Dynamic Optimization of the Golf Swing (P1)

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Advances in golf club performance are typically based on the notion that golfer biomechanics do not change when modifications to the golf club are made. The purpose of this work was to develop a full-swing, forward dynamic golf drive model capable of providing deeper understanding of the interaction between golfer biomechanics and the physical properties of golf clubs. A three-dimensional biomechanical model of a golfer, a Rayleigh beam model of a flexible club, an impact model based on volumetric contact, and a spin-rate dependent aerodynamic ball flight model are used to simulate a golf drive. The six degree-of-freedom biomechanical model features a two degree-of-freedom shoulder joint and a pelvis to model the X-factor. It is driven by parametric joint torque generators designed to mimic muscle torque production, which are scaled by an eccentric-concentric torque-velocity function. Passive resistive torque profiles fit to experimental data are applied to the joints, representing the resistance caused by ligaments and soft tissues near the joint limits. Using a custom optimization routine combining genetic and searchbased algorithms, the biomechanical golf swing model was optimized by maximizing carry distance. Comparing the simulated grip kinematics to a golf swing motion capture experiment, the biomechanical model effectively reproduced the motion of an elite golf swing.


Due to its predictive capabilities, a three-dimensional (3D) dynamic simulation of a golf drive is a valuable asset for providing insights on optimal golfer biomechanics and golf club behavior. Until recently, forward dynamic golf swing models have been limited to two-dimensions, i.e., the motion of the golf shaft has been constrained to a single plane. In 2009, MacKenzie and Sprigings published the first 3D forward dynamic model of the golf swing, motivated by evidence that the golf swing is not planar. Their four degree-of-freedom (DOF) rigid-body biomechanical model was actuated by parametric muscle torque generators designed to mimic biomechanical joint torque production. The biomechanical model was paired with a discretized flexible shaft comprised of four rigid sections interconnected by rotational spring-damper elements to simulate shaft deflection during the downswing. To vaidate the model, the simulated kinematics were regressed onto motion capture data of a “category-1” golfer using a genetic algorithm. Optimization of the golf swing was then performed by maximizing the horizontal clubhead speed at impact.

Dynamic Optimization of the Golf Swing (P1)

Balzerson et al. improved the model of MacKenzie and Sprigings, supplementing the biomechanical model with experimental passive joint torque profiles from literature and using an analytical flexible beam based on Rayleigh beam theory to model the golf shaft. Developed using the multibody software MapleSim (Maplesoft, Waterloo, ON, Canada), their golf swing model was combined with a momentum-based free-body impact model and a spin-rate dependent aerodynamic ball flight model to enable biomechanical optimization through maximization of carry distance as opposed to clubhead speed. Although providing a notable improvement to the model and optimization scheme of MacKenzie and Sprigings, the shaft deflection results of Balzerson et al. displayed spurious oscillations that were inconsistent with experimental measurements. The oscillations, possibly caused by a lack of damping, have since been resolved using an iterated flexible beam component incorporating internal damping, available in the 2016.2 version of MapleSim. The new flexible club model was validated against motion capture data in associated work by McNally et al. , showing good agreement with experimental shaft deflection in the full swings of ten elite golfers. In the same work, an analytical impact model based on volumetric contact was integrated with the flexible club and tuned using experimental data.

In addition to upgrading the flexible club and impact with these validated models, a number of biomechanical improvements were made to address the shortcomings of the preceding models: a body segment representing the pelvis has been added to provide insights on the significance of torsopelvic separation (X-factor), a DOF has been added to the shoulder joint to enable a dynamic swing plane, the backswing has been modelled to overcome shaft initialization issues, and the torquevelocity scaling function has been modified to account for eccentric contractions. It should be noted that this work is an extension of Balzerson et al. and therefore knowledge of the aforementioned models is helpful.

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