Dynamic Optimization Of The Golf Swing (P2)
Biomechanical Model Advancements
In a study examining the role of upper torso and pelvic rotation in driving performance for golfers of various skill levels, it was found that the relative rotation of the upper torso with respect to the pelvis, referred to as the X-factor, is correlated with ball velocity (r = 0.54, p < 0.001). Balzerson et al. made an initial step toward modeling the X-factor by including a non-linear passive resistive torque acting on the torso. Correctly modelling the X-factor using a relative angle of separation requires the addition of the pelvis. The pelvis was added to the model via a universal joint, allowing the pelvis to rotate about a vertical axis, while the torso rotates about its own axis tilted forward towards the golf ball. There are no experiments in literature measuring the passive resistance for pelvis rotation relative to the ground, so the torso’s passive torque was also applied to the pelvis.
The preceding models contained a single DOF shoulder joint capable of horizontal adduction. A second axis of rotation has been added, allowing vertical flexion-extension of the shoulder. The biomechanical rotational DOFs are displayed. The DOFs are actuated by the same muscle torque generators used in the preceding models, represented by the following equation:
where Tm is the maximum isometric torque, τ and τ are the activation and deactivation time constants, t is the total time from the start of the torque generator activation, and t is the total time after deactivation. Body segment lengths and inertia parameters were taken from de Leva, where the lower trunk segment was used for the pelvis, and the upper and mid trunk segments were combined for the torso. To actuate the vertical DOF of the shoulder, the maximum isometric shoulder torque was decomposed into two components:
where Ts is the maximum isometric shoulder torque, Tsh, is the horizontal component, Tsv, is the vertical component, and r is the shoulder torque ratio. The r-value effectively controls the plane of the swing.
Sprigings and Neal incorporated the Hill force-velocity relationship into their muscle torque generators by scaling their instantaneous isometric torque using the equation: