mandrin et al:
Interesting descriptive geometry construct, but let's relate it to a real-life golfswing.
If we assume the big black dot in your diagram is the centre of rotation, it should drop by an inch or so in the downswing and then rise back up to an impact position with the straightening of the lead leg and the changes in the length and orientation of the spinal column... creating another dimensional factor. Agreed?
Then there is the final pronation of the lead forearm/hand to square the clubface to impact. The pronation can be somewhat gradual for the longer length driver and quicker for the wedges. The hands coupling point distance between the rear hip low point and elevated impact point is when pronation, squaring and parametric elevation must be finally completed.
What this all leads to in reality, is that the 'flat spot' need only occur is say the last 2 inches into impact when there is a square clubface and pronation completed in the downswing.
Using circle geometry, that last 2 inches on a say 60 inch swing radius would only be a final rotative sweep of say 2 degrees. Without doing the trigonometry, I intuitively believe that the final 2 inches can be considered "flat" or tangentially straight on such a large radius circle. Agreed?
Suggesting that the flat spot can be as long as 18 inches per Moe Norman is questionable. Moe had a 'windmilling' swing with extremely extended arms, when I saw him twice in live demoes in the 1980s (and he was calling out his 200 yard drives as "300 yards"!).
If your geometrical figure had the arm-club segment fully straightened out for impact, then the clubhead would be rising after the shoulder span is rotating above level.
The question is: Do pro golfers optimally reach impact when their lead shoulder is slightly above level, or do they reach impact when their shoulders are level ... and everything happens so fast that it's impossible to eyeball it even on a youtube video? Kinetically I think it would be when the shoulders are level.
Perhaps the answer lies with the Manzella scientific team and their elegant testing equipment and procedures for a kinematic/kinetic solution.
Another consideration is that arc differences on a large radius circle or ellipse/oval as in a golfswing should be considered as a straight line for small incremental segments such as the ~3/4 inch of the impact event (3/8 inch of compression and 3/8 inch of rebound).... and the only difference is whether the "line of compression" is down, level or up. There is no circular scooping as suggested in TGM... and that thought should not enter into the minds of proto-scientific thinking golfers on this fine forum!
Your thoughts .....