Impedance Control For A Prototype Of Golf Swing Robot (P3)
where ms is the sensor mass; F ˆs is the reaction force from the arm to club; sf is the force obtained from the sensor, and its direction is perpendicular to the arm, as shown in Figure 5-10. The force sf can be calculated by
where TX and TY are the forces measured from the 6-dimensional force sensor, and they are perpendicular with each other.
Therefore, the reaction force Fr from the club to arm is obtained as
In Eq. (5-16), the arm angular acceleration αr && should be known in order to calculate the reaction force Fr. Here, a constant-coefficient kalman filter is used to obtain the arm angular velocity to reject undesirable position measurement noise, and then αr && is acquired by the filtered velocity using the difference method.
Lampsa thought that a pause usually occurs at the moment when a golfer completes his backswing and is just about to begin his downswing, indicating that the angular velocities of the arm and club are equal to zero at the start of the downswing. Therefore, it is assumed in this study that the swing commences with α = 0 β = 0,and the bending of the golf shaft at the start of the downswing is also ignored. The posture values of the arm and club at the start of the downswing are taken with α = 120 degrees, β = -90 degrees, which were regarded as the general initial configuration for professional golfers in the work of Sprigings. The simulation and experiment are terminated when the club head hits the golf ball, and the ball is placed at the center of the width of the golfer’s stance (the same golf ball position is shown in Figure 7-8 in Jorgensen).The gravity effect is neglected because of the horizontal positioning of the direct drive motor. The golf swing robot is defined as R, and three golfers, labelled by H1, H2 and H3, own the same arm length as that of the robot but with different arm masses, 5kg, 3kg and 2kg, respectively. It has been noted that there are many kinds of torque input functions of the shoulder joint applied in the previous research work of golf swing, and here these functions are referred to as τ1 employed at the shoulder joint O. Jorgensen thought that the shoulder input torque was constant during the swing, Milne and Davis used a ramp as the torque function and Suzuki and Inooka set the torque function as a trapezoid. In the present study, a trapezoid-shaped torque (Figure 5-11) is employed at the shoulder joint for the golfers. The torque is linearly increased with the rise time 0.148s and then up to the maximum amplitude 10 Nm which is maintained 0.05s, and finally is terminated at the time of 0.346s. By this torque, the suitable postures of the arm and club at impact for the general golfers with 5kg arm can be obtained: the arm and club will be a vertical line at impact, that is, o α = 270 degrees, β = 0 degree