Realised some finer details we missed on the previous day about the eggbeater gears. There are lots of scribbles because later on I found that some of the things I wrote were wrong, so they've been corrected here.
Above is the gear that changes direction. We'll call that the change gear. This one needs teeth all 360degrees around. The sectors on the right show that the direction you rotate matters. Because you'll only ever rotate the change gear 300degrees. So the point at which a left/right gear needs to catch on to the teeth to make it change direction depends on what direction you're turning the change gear. And once you go in one direction you have to go in that direction the whole time. Turn it back and it ruins the set up, then it won't work properly.
As explained above, the left+right gears need to be on very specific points on the change gear so that the teeth catch at the right time. The diagrams on the right show this. I also explain why exactly half the gear has to have teeth on it. The answer is that only one set of teeth should be interacting with the change gear at any one time. If it's more than half then two sets of teeth would touch the change gear. The left and right gears would then be in conflict, stopping the whole thing from working. If it's less than half then you get an awkward pause where nothing happens.
This explains how to get the size of the left and right gear. I'm not sure if this is completely accurate, but that's up to Jenny to test out.
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