Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137895?p_p_auth=8QnKtT9I.
I am to design a two step gearbox. The first step is to choose the number of teeth in each cog wheel in order to achieve a gear ratio of 17.3. In other words:
(N1 N2)/(n1 n2) == 17.3
where N1 and N2 are the number of teeth in gear 1 and 2, and n1 and n2 are the number of teeth in pinion 1 and 2. Is it possible to get Mathematica to "guess" the lowest number of teeth possible and still get as close as possible to 17.3? The number of teeth in the pinions must not be lower than 20. In addition, the number of cog teeth in the gears must not be divisible, i.e. only common factor has to be 1.