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We aim to clarify dynamics of the wrist turn of the golf swing and the effect of the parameters on dynamic behavior at the wrist turn using the double pendulum model and the modal analysis method. Eigenvalue analysis was carried out and natural frequency and mode were calculated by using linearized equation of motion assuming the exterior angle of the cock angle is small. We found out that the first mode is a rigid mode and the second one is a vibration mode of the double pendulum, and the mode shapes are constant during the wrist turn even though natural frequency changes. By applying the modal analysis method we obtained equations of motion for the rigid mode and the vibration mode separately. Furthermore, using the theory of linear superposition, the equation of motion for the vibration mode was separated again into 3 equations which can help to understand the mechanism of the wrist turn. After accuracy of the proposed method for small exterior angle of the cock angle was confirmed by comparing with the exact solution using numerical integration, the proposed method was applied to the general case with large exterior angle of the cock angle which has nonlinearity, and the mechanism of the wrist turn and the effect of the parameters of the arm and wrist torque on the dynamic behavior at the wrist turn were clarified qualitatively. Finally parameter survey using the numerical integration for the original nonlinear equation of motion was carried out to show the validity of the proposed method.

We aim to clarify the mechanism of the release point of the golf swing and the effect of the acceleration pattern of the down swing on the dynamic behavior at the release point. We consider that uncocking begins naturally without driving torque applied to the wrist joint when the angular velocity of the arm and the centrifugal force become to be sufficiently large compared to the angular acceleration and tangential inertial force,. We derive simple approximate equations which express the relationship between angular velocity and acceleration at the release point. By using the derived equations and the acceleration pattern of the down swing, we develop calculation methods to estimate the effect of the acceleration pattern expressed by the polynomial of time on the dynamic behavior at the release point which may affect significantly on the head speed. We discuss how the patterns affect to the release point for two types of acceleration pattern which are expressed by the 1st order function of time. Through the discussion, it can be seen that acceleration pattern which has positive gradient gives high angular velocity of the release point and later release point, and negative gradient pattern shows low angular velocity and earlier release point and these results can explain mechanism of so-called late hitting.

We aim to clarify the mechanism of the release point of the golf swing and the effect of the parameters of a club and a human body on dynamic behavior at the release point. First, the mathematical model of the golf swing is assumed to be a 2-dimensional double pendulum connected with a nonlinear rotational spring at the wrist joint. By applying Lagrange's equation to this system, we derive equations of motion of the golf swing. We consider that the wrist joint begins to turn naturally under the centrifugal force of the swing. When the angular velocity of the arm and the centrifugal force become to be sufficiently large compared to the angular acceleration and tangential inertial force, uncocking begins naturally without driving torque applied to the wrist joint. We derive simple approximate equations which express the relationship between angular velocity and acceleration at the release point. By using the derived equations and the equations of motion , we also derive some expressions demonstrating the effect of the parameters of a golf club on the dynamic behavior at the release point which may affect significantly on the head speed by using new modeling method, and calculation and discussion are carried out on the effect of the parameters of the club , the cock angle and the active wrist torque on the release point. Through the discussion, it can be seen that the derived simple approximate equations give us physical insight of the phenomena at the release point and help us to understand the effect of the club parameters on the dynamic behavior of the double pendulum at the release point.