[Mike O]

Matthew, (I've revised this one- made a few changes for clarification)
Now that I understand your perspective- I can see why you say low point of the overall orbit would/could be before the point that the clubhead passes the "in-line" location of the lead shoulder. So before I break it out a little further - and maybe take away a little of your original post- Let me say that you are correct and that I think it is an excellent understanding of what is happening in the full swing. Nice job!

Let's see how much of this post- that we can agree on- I'm hoping quite a bit if I understand the concept as you.

First I'd like to correct an error in my thinking in regards to my
"7" "simple machine" example. My "7" example was a one center rotation machine. It only rotated about the "neck" of the golfer and therefore I only had a center of rotation at the top left of the 7. All of that wasn't a problem as I was just trying isolate the low point concept with something that A) resembled the shoulder line and the primary lever line, and B) wasn't just a straight up and down pendulum. The error that I made was thinking that 7 would have a low point opposite the top right of the 7 whenever the bottom of the 7 passed beneath it. In fact, the low point for any single fixed center of rotation is directly beneath it- regardless of the fixed shape of the attachment. So that just gets me corrected- not saying you even commented on my machine or even considered it in your explanation.

Let me repeat that in a system where there is just one center- the low point of the fixed length rotating body will always be underneath the center of the rotation. As you pointed out- if the left shoulder doesn't move and the primary lever system would rotate around it - low point would be opposite the left shoulder. Likewise, for single center rotating machines- say in golf if the primary lever system was fixed and did not rotate around the left shoulder- then if you just rotate around the "neck" i.e. the pivot- the low point would be opposite the neck i.e. say a shot chip shot or something- or a putting stroke. Using this principle- In general, I'd say that if you set-up to any full golf shot- with the ball located perpendicular to the inside of your lead foot (Golfing Machine you'd relate it to "lowpoint" i.e. upperbody - so just ahead of your lead "nipple" (that's for you Bucket) - then you couldn't have a "one piece takeaway" since lowpoint would be opposite the neck/belly button- you'd need to have the clubhead dig a trough into the ground!

Matthew- As opposed to my simple machine - your machine has two centers of rotation. One lever pivoting around the "neck" and one lever pivoting around the "left shoulder". So while we consider the first center of rotation fixed in space- the "neck", the second center - the left shoulder- is moving in space- it is orbiting the fixed center "the neck"- and while that center is orbiting the neck it has a lever rotating around it- the primary lever assembly.

Again, not to take away anything from your post but to just look at this concept of dual rotating centers/levers where one center is rotating on the orbit of another -on paper- here is how I follow the logic. First, the two centers of rotation combine to form a "clubhead" orbit- that neither center could create on it's own. It's that orbit of the clubhead and that orbits lowpoint that we are comparing to the axis of rotation of the 2nd (moving center) (the left shoulder in our golf example).

The fact that the center of the axis of rotation (the 2nd center) that is moving around the fixed center is moving up- doesn't mean in all situations that low point of the overall orbit will be behind the axis of rotation of the moving center. In your example I believe you said at one point in the video "when the up overcomes the down" which maybe is your way of describing what I'm going to cover below. In principle, I see it as if the up of the end of the 1st lever (left shoulder in your example) rises more than the down ward motion of the end of the 2nd lever-(the clubhead in your example)- then you'd have that condition where the overall lowpoint would be behind the lowpoint of just the 2nd lever.

To show the logic behind dual centers of rotation when one is fixed and the other center is rotating around it- let's consider the hands as rotating in the golf swing on a fixed center point (say the head/neck) moving in a perfect circle (not saying they do) and the clubshaft rotates around the hands- so the hands are the 2nd center and that center is moving while the clubshaft is also moving around the hands center (say during the release in the downswing). If the shaft moves around the hands at a high rate of degrees per second while the hands are moving at a slow rate around their fixed center (say the head) - then the low point of the clubhead on the overall orbit might be descending after the point that the clubhead passes the 2nd center of rotation. So even though the clubhead has passed the hands - you could be still having the clubhead descending. That's just an example showing a "combined center lowpoint" that is after the point that the clubhead passes under the moving center of rotation i.e. the opposite of your example.

In summary, it's not so much if the 2nd center is rising that completely determines if the low point of the orbit created by the dual centers is before the center of rotation of the 2nd center (left shoulder in your example) but it's the correlation between the angular speed of the first center in relation to the 2nd centers angular speed - combined with where the individual levers are in their rotations.

Here are two points in case I've said something that's going to make your start firing bullets:
1) I'm not expecting but hoping that if we are on the same line of thinking that you'll follow my logic. Again, if you were strictly referring to the full golf swing then all you might have needed to cover is exactly what you did cover- however, my mind was looking at the principle involved and having a tough time accepting it (if the shoulder was moving up then the low point would be before the left shoulder)- based on what I described above.
2) I may indeed not have this correct or there may be additional issue of relationships of radius size, speed of rotations etc. but I look forward to your thoughts. And I'm not saying you didn't know any of this or that I'm disagreeing - I'm just putting my thoughts down on the possibilities and seeing if you agree or disagree.
Thanks,
Mike