A continuous analytical shaft model for fast dynamic simulation of the golf swing

Investigating the Influence of Shaft Balance Point on Clubhead Speed: A Simulation Study

“…All shafts were given the same outer radius profile by setting 𝑟 , and 𝑟 , to 8 and 5 mm, respectively. These dimensions are consistent with experimental carbon fiber composite golf shafts [10]. The shaft length was set to 1.105 m (43.5"), and the density of each shaft was calculated by assuming a total shaft mass of 65 g. Shaft A was given a constant wall thickness by setting 𝑡 to 1 mm and 𝑡 to zero.…”

“…Upon further investigation, it was found that shaft bending could be attenuated without scaling the bending stiffness by increasing the time constants 𝜏 and 𝜏 , which control the rate of activation and deactivation of the muscle torques. The selection of the time constants used in previous golfer models [6][7][8][9] is weakly supported, and so 𝜏 and 𝜏 were increased to 100 ms to reduce shaft bending to a level consistent with magnitudes found in the literature [10]. In doing so, the rate of torque development was reduced, and so the 0.65 scaling factor that was used to reduce the maximum muscle torques in [9] was removed.…”

“…The vertical lines in the radius plot indicate the center of mass position of each shaft. Fourth-order polynomials were fit to 𝐴(𝑥) , 𝐼(𝑥) , 𝐸(𝑥) , and 𝐺(𝑥) to parametrize the analytical shaft model [10].…”

“…The simulation experiments in this study make use of the dynamic golfer model presented in [9]. The referenced golfer model uses six biomechanical degrees-of-freedom (DOF) powered by muscle torque generators and a continuous analytical shaft model [10] to simulate full golf swings (backswing and downswing). Although there are DOF not captured by this model, e.g., pelvis translation, it provides good agreement to experimental results.…”

“…The purpose of this study was to investigate the influence of the shaft balance point on the generation of clubhead speed using a state-of-the-art dynamic golfer model [9]. Three hypothetical shaft designs with different balance points were represented in the golfer model using a continuous analytical shaft formulation [10]. Furthermore, improvements were made to the golfer model and optimization routine to help promote the generation of realistic golf swings.…”