The first thing to keep in mind is that these are not general purpose machines.  They only do one thing, which is estimate the trajectory of a particular type of bullet, given several inputs.<p>This lets the designer do a lot of precalculation, so they might use a series of cams that approximate known curves or differentials some known ratio.<p>Useful google terms are things like &quot;mechanical fire control computer&quot; or &quot;mechanical tide predictor&quot;.<p>Check out &quot;Old Brass Brains&quot; it might give you an idea of how to approach this kind of problem mechanically; or at least how sophisticated a mechanical approach can be.