Thread: Integration of a cycloid.

This is a linear plate cam profile that I am trying to design, so our machine can do different size parts other than what it was originally designed to do. The cam has a low dwell and a high dwell (left to right respectively as shown). The height change between the two dwell sections are Y2 (5.245) the height of the rectangle. The distance in which I have to move the cam from low to high is the width of the rectangle X2. So within those two distances which are not changeable (per each configuration of the system, which is what I am trying to design) I need to have the curve we have been working on (as shown in the lower left at (0,0)) be able to smoothly speed up the cam follower along the curve, having zero acceleration at the start, then zero acceleration at the end of the curve... but have a velocity to travel along the straight line, the "constant velocity" section, then directly feed into the exact same acceleration curve (but reversed and inverted) to take it from a velocity with no acceleration, then -acceleration to bring it back to no acceleration and no velocity at the point (X2,Y2).

AHHHHHHHHHHHHHHHHHHHH!!!!!!

I just had to take a break for a while... figured out what I wasnt doing. Good think I wrote that above, it made me think of it. I needed to divide X2 and Y2 by 2. BAM! the answer!

I'm good for now!

When I start playing with the size of the box and make it too much smaller than what I have above... the only real answer I get is a negative r... I'm trying to wrap my brain if there is such a thing as a negative radius in my world... It doesn't seem to work out graphically when I use the absolute value of it.
Is it a "real" math solution... but not a "Real world" solution