If we know roughly what is gear ratio (N) we want to use, how big of our drive unit is going to be (R, Rr, E), then we can bring those number into the X,Y equations and plot the curve by varying θ from 0 to 360.

If you are using Solidworks, there is a tool “Equation Drive Curve” which you can input these two equations and the variable angle θ then it would generate the corresponding curve for us.

I have made up a simple python code, which is going to generate two equations form then we can just copy and paste these equations into Equation Drive Curve tool of Solidworks. Please check out the code here.

The parameters you chose should make sense in term of size and it should be reasonable, otherwise you will get a really strange curve or it might not even generate any curve for you.