Rewriting this whole question as I've learned a lot more since I first tried to ask.
I'm building a tiny bot and looking to use two motorized wheels for movement, but only one motor. I'll have a 3rd wheel (caster) for balance.
My goal is to have the wheels move opposite to each other when the motor turns and each wheel reverse direction when the motor reverses direction.
The tricky part is I want the ratio to be uneven between the wheels. By this, I mean when one wheel rotates clockwise, it should rotate faster than the other wheel rotating counter-clockwise. This needs to hold true regardless of which wheel is rotating which way.
The end result should be that I could run the motor in one direction continuously to have my bot drive in a small circle. If I switch motor directions, it would drive in the same size circle the opposite direction. If I alternate motor directions frequently enough, the bot should move in a fairly straight line (or if I alternate the motor too infrequently, an S like pattern).
The closest I can envision so far (thanks to those that have responded here) is to use bevel/miter gears to have my wheels rotate opposite to each other and then to use two differently sized ratcheting mechanisms per wheel working in opposite directions. This would allow each ratcheting mechanism to trigger only in one direction and the RPM per direction would be related to the size of that direction's ratcheting mechanism.
Is this the best way to achieve my goal? Is there a name for this concept or is it so uncommon I'll have to build/fabricate it all myself? As far as a ratcheting mechanism, I believe I'd be looking to use a freewheel clutch or I'd need an oscillating lever carrying a driving pawl over top a ratchet gear. My biggest struggle in finding affordable parts is the ratcheting mechanism.