Did tons of math and tons of brainstorming. The math is absolute hell and annoying but desmos is carrying. I got a shape for the non-circular gears for now (they can’t be called elliptical), see the first image. The sharp angles might be a problem with the gears depending on how many teeth are on them, so I may have to change a fully flat output to something very slightly oscillating.
I spent a good amount of time thinking about how to eliminate the clutch. I am no longer as confident about there being a solution as right after opensauce, but I may be onto something. I came up with a mechanical “absolute value” system which takes an input and basically gives the absolute value of it. The input will be both geared and belted to an output shaft, and the recieving gear and pulley will have a one way bearing on them. Since the direction of each recieving thing is opposite to eachother (the gear changes direction while pulley keeps it the same), one bearing will always be ratcheting while the other is transmitting torque. Therefore, regardless of how you spin the input, the output always spins in the same direction.
Also, after doing the math, it turns out that the output osciallting speeds isn’t symettric in both directions: it’s actually faster when spinning one way than the other. This is really good because it gives me a way to differentiate between the two directions. I sitll haven’t figured this out yet but I think I’m in the right direction.
Overall, the math is complete hell and I’m not too sure whether it’s even possible to eliminate the clutch entirely and shift to a system of one-way bearings. However, I do feel like I’m somewhat onto something.