Up front I apologize for my lack of familiarity with the relevant mathematical concepts, it’s been a long time since school.
I’m trying to build a draw bot similar to https://create.arduino.cc/projecthub/ArduinoFT/polar-drawing-machine-f7a05c?ref=search&ref_id=Polar&offset=0 where it naturally uses the polar coordinate system, but instead of using a linear axis, I want to use two rotating axes.
Something like this: 
So I was wondering if this was a kind of known coordinate system, where the rotation “a” of the larger circle is used instead of a radial distance from the origin of b, resulting in two rotations, that of the primary origin circle b, and the rotation of a (and a constant radius ratio) being the coordinates used to define a point.
Regardless of this being an existing concept, how would I go about translating from normal x,y coordinates into this new system?