A three-dimensional forward dynamic model of the golf swing optimized for ball carry distance

Abstract

A 3D predictive golfer model can be a valuable tool for investigating the golf swing and designing new clubs. A forward dynamic model, which includes a four degree of freedom golfer model, a flexible shaft based on Rayleigh beam theory, an impulse-momentum impact model and a spin rate dependent aerodynamic ball model, is presented. The input torques for the golfer model are provided by parameterized joint torque generators that have been designed to mimic muscle torque production. These joint torques are optimized to create swings and launch conditions that maximize carry distance. The flexible shaft model allows for continuous bending in the transverse directions, axial twisting of the club and variable shaft stiffness as a function of the length. The completed four-part model with the default parameters is used to estimate the ball carry of a golf swing using a particular club. This model will be useful for experimenting with club design parameters to predict their effect on the ball trajectory and carry distance.

Dynamics of the Golf Club-Grip Interaction

“…In recent studies by Mackenzie and Sprigings [2] and Balzerson et al [3], a four DoF golfer model incorporating a flexible club was shown to provide close comparison to experimental kinematics and kinetics of a low-handicap golfer. This model is represented in Figure 1.…”

“…Revolute joints between bodies represent the torso, shoulder, forearm, and wrist joints. As with the model used in [2,3], the torso was inclined 30° to the vertical, and the swing plane of the arms was rotated 50° from the horizontal. Body segment inertial parameters matching another advanced biomechanics golfer model were used in this study, including location of the hips above the ground [4].…”

“…This method of determining optimal joint torques has been effective in producing similar results to actual golf swings [2][3][4]. It is of interest to compare the optimal control generated without a restriction on the threshold and frequency of activation that drives the joints in the model.…”

Predictive Dynamic Simulation of Seated Start-Up Cycling Using Olympic Cyclist and Bicycle Models

“…The torque values were scaled at each time point based on the joint angle and angular velocity to represent the muscle force-velocity and force-length relationships. Each joint had a maximum rate of torque development that was based on muscle activation and deactivation time constants used by Balzerson et al [4]. Passive joint torques were also included for each joint.…”

“…This reduces the number of variables and simplifies the optimal control problem. Joint torque models have been implemented extensively in predictive simulation of human movement, especially with sports applications [3,4].…”