A cycloidal gear generator made using the desmos API! It generates an epitrochoid function (aka - a circle rolling around another circle) using four of your parameters: overall radius (R), number of teeth/pins (N), radius of pins (S), and eccentricity (E).
In order to use the generator, you can copy the format I provided to add your own function into the Equation Driven Curve Add-In in Fusion 360! You can try out the generator in the embed below, and actually get an exportable cycloid using this link: HERE.
I made the generator using parametric trig functions, but there are many ways to generate cycloids. This was designed with an X and Y component in mind to use for the Equation Driven Curve Add-In though, so its based around two individual functions x(t) and y(t) which use the same 4 variables (R,S,E,N), and a z(t) component of 0.
The generator also has a few other features, such as the ability to animate the cycloid, and a slider to change the number of teeth/pins. I had a lot of "remnant" functions from when I was trying to create the generator, as I made many which would "work" but wouldn't be able to easily be utilized in Fusion 360, so I decided to keep them in the generator (though they are turned off) in case you want to play around or see simpler/condensed ways to generate epitrochoids.
I personally used the generator to create all of the cycloidal actuators in my 6DOF robotic arm project, and they have turned out well with nearly zero backlash and backdrivability!
I also used the generator to create the curves for my pneumatic liquid piston engine, which you can see below. They were slightly modified in CAD afterwards to adjust for the material tolerances & other small things, but the curves were largely successful and smooth.
A website where you can use the tool & learn some of this math is coming soon!
