Calculating Gear Ratios With Restrictions

[DarthRiko]

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.

 

[Tommaso_Russo]

I have three sizes of gears with 14, 34, and 84 teeth respectively.
I need an exact 1:60 gear ratio. ...
Assume I have unlimited gear and space.

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.

For those of you wondering, I'm attempting to build an accurate K'nex clock.

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...