#
Dynamic Optimization of the Golf Swing Using a Six Degree-of-Freedom Biomechanical Model^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Biomechanical Model Advancements

_{max}/Γ. The pioneering experiments of Katz [10] suggest that the force-velocity relationship diverges from Hill’s model when a force greater than isometric tension is applied. The divergence was illustrated by a discontinuity in velocity at the onset of lengthening and an exponential increase in the rate of lengthening with increasing applied force. Van Soest et al. [11] provide a generic equation for the eccentric force-velocity relationship observed in the experiments of Katz. The rotational equivalent of this equation was manipulated to use the same variables as Sprigings and Neal:

#### 2.2. Golf Drive Simulation

#### 2.3. Optimization

- the torso and shoulder activate and deactivate simultaneously,
- the pelvis, torso, shoulder and arm all activate at t = 0 to initiate the backswing, and

## 3. Results, Discussion and Conclusions

_{p}. The optimized biomechanical timings indicate that the torso activated before the pelvis to commence the downswing. This result is inconsistent with real golf swings, where the rotation of the pelvis typically initiates the downswing. The model is not exploiting the extra power that could be generated by creating a large X-factor. It is possible that biomechanical constraints render the model’s X-factor ineffective at generating extra clubhead speed with a favorable clubhead delivery. One of the major limitations of the biomechanical model is the rigid body representation of the torso. In a real golf swing, the spine bends and contorts, causing a noticeable displacement of the thorax during the downswing. The flexibility of the spine could be what permits the sequential driving of the pelvis followed by the torso during the downswing.

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison of simulated and experimental grip kinematics from elite golfers. (

**a**) Grip position; (

**b**) Grip orientation defined by Y-X-Z Euler rotations. The shaded bands represent one standard deviation of the measured kinematics for the ten elite golfers (100 golf swings total).

Variable | Lower Bound | Upper Bound | Solution | Variable | Lower Bound | Upper Bound | Solution |
---|---|---|---|---|---|---|---|

0.3 | 1.2 | 0.856 | ${\mathrm{P}}_{\mathrm{off},\mathrm{down}}$ | 0.8 | 1.0 | 1.000 | |

${\mathrm{h}}_{\mathrm{p}}$^{1} | 0.45 | 0.55 | 0.496 | ${\mathrm{TS}}_{\mathrm{off},\mathrm{down}}$ | 0.8 | 1.0 | 1.000 |

${\mathrm{P}}_{\mathrm{off},\mathrm{back}}$ | 0.5 | 0.8 | 0.688 | ${\mathrm{A}}_{\mathrm{on},\mathrm{down}}$ | 0.7 | 1.0 | 0.888 |

${\mathrm{TS}}_{\mathrm{off},\mathrm{back}}$ | 0.5 | 0.8 | 0.619 | ${\mathrm{A}}_{\mathrm{off},\mathrm{down}}$ | 0.8 | 1.0 | 0.987 |

${\mathrm{A}}_{\mathrm{off},\mathrm{back}}$ | 0.0 | 0.6 | 0.103 | ${\mathrm{W}}_{\mathrm{on},\mathrm{down}}$ | 0.7 | 1.0 | 0.899 |

${\mathrm{W}}_{\mathrm{on},\mathrm{back}}$ | 0.0 | 0.6 | 0.252 | ${\mathrm{W}}_{\mathrm{off},\mathrm{down}}$ | 0.8 | 1.0 | 1.000 |

${\mathrm{W}}_{\mathrm{off},\mathrm{back}}$ | 0.4 | 0.8 | 0.771 |

^{1}${\mathrm{h}}_{\mathrm{p}}$ is the ratio of the height of the pelvis in the model to the overall height of the golfer standing upright.

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McNally, W.; McPhee, J. Dynamic Optimization of the Golf Swing Using a Six Degree-of-Freedom Biomechanical Model. *Proceedings* **2018**, *2*, 243.
https://doi.org/10.3390/proceedings2060243

**AMA Style**

McNally W, McPhee J. Dynamic Optimization of the Golf Swing Using a Six Degree-of-Freedom Biomechanical Model. *Proceedings*. 2018; 2(6):243.
https://doi.org/10.3390/proceedings2060243

**Chicago/Turabian Style**

McNally, William, and John McPhee. 2018. "Dynamic Optimization of the Golf Swing Using a Six Degree-of-Freedom Biomechanical Model" *Proceedings* 2, no. 6: 243.
https://doi.org/10.3390/proceedings2060243