Isochronic

Ah, a bit of a twist here.  Let's talk isochronic curves.

"What's that?" I hear you say.  If you were one of the enlightened back in the 16th or 17th century you would know about it.  Indeed some of the old Greeks know of it.

Herman Melville mentioned it when describing the properly shaped pot in which to boil whale oil.

It is also known as a valve curve as it can be described as the path a bicycle valve takes as a wheel rolls.

One property of this curve is that when constructed as a ramp a ball released from any point on the curve will hit the bottom point at the same time.  You can drop marbles from any heights, same or different, on the sides and the marbles will smack together at the bottom.

There is a video on YouTube to show you this.  Quite interesting, I thought.

Now how does this fit into golf?

I've had a modest correspondence with a physicist, Dave Tutelman.  He is also an avid golfer.  He has modeled the swing and worked with golfing machines.

My earliest question to him was if the Iron Byron machines did anything special in re the wrist joint.  He stated that it was a pivot and that there was no input from the wrists to square or rotate the club.

That's all well and good.  But the next question I had was how is it that the club always squares up regardless of its speed or from where it is swung.  You can take it back a long way or a short one and the club will perform its "magic."  Dave remarked that this was an excellent question.  But as I recall he didn't have an answer.

I found out about the isochronic curve Friday.  It seems to me that it's playing a part in the club squaring regardless of its start point.  But the time element is dependent on the speed of the club, so it's really possible that I'm wrong on this.  And we are not letting the club drop, but actively trying to accelerate it along its path. 

One more point would be that if you created a curve drawn from a larger wheel, there the marble is going to be moving faster.  So the time would be shorter to get to the low point.

And we have the entire circle that might be used in a long swing.  Hands are taken up almost above the head in some swings, particularly the long driver competitors.

In conclusion I have no answers.  I think there are some interesting properties in this curve and it derives from a circle, so I think it has to be in there somewhere.

By the way, there are other curves out there with interesting properties.  For more info, here's a link: http://www.2dcurves.com/roulette/roulettec.html#isochrone

The YouTube video is here: https://www.youtube.com/watch?v=eBc827pwKf0