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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.