 0 354

## Optimization method

Based on the above part (3.1 Mathematical model), the bending displacement of club head, yc , is given by

Where φ1(a3) and φ2(a3) are the first and second mode shape functions of bending vibration for the end of golf shaft, respectively.

The horizontal component of club head velocity, v(h) , is written as

Substituting Eq.(3-33) into Eq.(3-34), and then differentiating the result with respect to time, it is found that h v will reach a maximal value when

The fourth-order Runge-Kutta method at intervals of 5 1001 − ×. s was used to solve Eq. (3-32), and the left-side expression of Eq. (3-35) was evaluated at each time-step. The optimum time t(o), at which the horizontal club head velocity arrives at a maximal value, was achieved when the left-side expression of Eq. (3-35) is most close to zero. Then the corresponding values of y(c),,,, βα βα and y(c) & at t(o) could be calculated. The optimum ball position, p(h) , is also calculated at t(o) :

## Wrist action simulation

Both Jorgensen and Sprigings & Neal have suggested that the optimal ‘timing’ of the activation of positive wrist torque occurred when the left arm was about 30 degrees below the horizontal line through the shoulder joint ( o = α=210 degrees in this chapter). This conclusion is also consistent with the result obtained from Chapter 2. Therefore, the neutral and positive wrist torques, activated from the optimal ‘timing’ mentioned above, are used to re-examine whether the club head speed could be improved by means of the optimization method (maximum horizontal club head speed at impact). In the present study, the positive wrist torque is not constant but increased linearly with time from 0 to 8 Nm, as muscles could not be activated to their full torque magnitude instantaneously.