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Lathe Change gears

combustable herbage

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I love it when your I'm right gut instinct is so wrong and I am so glad I am able to put blind faith in Lapua's counting skills and not stare at a picture for an hour;).
 

Susquatch

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Other than the odd number, that gear could still be used instead of a 127 tooth. The error would be less than 1%

Yup. 0.79%

But surely it wasn't intended for that. Just as easy to do it right.
 

Susquatch

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forgive my ignorance, but why is 127 a special number for gear teeth?

There are EXACTLY 2.54 cm in one inch. 254 / 2 = 127. So a 127 (or a 254) gear provides for a perfect metric imperial conversion.

A 254 gear is too big. 127 is the smallest gear that can serve this perfect function.
 

Susquatch

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in combination with a 5 tooth gear? Surely it is the ratio that matters. This must be some kind of standard that I know nothing about

Yes, it is the ratio that matters.

Maybe it's obvious, maybe it's not. But after you have a gear that provides for an exact conversion, you can then add any number of other gears to get to the desired metric or imperial pitch.

But 127 is the smallest gear that will get you to an exact conversion. It isn't a standard per-se. It's just an exact mathematical conversion factor that needs to get stuck into the gear train somewhere.

If you write out a formula for getting any pitch from metric to Imperial, that formula will contain 254 or 127 or some multiple of that. That just the way it is. We can be grateful that it's not some flaky number like 2 276390234767.
 

mbond

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There are EXACTLY 2.54 cm in one inch. 254 / 2 = 127. So a 127 (or a 254) gear provides for a perfect metric imperial conversion.

A 254 gear is too big. 127 is the smallest gear that can serve this perfect function.
Yes, all imperial units have been redefined in terms of SI ones. Inches and feet, pounds weight and force, acceleration. Everything.

And the SI ones are all supposed to be derived from fundamental physical constants. But that's not true

As an even number, the first prime factor of 254 is 2. 127 is also a prime number, so no further factorization is possible. Surely there are other tooth counts that generate the same _exact_ ratio. But I guess this is the simplest / standard one
 

Susquatch

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127 is also a prime number, so no further factorization is possible. Surely there are other tooth counts that generate the same _exact_ ratio. But I guess this is the simplest / standard one

I wasted a fair bit of time (thankfully on the payroll) many many years ago trying to find a better way. The problem is that gears can only be integers. Although any higher multiple will work, 127 is the lowest number of teeth that will do the job. Everything else is an approximation. At least that was my conclusion at the time. I should add that my boss's boss was a member of Canada's metrication committee. He is the one who convinced the entire North American Auto Industry to go Metric (including the US auto industry). He loved math even more than I do. He supervised my gear work and agreed that that there was no other way.

Having said that, if you can think of one, I'm all ears and would love to explore it with you. Never ever say never!
 

mbond

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I was teaching my son about prime factorization a few weeks ago. He is in grade 3, but very keen on math. I'm not sure how much he actually understood, but he seemed very excited.

I didn't understand the point, but the math is simple enough. Somewhere in the gear train you want a 254:1 (or 254:10 or 254:100) gear ratio. The fact that 254 has only 2 prime factors (2 & 127) means that you are stuck with these numbers and their multiples. There is no combination of 3 or 4 or 17 gears that will ever get you to that exact ratio. It is only possible with the number itself and 1, or combinations of prime factors. You then add other gears as needed.

I see that there is a whole other thread exploring this topic in a lot more detail.
 

Susquatch

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I have a wonderful book recommended to me by our member @StevSmar several years ago that covers a lot of this stuff. I'm on my second reading of the book. Here are some interesting facts about imperial and metric as it relates specifically to length.

The earliest known use of the inch appeared in the 7th century and was commonly known to be the width of a man's thumb at the root of the nail. Hardly a precise unit of measure but good enough for the time. (Can you imagine a thou being 1/1000 of your thumb width!)

The earliest use of the cm coincided with the earliest use of the meter. The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle through Paris.

The two units existed separately until 1959 when an international agreement established that the inch would be officially defined as exactly 2.54 cm.

It can be said that the meter and centimeter are based on a physical parameter associated with the size of the earth. But the modern inch is actually based on the size of a centimeter. Go figure!
 

Mcgyver

Ultra Member
That was painful. Especially for an old guy with one good eye......

But I totally and completely deserved that. Kudos to you for very kindly and gently getting me to do it.

Truth be known, I never did finish. I've probably tried 6 times now. Each time I thought I was gunna make it, that part in the shadow kicked me so hard I lost count!

I'm still laughing. o_O;):D

Just sell it to Susquatch and tell him its 127
 

Bandit

Super User
Thought the meter was based on distance from earth to the moon. So are you also saying any measuring tools pre 1959 may not be any good? Eg. as in pre 1959 what was the centimetre to inch measure?
It's all O.K. With the gear, every time it's counted will be different, so may good for 125 to 130 teeth jobs! As long as inside and outside threads are turned with the same setup, all will be good.
 
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