The velocity I am trying to get to is 390 inches per second... I figured that if I dropped that into the equation for the velocity plot it would give me back an acceleration of an appropriate magnitude.
As far as why I am using a cycloid... Short answer is I am trying to figure out how it was done before. I have a cam design book that I picked up and it compared your sin profile, with a cycloid profile, and a "modified trapazoid" profile. of the 3 it shows that the cycloid has the least amount of required driving torque of the three. I do get kind of annoyed when end of the day the position plot to make the profile between the three different profiles... is almost negligible as far a manufacturing tolerances. That being said, at the high speed that this machine is running at... we need to make it as efficient as possible and that points to the cycloid.
The other reason for the cycloid is another little portion of the information that the machine came with... said that it's a "dual frequency" cycloid to keep vibration down. I was hoping that if I learned about the cycloid I would eventually come across what they meant by "dual frequency"... so far I'm still lost.
What we are working on is one acceleration corner of a cam profile going from a dwell to a constant velocity section that is lifting a follower. Then I have just had to use the same profile mirrored and reversed to bring the follower from constant velocity to dwell again at the top of the follower lift. As far as I can tell to maintain the same constant velocity coming out of acceleration then going into de-acceleration to go to zero... both of the corners have to be of identical profile otherwise they wont match up.
Anyway... the point of this all is to try to understand a machine that was designed and built by very smart people in the 1950's...of which the engineering records no longer exist and I am sadly no where near as smart as those old guys who managed to get this all done with 3 significant digits on a slide rule.