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I'm thinking about a simple 1-second pendulum clock with a 30-tooth, 1 rpm (second hand) escape wheel. I want to put in 3 more wheels, with the 3rd wheel running at 1/720 rpm (hour hand). There are plenty of intermediate ratios to choose from, with the most obvious being a train of 8:1, 9:1, and 10:1 (total 720:1). The problem with integer ratios is the same tooth on the wheel always hits the same tooth on the pinion so wear from imperfections is not spread out over all the teeth, but concentrates on just a few. So I want there to be NO INTEGER RATIOS.

No problem. I wrote a Java program in about 20 minutes that allowed me to search through various tooth counts to get what I was looking for. I had the program try lots of values that were still reasonable. So here's one possibility:

Hour wheel: 84 teeth. Mates with 8 leaved pinion on 2nd wheel. Ratio: 10.5.

2nd wheel: 64 teeth. Mates with 7 leaved pinion on 3rd wheel. Ratio: 9.143.

3rd wheel: 45 teeth. Mates with 6 leaved pinion on escapement. Ratio: 7.5.

But that's 3 different pinon cutters to make. So I thought maybe this one is easier:

98:7 , 60:7 , 42:7. This has the advantage that all the pinions are identical, but does introduce an integer ratio there at the end (42:7 = 6:1).

I'm considering buying a cutter set (probably 0.5 or 0.4 modulus). Then I thought if I constrained the pinions to at least 10 leaves, I wouldn't have to make any pinion cutters at all. Usually a cutter set of a particular modulus includes cutters down to 10 teeth. So I thought maybe:

120:13, 104:10, 75:10.

Now we're getting up there with 120 teeth on the hour wheel (only 1.5 degrees per tooth)!

What's the thinking here? What should I be looking for in my huge table of possible gear ratios? Any help would be greatly appreciated.

No problem. I wrote a Java program in about 20 minutes that allowed me to search through various tooth counts to get what I was looking for. I had the program try lots of values that were still reasonable. So here's one possibility:

Hour wheel: 84 teeth. Mates with 8 leaved pinion on 2nd wheel. Ratio: 10.5.

2nd wheel: 64 teeth. Mates with 7 leaved pinion on 3rd wheel. Ratio: 9.143.

3rd wheel: 45 teeth. Mates with 6 leaved pinion on escapement. Ratio: 7.5.

But that's 3 different pinon cutters to make. So I thought maybe this one is easier:

98:7 , 60:7 , 42:7. This has the advantage that all the pinions are identical, but does introduce an integer ratio there at the end (42:7 = 6:1).

I'm considering buying a cutter set (probably 0.5 or 0.4 modulus). Then I thought if I constrained the pinions to at least 10 leaves, I wouldn't have to make any pinion cutters at all. Usually a cutter set of a particular modulus includes cutters down to 10 teeth. So I thought maybe:

120:13, 104:10, 75:10.

Now we're getting up there with 120 teeth on the hour wheel (only 1.5 degrees per tooth)!

What's the thinking here? What should I be looking for in my huge table of possible gear ratios? Any help would be greatly appreciated.

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