Dear armourall,
If you consider the relative masses involved, the TWO arms grossly out-mass the putter itself. The arms and hands are about 10 times more massive, so the MAIN mass that hangs in gravity is that of the arms and hands, and the putter itself exerts some influence on this assembly but it is easy to overexaggerate the degree of influence.
The "coupling" function performed by the hands on the handle is the only real structural part of the body involved in maintaining the "angle" of the putter out of the naturally hanging arms. With a minimal or threshold grip pressure in the hands on the handle at setup, the forearm-hand muscle complex is essentially unified and stabilized. To me personally, this grip pressure threshold that keeps the putter angled out the same angle is about a 1.4 on a scale of 1 to 10 with 10 being a death-grip and 1.0 being a "dead fish" handshake (very flaccid). In other words, it doesn't really take much grip pressure in the hands and forearms to set the angle of the putter to match the forearm axis and keep the putter at this same angle in the stroke motion. Then when the stroke motion is powered by the shoulders, the hands are "dead" in the sense of inactive above the grip pressure set at address, but the hands and forearms are not "loosey-goosey". The have a mildly firmed-up form.
I understand what you are suggesting, as there is a canter-levering force inside the hands by which the putter head held out at an angle at the end of the shaft tends to angle the wrists downward. In the natural hanging of the arms and hands without a putter, the total masses of the upper arms (being vertical) and the forearms (being slightly angled outward out of vertical) results in a combined COG that is slightly outside the line of gravity directly beneath the shoulders. This results in the "natural hanging" of the arms and hands having a very slight inward bias in which the elbows are a little closer in to the body and so are the hands. This seems to be on the order of 1/4" up to 1/2" at most. But this is irrelevant once the hands reach their hanging equilibrium. At this point, it's just an academic discussion about how exactly the bones relate to one another.
But then taking the putter in hand at address again re-locates the overall center of gravity of the arms+hands+putter assembly slightly farther out of the line of natural hang, tending to swing the whole back toward the body to get the COG in line with gravity below the shoulders. But the truth is that just a little squeeze in the hands-forearms muscles overcomes and counters this downward/inward force, and so as long as the grip pressure is at or above this level, the "naturally occurring" position of the naturally hanging hands is not closer in to the body due to having a putter in the hands. The outward-supporting muscle tension that resists the COG trending back towards the legs is located mainly, unless I am mistaken, in the underside muscles of the upper arms and a little in the muscles that stabilize the elbows and wrists, and a little in the tension of the three fingers of each hand wrapping underneath the handle. (The only way the outside / inward-directed COG can express itself is against the supporting underside fingers, against the wrist to angle further downward out of line with the forearm axis, in the extension of the elbow towards straighter, and in the shoulder joint with the upper arms moving rearward along the sides of the chest. Accordingly, muscles that resist and counterpoise these forces will have a little extra tension in them, but it doesn't really require much at all.)
As an experiment, set a putter soled flatly on the ground and adopt your setup by "docking" the naturally hanging hands to the handle and test that the hands are not reaching out or in from this naturally hanging position by letting the right hand swing free and observe it swing only sideways. Then place this hand back on the handle with too-loose form in the hands-forearms, and raise the torso as a whole slightly so that the putter sole lifts off the ground just a wee bit (don't use the hands and arms to lift the putter up, as this will tighten your grip pressure -- leave the grip pressure too-loose). In this case, the putter head will drift inward towards the feet and bring the hands in closer as well. BUT if you seek the threshold grip pressure where this inward-drooping action stops, you will find that the threshold is a very mild requirement of grip pressure. No big deal.
So yes, there is a minimal grip pressure, but the natural hanging position of the hands is not required to be any closer in to the thighs due to these forces of the canter-levered putter.
And if you stop to consider (and compare) these two situations, we can discern a positive in this grip pressure "keeping" the putter at the same angle: First, a setup hang with putter in which the arms+hands+putter assembly finds its independent equilibrium hanging position in which the total COG seeks to line up directly beneath the shoulder sockets; Second, a setup with the threshold grip pressure (combined tension of fingers, hands, forearms, and upper arms) that stabilizes the angle of the putter. In the latter setup, there is a sense of definition that arises from the tension that makes a contrast-boundary between a stroke that stays the same distance out from the body (at least in terms of the upper arms, if not always in terms of the forearms and hands) and one that gets inside or outside of this proprioceptive boundary. In the former setup, the very looseness of the body parts "letting" the putter dangle into the gravity line tends to blur the boundaries and the sense of the body in motion, so there is not good proprioceptive feedback about how the arms and putter are actually swinging in space in relation to the trunk and lower body. I think that if you experimented with these two sorts of setups with a putter's toe near the baseboard of a wall, you would see that the truer swing USES the counterpoising of the inward-directed COG to good effect.
I believe it was Paul Runyan who commented about the importance of the last three fingers on the handle, and I agree, for the reasons I set out above.
Cheers!
Geoff Mangum
Putting Coach and Theorist
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