I have three sizes of gears with 14, 34, and 84 teeth respectively. I need an exact 1:60 gear ratio. The problem I am finding is that 14:34 and 34:84 are very close to the same value. 14 and 84 is 1:6, but without a 1:10, that doesn't get me far. The closest I can get is 7:612 (1:87.42857....) I would greatly appreciate some help here. Assume I have unlimited gear and space. For those of you wondering, I'm attempting to build an accurate K'nex clock.
It's simply impossible. Decompose your numbers in prime factors: 14 is 2x7, 34 is 2x17, 84 is 2x2x3x7, 60 is 2x2x3x5. When you couple two gearwheels with N1 and N2 teeth, their rotational speed ratio is the rational (Oh really? ) number N1/N2; for a gear train, will be N1/N2*N3/N4*N5/N6..., i.e., with your gears, a number expressed by a fraction containing products of several 2,3,7 and 17 in both numerator and denominator. It will never be 60, at most some approximation. If you cannot use gears with a teeth number multiple of 5, after days, months or years, your minute clock hand will be on 12 while the hours hand is between 1 and 2...