12PB
You wrote-: "If you want the hands to move in a constant consistent arc . . . then why would you want to move off the ball???? That's the WHOLE POINT OF THE CENTERED PIVOT . . ."
When I stated a "constant consistent arc", I only meant a hand arc that is smooth without any sharp, abrupt (V-shaped) curves. I didn't mean a very rounded hand arc. The hand arc actually shouldn't be too rounded because that predisposes to a sweep release. To get a late release, like Sergio Garcia in the next photo, the hand arc must be distinctly U-shaped with a tight curve at the lower end of the U-shape (equivalent to going around a small pulley at the end of the endless belt).
I also have never recommended a non-centered pivot. I wrote a review paper on weight shift in the golf swing and I used the following diagram in that paper.
Image 1 shows a "hypothetical" perfectly centered pivot where the golfer rotates around an imaginary central axis (dotted line). The head is central, the spine is vertical and the golfer simply pivots around the central axis. However, that would only be possible if human beings had only one leg which was in the center of the pelvis and perfectly in line with the spine.
The reality is that human beings have two legs and a golfer has to pivot over the right leg in the backswing and over the left leg in the downswing, which means that there are really two pivot axes for the pelvis in a golf swing. There are biomechnaical consequences to this biomechanical fact.
One can choose to keep one's head centralised (in a tripod fashion) and then pivot centrally => that prediposes to a left-centered pivot action where the spine will tend to lean leftwards at the end-backswing (slight reverse pivot).
Alternatively, one can adopt a small amount of rightwards spinal tilt at address and allow the head to move slightly to the right-of-center of the stance. That allows a golfer to acquire secondary axis tilt naturally during the backswing pelvic action (which moves the lumbar spine left-laterally and aligns the lumbar and thoracic spine into a "straightish" spine that is tilted to the right at the end-backswing.
By my
arbitrary personal definition, both a leftwards-centered pivot action and a rightwards-centered pivot action are
centralised swing actions - because the head remains within the inner boundaries of the feet and there is no unnecessary lower/upper torso swaying movements off the ball.
Jeff.