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Nonlinear Dynamic Model of Basic Tennis Actions

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Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript

Abstract

Background

A number of factors influence the game of tennis. These include different shapes and sizes of the racket and string bed, initial tension in strings, racket-holding techniques, impact force, as well as damping and stiffness of players’ shoulders and wrists.

Purpose

A nonlinear analytical dynamic model of basic tennis actions involving the racket, string bed, and players’ anatomy has been proposed. A dynamic model for the assessment of vibrations induced in players when playing tennis by means of four motions and involving basic parameters concerning the racket and string bed as well as players’ shoulder and wrists is proposed.

Methods

In the proposed model, the racket, string bed, shoulder, and wrists are approximated as a flexible beam, thin membrane, torsional spring, and damping system, respectively. The dynamic model predicts vibration characteristics caused by the action of an impact force on the racket through use of Lagrange’s equation. A governing equation considering four motions is computed using Runge–Kutta techniques. To assess the accuracy of the proposed model, vibrations predicted in the player’s shoulder and racket handle are compared against those obtained via experiments using inertial measurement units (IMUs).

Results

The proposed model represents a method to assess risks associated with the occurrence of injuries when playing tennis and measures to be taken to avoid the same through comparison of proposed-model-predicted results against experimental data and three sets of comparisons.

Conclusions

Conclusions of this study demonstrate that using a small impact force and holding the racket at a greater distance from the butt-end of the grip are useful techniques towards reducing the risk of injuries to the shoulder and wrist, and differences in string tension have a little effect on vibrations set up in the shoulder and wrist.

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Acknowledgements

This project was supported by the Postgraduate Creative Fund of JiangSu Province in China (Grant no. CXLX13-081). The project supported by scientific and technological research program of Chongqing municipal education commission (Grant No. KJ1603004). The research was also supported by the China Scholarship Council (Grant no. 201406090035) and conducted in part at the University of Michigan where the first author (H. Hong) visited during 2014–16.

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Authors and Affiliations

  1. School of Mechanical Engineering, Southeast University, Nanjing, Jiangsu Province, China

    Huihui Hong, Liang Han & Liang Chang

  2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

    Huihui Hong

  3. Chongqing Industry Polytechnic College, Chongqing, China

    Yunfei Liao

  4. Department of Mechanical Engineering, McMaster University, Hamilton, ON, L8S4L8, Canada

    Chuan Hu

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  1. Huihui Hong
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  2. Liang Han
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  3. Yunfei Liao
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  4. Chuan Hu
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  5. Liang Chang
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Correspondence to Liang Han.

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Hong, H., Han, L., Liao, Y. et al. Nonlinear Dynamic Model of Basic Tennis Actions. J. Vib. Eng. Technol. 7, 497–505 (2019). https://doi.org/10.1007/s42417-019-00147-8

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  • DOI: https://doi.org/10.1007/s42417-019-00147-8

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