Study On The Dynamics Of Golf Swing
The dynamics of golf swing have been studied for many years in an effort to improve the swing skills of golf players and to optimize the design of a golf club. The golf swing has been always modelled as a planar two linked system, named the “double pendulum” with the upper fixed pivot located at a point between the left shoulder and chest and the lower pivot point at the player’s wrist joint. Most of these studies have regarded the golfer’s arms and golf club as rigid rods, but others modelled the golf shaft as a flexible link. Several researchers have presented a three-segment planar model that incorporated truck rotation (about the spine) in addition to the shoulder and wrist actions. Note that the validity of the two-link model (arm and club), in particular for the rigid-rod system, has been confirmed by many researchers through actual swing experiments. That is, the known inputs for the model (input torques of shoulder and wrist) would result in the outcome, including the club head speed and the arm/club positions during the downswing, which is very much the same as that from actual golfers’ swings. For example, Jorgensen used the assumed constant shoulder torque to drive the model, and found that the club head speed was consistent with that from a professional’s swing; Williams applied the input torques of shoulder and wrist, obtained from the pictures of Bobby Jones’s swing using inverse dynamics, to the model, and found that the swing motions of the arm and club in simulation agreed with those from pictures. Such work was, however, lacked in the field of golf swing modelling where the flexible golf shaft or three-segment bodies is included.
The wrist action of a golfer is deemed to be of great significance in the determination of his final club head speed. To date, researchers have been asking: what kind of wrist action can provide an advantage in club head speed. In order to find the answer, a large number of dynamic models of golf downswing have been developed. Using a two-rigid-segment and two-dimensional linked system, Williams stated that neutral (zero) wrist torque was employed by the legendary golfer, Bobby Jones, at the latter stage of the downswing. Considering the bending flexibility of golf shaft,
Suzuki & Inooka also thought that the neutral wrist torque should be used in order to effectively utilize the shaft elasticity. But Jorgensen and Cochran & Stobbs found that the negative wrist torque (the so-called “late hit”) could increase the club head speed, using the same model as that in Williams. Milne & Davis, using a two-segment and two-dimensional model in consideration of shaft bending, suggested that a negative wrist torque before impact decreased the club head speed. This finding was consistent with the point of Budney & Bellow. Jorgensen and Cochran & Stobbs stated that the club head speed could be improved by the appropriately “timed” positive wrist torque. Based on a three-rigid-segment model, Sprigings & Neal also confirmed the role of the positive wrist torque in the improvement of the club head speed.
All the golf ball positions at which impact occurs were, however, constant in their work. Since the ball position played an important role in the improvement of the final club head speed, the ball position in this paper is not assumed to be constant but a variable in the optimization models.
To date, many types of golf swing robots have been developed. For these robots, the swing motions of various professional golfers were expected to be emulated by them and the evaluation of the golf club performance by humans to be replaced.
Although much progress has been achieved in this area, there still remains a long-standing challenge for a golf swing robot to accurately emulate the fast swing motions of professional golfers. It has been noticed that conventional golf swing robots on the market are usually controlled by the swing trajectory functions of joints or of the club head directly measured from professional golfers’ swings. The swing motions of these robots, unfortunately, are not completely the same as those of the advanced golfers, in that they do not involve the dynamic interactions featured by different characteristics of golfers’ arms and golf clubs. Suzuki & Inooka proposed a new golf swing robot model consisting of one actuated joint and one passive joint. In their model, the robot like professional golfers, was able to utilize the interference forces resulting from the dynamic features of individual golf clubs on the arms, and the corresponding optimal control torques of the shoulder joint could be obtained. Ming & Kajitani gave a new motion planning method for this type of robot to gain the optimal control torques by using different cost functions. The control input for the robot in their work was the torque function of the shoulder joint instead of the general ones such as the trajectory functions of joints or of club head. The change of the control input mainly results from the special dynamical characteristics of this new type of robot: the swing motion of the wrist joint is generated by the dynamic coupling drive of the shoulder joint. This point was specifically explained in the work of Ming & Kajitani. In their research, however, the difference between the golfer’s arm and the robot’s arm in mass (or the moment of inertia of arm) was not considered. In order to indicate the vital of a golfer’s arm mass, a two-dimensional double pendulum model of golf swing with normalized parameters is established. The simulation results clearly show that the mass ratio of clubs to arms and the arm mass are important factors to influence the golf swing performance. Therefore, if the optimal control torque from their work is applied to other golfers who own different-mass arms, the various swing motions would occur. In other words, the robots proposed by them at most can emulate one kind of golfers who must have the same arm mass as that of the robot. The limitation of the golf swing robots promotes us to investigate a new control method to make the robots emulate more general golfers.
The objectives of this dissertation are first to investigate what kind of wrist action can improve the horizontal club head speed at impact in consideration of the golf ball position, and to determine the optimum ball position at impact for various types of wrist actions; and second, to make a prototype of golf swing robot emulate swing motions of different-arm-mass professional golfers, using an impedance control method.
The dissertation is organized as follows: gives the wrist action study using a two-dimensional double pendulum model of golf downswing. A new two-dimensional model of golf downswing considering the bending flexibility and centrifugal stiffening of the golf shaft is established to investigate the role of the wrist action. Chapter 4 is devoted to the understanding of the importance of the dynamic interactions between humans’ arms and golf clubs during the golf swing. An impedance control method for a prototype of golf swing robot is developed. Conclusions are drawn.