Instantaneous center & radius - comparison of two golf swings

Fig1 and Fig3 show swings apparently quite similar. Same start and virtually identical impact positions. However there is a distinct difference. In the swing shown in Fig3 there is a gradual releasing starting from the top whereas the swing shown in Fig1 there is a better retaining of the angle.

Notice how these two swings appear very different when clubhead trajectory, instantaneous centers (evolute) and radii of these two swings are shown, respectively in Fig2 and Fig4. Basically the mathematical operation consists of finding for various locations on the clubhead trajectory curve the instantaneous radii (black lines) and the associated instantaneous centers (red dots).

Notice how the intriguing loci of the instantaneous centers (evolutes) for these two swings are quite different. It is easier to follow the trajectory of the evolute during the downswing when starting on the clubhead trajectory and following the radii inwards till the red dots. When the red dot moves quite a bit away from the inner physical pivot means that there is a flattening of the clubhead trajectory.

For instance, the premature releasing flattens the clubhead trajectory substantially during the early instants of the downswing, see Fig4. For swing 1, the release only starts halfway down into the downswing. Notice now from Fig2 that this results again in some flattening of the clubhead trajectory and hence an increase in the associated instantaneous radius.

Fig1

Fig2

Fig3

Fig4

mandrin