Okay, have a look at that picture I drew...

What you are looking at is a reproduction of a diagram on a blueprint for a VERY old Jaguar XK over head cam design (I can't post).

I provided what I thought were prudent dimensions... everything else... you should be able to assume. If not please ask. (okay the circle... to make drawing the plot lines easier, I used the right side for the 30° and the left side for the 15°+30° increments)

The description on the blueprint is "cycloidal motion curve"

Take a look at my older thread...

Integration of a cycloid.

and you will see what I have been working on.

I have to ask... is this diagram I posted... a graphical proof of one of the integrals for a cycloid?

It looks a lot like the 1st integral plot... but also looks a lot like the first part of the 2nd integral plot.

I would love some insight to this!