2-C-3 Ballistic Path
 

A concise and intelligent answer to this question requires that readers have an in-depth knowledge of TGM. Ideally, I'd also be able to demonstrate. Otherwise, this question is impossible. I know, I've just tried several times! It is simply too advanced and requires too much supporting conceptual information. So, with apologies to the many, here we go with a reasonably complete answer to the few.

The theory of Hinge Action dictates that Low Point is directly opposite the hinge pin. It is thus the only place where the Flat Left Wrist is Vertical to the ground for all three Hinge Actions. Hinge Action by definition is in operation from Impact to the end of the Follow-Through. So, Hinge Action is an Impact Concept. With the Ball positioned at Low Point and the Grip taken in the precision Flat, Level and Vertical Impact Alignment, the Left Wrist is, by geometrical coincidence, simultaneously Vertical to each of the Three Basic Planes, i.e., Horizontal, Angled and Vertical. And that was the basis of my post. The Left Arm, the Clubshaft, the Ball and the Flat Left Wrist are all in the same Plane -- the plane of the Left Arm Flying Wedge -- and the Left Wrist is simultaneously vertical to the ground for all three Hinge Actions.

But...Low Point is the most difficult of all Ball Locations from which to play. Virtually all Clubs are manufactured to produce a Straightaway Flight with a Ball positioned well back of Low Point. Nevertheless, it is desirable to maintain as many 'samenesses' as possible for all Golf Strokes. And the most important sameness of all is the Flat, Level and Vertical Left Wrist Impact Alignment. Unfortunately, unlike the Low Point Impact Ball Location, only Horizontal Hinging has the Left Wrist Vertical to the ground for all other Ball Locations. To maintain the Left Wrist Vertical to the Ground for Vertical and Angled Hinge Action, the Clubface must be adjusted.

The 'Vertical to the ground at Low Point' procedure has certain practical applications. For example, avoiding the 'bouncing' of the Clubhead into the Ball when playing off hardpan. Also, using a 'Reverse Loft' Putter to produce a true Overspin. Aside from these and other exceptional cases, the "precision [Hinge] position per 2-G" (7-10) is best considered a theoretical concept.

2-C-3 Ballistic Path GM#132
 

There are three major concepts in The Golfing Machine:

1. Hinge Action (Clubface control);

2. Angular Motion (Clubhead Control); and

3. The Inclined Plane (Clubshaft and Sweetspot Control).

To these Three Major Concepts is attached endless supporting detail. Unless and until the 'Big Three' are understood, that detail continues to baffle and confuse, and the Book -- not to mention the Golf Stroke -- remains a mystery.

Now to your question. The Golfer's Flail is the means by which Angular Motion and Momentum is generated (2-K). It is a Clubhead concept and thus totally distinct from the Hinge Action (a Clubface concept). To be sure, there are interrelationships, but these do not override the separate identities of each.

Reading between the lines of your question, the Hinge Pins of the Golfer's Flail (in the Left Wrist and Shoulder) are there to permit, create and sustain Clubhead Momentum. They are not to be confused with the Hinge Pins of the Left Shoulder Hinge Assembly, which are there to control the Clubface and maintain the Clubshaft On Plane.
Topic:2-c-3 Ballistic path

2-C-3 Ballistic Path GM#134
 

First, the direct answer you seek and that I thought I supplied:

The Flail plays zero part in my explanation of Hinging.

Second, the Flail is used by both Hitters and Swingers to generate Angular Momentum. The first Flail (Sketch 2-K #1/#2/#3) illustrates the concept and the three-phase Law of the Flail. The second (2-K #4/#5) illustrates the Golfer's Flail with the Flat Left Wrist and the Left Forearm Swivel.

Third, unfortunately, we won't be able to make additional progress in this discussion because your concept of Hinging is a Clubhead Power concept and the TGM concept is one of Clubface Control. For further information on the TGM application, see 2-G, 7-10 and 10-10.
Topic:The Stationary Head

2-C-3 Ballistic Path GM#166
 

From Release to Follow-through, the proper rotation of the Left Forearm (6-B-3-0) maintains the precision Alignment of the Left Arm Flying Wedge (6-B-3-0-1). This Alignment dictates that the Clubshaft remain in the Plane of the Left Wristcock Motion.

Assuming the 'Left Wrist Vertical to the ground at Impact' procedure (7-10), the Clubshaft position at Low Point will be determined by the Ball Location and the Clubhead Travel (Rhythm) of the selected Hinge Action. Assuming the 'Left Wrist Vertical to the ground at Low Point' procedure, the Ball Location will be at Low Point, and the Shaft will be vertical, regardless of the selected Hinge Action.