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## Main Question or Discussion Point

A few weeks ago, I decided to challenge myself, and design a wooden pendulum clock. It's been loads of fun, especially the hard parts. One such hard part prompted me to make this thread.

Here is the problem:

Like any regular clock, The hour, minute and second hands are on the same axis, however, most wood clock kits I see don't include a second hand. Placing the hour and minute hand (reduction of 12:1) on the same axis wasn't too difficult. The challenge there was to have 2 pair of gears whose final ratio was 12:1, and the sum of the diameter of each pair were the same (so i had 0.4":1.6" and 0.5":1.5", where 0.4"+1.6" = 0.5"+1.5" = 3"). The problem for the second and minute hand is exactly the same, only with a 60:1 ratio. My approach with the first set was trial-and-error, but I'm looking for an analytical approach since trial-and-error isn't working here. I tried setting up simultaneous equations, but there are only 2 equations with 4 unknown gear diameters.

This problem has obviously been solved many moons ago, but I'm not sure what to call it so I can search for a solution.

Here's the clock so far. You can see the 12:1 gear set on the main face.

http://img189.imageshack.us/img189/8929/1009jc.jpg [Broken]

Here is the problem:

Like any regular clock, The hour, minute and second hands are on the same axis, however, most wood clock kits I see don't include a second hand. Placing the hour and minute hand (reduction of 12:1) on the same axis wasn't too difficult. The challenge there was to have 2 pair of gears whose final ratio was 12:1, and the sum of the diameter of each pair were the same (so i had 0.4":1.6" and 0.5":1.5", where 0.4"+1.6" = 0.5"+1.5" = 3"). The problem for the second and minute hand is exactly the same, only with a 60:1 ratio. My approach with the first set was trial-and-error, but I'm looking for an analytical approach since trial-and-error isn't working here. I tried setting up simultaneous equations, but there are only 2 equations with 4 unknown gear diameters.

This problem has obviously been solved many moons ago, but I'm not sure what to call it so I can search for a solution.

Here's the clock so far. You can see the 12:1 gear set on the main face.

http://img189.imageshack.us/img189/8929/1009jc.jpg [Broken]

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