Howdy yall, this is my first post, looking for some help with a question I have on a project that I am working on at work.

So what I have here are two equations that give the (x,y) coordinates to plot a Cycloid having a radius of r, and rolls along a time/position of t.

I am trying to build a cam path that operates as smoothly as possible and my limited understanding of calculus has left me puzzled as to how I can integrate these…twice.

x=r(t-sin(t))

y=r(1-cos(t))

The idea that I am using a Cycloid form in the acceleration portion of my cam path, so that at the start and finish there is zero acceleration that leads right into my constant velocity sections of the cam hopefully making the machine operate very smoothly at high speed.

The trick is I will know what my maximum allowable acceleration is once follower design is done based on the force that the strength of the follower can handle. So when I know this… how do I work this cycloid acceleration plot down to a displacement plot so that I can actually design the cam path to be cut?

My first thought was to integrate them both separately… but I don’t know enough if this will work or not. The next thing was looking on Wikipedia they have

x=r*acos(1-(y/r))-(y*(2*r-y))^(1/2)

I plotted that out… and to tell ya the honest truth… I can’t figure out how to make this thing equal to y and get my ti-89 do the work.

Anything would be great! Thanks!!!

(quick link to wikipedia cycloid Cycloid - Wikipedia, the free encyclopedia)