question about precision curve control

How would I go about making an epitrochoid with and inscribed reuleaux triangle without just guessing. Are there any plugins that let me input the equations I need or are there other programs out there I can do it in then port to Blender?

There is Python plug-in for parametric objects you may play:
Also, I believe you can create such thing with GIMP or Inkscape via spirograph-like plugins, then export as SVG paths and import into Blender.
Hope I’m helpful.