I would suggest experimenting with a completely no-hands thru-stroke for short putts powered either by gravity alone (with the shoulder frame just "riding" with the putter head but not pulling or pushing) or by a gentle rocking of the shoulders in tempo. If the shoulders and the putter head stay in sync throughout the stroke, the putter face will be square and moving straight online thru the critical impact area.
The key to the no-hands stroke is, first, keeping the pivot at the base of the neck still during the downstroke, and second, resisting the i,pulse to move the putter head with anything other than gravity or the in-sync rocking motion of the shoulder frame. If you will note, I say that the stillness of the pivot really only becomes critical once the backstroke reaches the top of the backstroke, and motion momentarily pauses in transition from back and up to forward and down. if you can set the pivot at this point in a state of frozen stillness (like a small bunny rabbit when a person walks too near) and ALLOW the shoulder frame effortlessly to ride the putter head down and thru as the rocking shoulders let the arms and hands swing / fall beneath the still neck, then a straight and square impact on a slight rise into the ball is nearly guaranteed. This sort of pivot-plus-relaxed-stroke action produces a thoughtless and effortless straight putt, which is usually what you really need on short putts (where line is more critical than touch).
If that's not enough, I suggest another technique that works well with a voluntarily accelerated (faster tempo) stroke. If you envision a small nail angled straight thru the center of the ball from exact back of ball (farthest point on ball's equator from target and closest point to putter face) out front of ball (nearest the target), so that the nail is not level, but enters the back one dimple below the level equator of the ballm and the pointed end of the nail exits the front of the ball one dimple higher than the equator, with only a short distance left from the head of the nail until it is flush against the back of the ball, then the objective os to deliver the putter face flush to the nail head on a slight uprise, and drive the nail straight into the ball. This image helps you avoid hitting the head of the nail while the putter face is twisting out of square. The squareness of the blow has to persist for a moment as the putterhead rises thru the spaces where the center of the ball and then the front exit dimple of the ball are located. With this trajectory of the putter head thru the ball in mind befire executing the stroke, the task of making this happen with even a quickish blow is made notably easier to perform accurately and reliably.
This dynamic is also accomplished by fixing the pivot at the base of the neck so the pivot may rotate in the shoulder rock, but does not curl about. The chest needs to stay square, without twisting after the putter head thru the stroke. Keeping the chest square during the stroke is helped by setting the line of the neck to match the top edge of the putter face at address, and then keeping the neck straight over this line as the shoulders rock back and thru beneath the neck. Because the base of the neck (with the line of the neck kept steady) prevents the chest from twisting in the stroke, the keeping of the neck line steady also requires that the lead shoulder rock vertically upward in the thru-stroke and that the coordinated, same-plane motion of the rear shoulder works directly back under the neck. Neither shoulder turns out of a plane of motion parallel to the putt line.
The form of this action is the same regardless of the "pace" or tempo of the stroke. Usually, though, hurrying the stroke means hurrying the hands out of sync with the shoulder motion. The putter head gets faster than the shoulder frame. This dynamic will twist the path of the stroke off line to the inside. If the hands get ahead of the putter head a little (and both hands and putter head are faster than the shoulder frame), then the putter face tends to lag open (especially with Scotty Cameron style toe-flow putters). (This is one of the main ways a cut stroke develops -- first the toe lags open, then the golfer adapts by altering his path from straight thru the ball to one that cuts from out to in to counteract the open face.) So, all things considered, I wouldn't advise a quickish stroke even on short putts -- instead, just view the length of the putt as merely a few rolls of the ball and then execute it. (A single roll is over 5 inches, so there are about two rolls for every foot of the putt -- a three-foot putt is only 6-7 rolls of the ball.)
Cheers!
Geoff Mangum
Putting Theorist and Instructor
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