Good news for those who got a headache looking at the complicated formula for the instantaneous radius in my post - 'Interesting Challenge'. The complex expression presently is reduced to a simple graph shown below in Fig1. Nice, simple and elegant. It shows for a somewhat particular swing, shown in Fig2., how the magnitude of the instantaneous radius of curvature of the clubhead trajectory varies during the down swing.
For illustration purpose a swing was chosen with 100% pinning, Fig2. Now compare Figs 2 and 3. The only common element is the red dot, representing the clubhead. Fig3 gives more detailed information about the instantaneous radius of curvature, being a vector presentation. The length of each line segment is equal to the instantaneous radius of curvature as shown in Fig1. But moreover it also shows the orientation in space and last but not least, the evolute of the clubhead trajectory, ie., the locus of its centres of curvature.
Hence from Fig3 we can see during the down swing the instantaneous center. Notice that it remains first centered at the axes' origin, corresponding to holding the angle. When the angle opens this center moves sharply to the right, the swing radius increases. Subsequently the swing center returns quickly to the hands were it remains for the last part of the downswing. It is very evident that just prior to impact there is a substantial 'shortening of radius'.
This is most likely the very first time anywhere this type of presentation of a swing has been given. Enjoy.
mandrin