I believe you wish to design a plate cam. There is no definite equation to create a plate cam. The equation would depend on the type of motion required required to be given to the follower.Generally, Cycloidal profile is preferred for a cam which gives a sine acceleration to the follower. I am attaching a WF2 file. Though the equations are not defined, the curve is a look alike of regular cycloidal curve achieved thru splines. This would give you a general method to create the cam using graph.
r = exp(constant*theta) yields a logrimithic spiral which has a constant angle of contant depending on your constant of spiral in the equation. I am designing a rock climbing cam and they often use a constant of .25. Seems like a normal cyclic cam would need the same constant angle of contact but I don't know.
This may not help at all but might be worth a shot