> gear size, etc. are interesting, but I don't see how they're strictly necessary. Can you explain? Simple: The chain won't grip the gear. Gears must be desi

> gear size, etc. are interesting, but I don't see how they're strictly necessary. Can you explain? Simple: The chain won't grip the gear. Gears must be designed such that the chain never intersects the gear (two things can't be in the same place at the same time). That precludes 'hooks' on the teeth of the gear, and means that the face of the gear tooth must be perpendicular to the chain link. However, that means that at any other angle, the angle of the tooth is providing a small component in a direction that pushes the chain off the tooth. When your chain is contacting many teeth, this force gets smaller by 1-cos(angle between teeth) per tooth - so after about 6 teeth or so, the force is so tiny as to be irrelevant. However, in OP's design there is minimal tension and only 1 tooth touching at a time, so the chain will jump off the teeth. There is a huge and very old field of chain and sprocket design, the details of which I am not very familiar, but I do know the basic rules of "some non-zero tension", "bigger subtended angle=better" and "engage as many teeth as possible". (other interesting chain facts: the invention of the bicycle was enabled by the invention of sufficiently good chains. chains are better lubricated by grease not oil. chain wear gets exponentially worse, not linearly. centripetal force limits fast moving chains. )