Gears-Geometry of Tooth Profile

We dealt in our first paper geometry governing the transmission of rotational motion of one shaft to another. It was assumed that drive was transmitted through friction between pitch surfaces. In actual practice however teeth are provided on the pitch surface to ensure that the motion may be positive. This necessity of providing some sort of driving agent was felt even by the ancients. This took the form of pegs driven on the periphery of the wheel and spaced equally. Such wheels were known as cog wheels. It will be easily seen that the worming of such a pair of wheels cannot be satisfactory. So far as it known, the famous Danish astronomer Ole Roemer (1644-1710) made a systematic attempt to study this problem.