"Marv" wrote in message
...
On Wed, 26 Nov 2008 13:14:17 -0600, "Karl Townsend"
wrote:

I'm setting up rigid tapping on my mill. The encoder is ahead of the
backgear so I'm wanting the exact gear ratio. I set up an encoder on both
the shaft before the backgear and at the cutting tool so I could measure
the
turns of the spindle down to .01 revolution accuracy and took this data

Turns at tool turns at drive
1 6.1245
8 49.0573
80 490.65
163.050 1000

Is there a math wiz out there that can tell me how many teeth on the drive
gear and how many on the driven gear? (integer ratio of this data)

Karl


As asked, your question has an infinite number of answers. There are
an infinite number of ratios of integers that can yield a value of
1/6.1245 = 0.163279.

That said, plugging 0.163279 into my RFRAC program (see my page), we
find that that number can be approximated (using continued fractions)
by the integer ratio 8/49 with an accuracy of 0.008%. Thus whatever
gears are actually mounted, their tooth counts should come close to
being some multiple of 8/49, e.g., 16/98, 24/147, etc..

If you want a more accurate approximation than 0.008%, download the
program - one of its inputs is the desired accuracy of approximation.

Regards, Marv

Home Shop Freeware - Tools for People Who Build Things
http://www.myvirtualnetwork.com/mklotz

No way this is a substitute for Marv's method, but you could just use a
spreadsheet. Set up a column going from 1 to 100 (more if you want) and
multiply your fraction by each number in turn. It should be quick enough to
spot the close matches: here's a section

47 7.674113
48 7.837392
49 8.000671
50 8.16395
51 8.327229
52 8.490508