei Lin received his Masters degree in Machinery and Electronics Engineering from the Jiangxi University of Science and Technology, China, in 2013. At present, he is pursuing a Ph.D. in Aerospace Science and Technology from Nanjing University of Aeronautics and Astronautics. His current research interests include spacecraft structure and mechanism design and nonlinear stochastic dynamics.

Chuanzhi Chen holds a Ph.D. in Aerospace Science and Technology from Nanjing University of Aeronautics and Astronautics. His research interests include low-impact docking mechanism, spacecraft structure and institutions, and structure dynamics of spacecraft.

Jinbao Chen holds a Ph.D. in Aerospace Science and Technology from Nanjing University of Aeronautics and Astronautics. His research interests include structure dynamics of spacecraft, spacecraft structure, and mechanism design.

Meng Chen obtained his Ph.D. in Mechanical Design and Theory from the Huazhong University of Science and Technology, China, in 2003. Currently, he is a Deputy Chief Engineer at Aerospace Systems Engineering Shanghai, China. His research interests include structure dynamics of spacecraft, spacecraft structure, and mechanism design.

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Lin, F., Chen, C., Chen, J. et al. Accuracy analysis of spatial multi-loop mechanism effected by paired bearings support joint clearance. J Mech Sci Technol 34, 987–1003 (2020). https://doi.org/10.1007/s12206-020-0202-8

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  • DOI: https://doi.org/10.1007/s12206-020-0202-8

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