Skip to main content
Log in

Optimal control of joint torques using direct collocation to maximize ball carry distance in a golf swing

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

Forward dynamics golf swing simulations are important to gain insight into how a golfer should swing a particular club and which design improvements should be considered by golf club manufacturers. A new method of optimizing a four degree-of-freedom (DoF) biomechanical golfer model swinging a flexible shaft with a rigid clubhead was developed using a direct orthogonal collocation approach. The kinematic and kinetic results of the simulation confirm previous findings on optimal joint angle trajectories, shaft deflection patterns, and joint torque profiles in a golf swing. This optimization approach is a promising development in biomechanics research, and future work will implement this method in three-dimensional swing models that have been shown to have higher robustness and fidelity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Economic Impact of Golf in Canada (2014). Online. Accessed 10-December-2018. http://canadagolfs.ca/wp-content/uploads/2014/06/SNG-Golf-2014-Executive-Summary-FINAL-Report-JUNE-2_ENG.pdf

  2. Betzler, N., Monk, S., Wallace, E., Otto, S.R., Shan, G.: From the double pendulum model to full-body simulation: evolution of golf swing modeling. Sports Technol. 1(4–5), 175–188 (2008)

    Article  Google Scholar 

  3. Cochran, A., Stobbs, J.: The Search for the Perfect Swing: An Account of the Golf Society of Great Britain Scientific Study. Heinemann (1968)

    Google Scholar 

  4. Jorgensen, T.P.: The Physics of Golf, 2nd edn. Springer, New York (1999)

    Book  Google Scholar 

  5. Lampsa, M.A.: Maximizing distance of the golf drive: an optimal control study. J. Dyn. Syst. Meas. Control 97(4), 362–367 (1975)

    Article  Google Scholar 

  6. Sprigings, E.J., Neal, R.J.: An insight into the importance of wrist torque in driving the golfball: a simulation study. J. Appl. Biomech. 16(4), 356–366 (2000)

    Article  Google Scholar 

  7. MacKenzie, S.J., Sprigings, E.J.: A three-dimensional forward dynamics model of the golf swing. Sports Eng. 11(4), 165–175 (2009)

    Article  Google Scholar 

  8. Balzerson, D., Banerjee, J., McPhee, J.: A three-dimensional forward dynamic model of the golf swing optimized for ball carry distance. Sports Eng. 19(4), 237–250 (2016)

    Article  Google Scholar 

  9. McNally, W., McPhee, J.: Dynamic optimization of the golf swing using a six degree-of-freedom biomechanical model. In: MDPI Proceedings of the 12th Conference of the International Sports Engineering Association, vol. 2, no. 6 (2018)

    Google Scholar 

  10. Yeadon, M.R., King, M.A.: Evaluation of a torque driven simulation model of tumbling. J. Appl. Biomech. 18, 195–206 (2002)

    Article  Google Scholar 

  11. King, M.A., Wilson, C., Yeadon, M.R.: Evaluation of a torque driven-model of jumping for height. J. Appl. Biomech. 22, 264–274 (2006)

    Article  Google Scholar 

  12. Kentel, B.B., King, M.A., Mitchell, S.R.: Evaluation of a subject-specific, torque-driven computer simulation model of one-handed tennis backhand ground strokes. J. Appl. Biomech. 27(4), 345–354 (2011)

    Article  Google Scholar 

  13. Rao, A.V.: A survey of numerical methods for optimal control. Adv. Astronaut. Sci. 135(1), 497–528 (2009)

    Google Scholar 

  14. Laschowski, B., Mehrabi, N., McPhee, J.: Optimization-based motor control of a Paralympic wheelchair athlete. Sports Eng. 2, 1–9 (2018)

    Google Scholar 

  15. De Groote, F., Kinney, A.L., Rao, A.V., Fregly, B.J.: Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem. Ann. Biomed. Eng. 44(10), 2922–2936 (2016)

    Article  Google Scholar 

  16. De Leva, P.: Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. J. Biomech. 29(9), 1223–1230 (1996)

    Article  Google Scholar 

  17. Sandhu, S., Millard, M., McPhee, J., Brekke, D.: 3D dynamic modelling and simulation of a golf drive. Proc. Eng. 2(2), 3243–3248 (2010)

    Article  Google Scholar 

  18. McNally, W.: Forward Dynamic Simulation of a Golf Drive: Optimization of Golfer Biomechanics and Equipment. Master’s thesis, University of Waterloo (2018)

  19. Patterson, M., Rao, A.: GPOPS II: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans. Math. Softw. 41, 1–37 (2012)

    Article  MathSciNet  Google Scholar 

  20. Bastian, A.J., Zackowski, K.M., Thach, W.T.: Cerebellar ataxia: torque deficiency or torque mismatch between joints? J. Neurophysiol. 83, 3019–3030 (2000)

    Article  Google Scholar 

  21. Quintavalla, S.: A generally applicable model for the aerodynamic behavior of golf balls. In: Science and Golf IV: Proceedings of the 2002 World Scientific Congress of Golf, pp. 341–348 (2002)

    Google Scholar 

Download references

Acknowledgements

The authors acknowledge financial support from McPhee’s Tier I Canada Research Chair in Biomechatronic System Dynamics.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Colin Brown.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Brown, C., McNally, W. & McPhee, J. Optimal control of joint torques using direct collocation to maximize ball carry distance in a golf swing. Multibody Syst Dyn 50, 323–333 (2020). https://doi.org/10.1007/s11044-020-09734-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-020-09734-0

Keywords

Navigation