View Full Version : stupid math!

01-16-2014, 05:03 PM
I have a 16tpi lead screw that I want to put a hand wheel and dial on. My 5th grade math tells me a dial with 80 divisions will give me 0.05" per mark. 160 divisions 0.005. Is my math good?

01-16-2014, 05:22 PM
No. You will move .0625 per revolution, 1/16". You will move .125 per 2 revolutions, 1/8". To move .001 per mark you would need 62-1/2 divisions on the dial. To move .005 per mark you would need 12-1/2 divisions on the dial.

01-16-2014, 05:23 PM
If I were a math teacher I'd probably say, "show your work".


My back-of-envelope calc says that if a lead screw is 16 tpi then one turn gives 1/16 of an inch travel (or 0.0625").

Dividing 0.0625 by 80 I get 0.00078125 per division.

And dividing 0.0625 by 160 I get 0.000390625 per division.

Yes, I know that I have too many significant digits in those answers, so please ignore the excessive precision.

But maybe I've overlooked something or misunderstood something.

Bob Fisher
01-16-2014, 05:33 PM
Maybe, you should have stayed a couple more years.Bob.

01-16-2014, 05:41 PM
This is a good question. I have a 6 tpi leadscrew that I need to translate into understandable divisions. My plan is to put the indicator dial separately and drive it through a gear ratio- if I'm not mistaken, it would take a 100 tooth gear on the leadscrew and a 60 tooth gear on the indicator dial. That way I can get a direct reading of thous if I mark out the dial properly.

Your procedure could be the same- except that you mount a 100 tooth gear on the leadscrew and a 160 tooth on the separate dial.

What I had in mind was to put a toothed belt around the 'gears' instead of engaging them as normal gears. That way I believe you get a smoother transition- a more linear relative rotation of the second, indicator, gear. If your gears mesh really well with little to no play, then perhaps that's just as good.

I'm open to correction if I did the math wrong, and I welcome comments on this idea.

01-16-2014, 07:40 PM
If you put 60 divisions on the dial each will be .001041" - Is that close enough to what you're looking for?

01-16-2014, 08:17 PM
You would be out 2-1/2 thou per rotation of the dial. That's a lot closer than the dials I've seen on at least one combo machine :(, but you'd still have to make sense of having 60 thou per turn, and then count them up if you're moving a few inches- then add in the error. I don't think it's worth the hassle- set it up right the first time. MHO

01-16-2014, 08:36 PM
Bob, if I stayed in school I would not had the opportunity to experience chronic knee pain from refinishing floors :(

1/16 = 0.0625 (random #'s I should have wrote down\0.0625)*something=80
dang it! It made sense a week ago when I signed up for the other forum, that still hasn't "approved" me, clearly I was wrong. Thanks for the helpful replies.

darryl, maybe if you used a pulley with a tight rubber band or some such, there wouldn't be any slop in the gears. If the hand wheel drove the screw directly with the belt driving the dial you wouldn't have to worry about slippage.

01-16-2014, 09:25 PM
If you put 60 divisions on the dial each will be .001041" - Is that close enough to what you're looking for?
62 divisions is .00100806" error of .00048387 per revolution (under 5 tenths), .00774192 per inch or 16 turns, and .0920304 per foot . . . You will never see the error unless moveing quite a way then just set a new index point or do the math to correct using the error numbers I just gave you.

01-16-2014, 09:39 PM
I love your handle I miss my atlas.
I has a 10" F model Atlas lathe with babbit bearings.
It was kinda shltty for a lathe, but I learned a lot on it.
I miss my Atlas too.


Paul Alciatore
01-16-2014, 11:32 PM
The simple answer here is a 16 TPI lead screw is not a good choice if you want 0.001" divisions. Nor are any other TPI numbers where the exact answer to 1/TPI has more than three decimal places. Thus; 5, 8, or 10 TPI would be good choices as 1/5 = 0.2", 1/8 = 0.125" and 1/10 = 0.1". All of these have three or fewer decimal places.

If you want to put a thousandths dial on a 16 TPI lead screw you will need to use some kind of trick. For instance, you could put 125 divisions on the dial and use alternate divisions on each rotation. That would be very confusing.

Another way would be to use either gears or a timing belt to a second, parallel shaft with the divided dial. The gear or pulley on that second shaft would twice as many teeth as the one on the lead screw. Then 125 divisions on the secondary shaft would product two rotations of the lead screw and each of the 125 divisions on it's dial would be exactly 0.001".

A ring and planet gear system could probably put this gearing on the same axis, but would be more complex.

The good TPI choices for getting 0.001" divisions are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100. Outside of that range there are others, but it gets ridiculous. Any others in that range would require gearing or some other trick.

Paul Alciatore
01-16-2014, 11:39 PM
Math is not stupid. Math works. Math is the most logical thing you will ever encounter.

Math is your friend! Embrace it.

michigan doug
01-17-2014, 09:19 AM
Starts to make a Digital Read Out look very attractive doesn't it? They have come down in price, and there are some quick and dirty ways to use a 6" vernier calipers with magnets and/or clamps to give you a very useful "travel dial" of sorts.


phil burman
01-17-2014, 12:52 PM
You could buy a 20 tpi lead-screw for about 10 bucks a foot, thereby saving the cost of a pack of paracetamol:)


01-17-2014, 01:16 PM
Using a 16tpi lead screw 125 divisions on the dial will give you a resolution of 0.0005/division. In my mind the fact that the lead screw moves 0.0625/rev is a major drawback. When traversing having to count by 16ths of a inch is pain when working to decimal inches. I'd switch to a 10tpi lead screw with 100 divisions on the dial (0.001/div, 0.01/rev).

01-17-2014, 03:54 PM
Starts to make a Digital Read Out look very attractive doesn't it? They have come down in price, and there are some quick and dirty ways to use a 6" vernier calipers with magnets and/or clamps to give you a very useful "travel dial" of sorts.


Got a digital read out display and scale on Ebay for $36 or so, with that you could have inches, metric and factional inches. Good for .001 per 6 inches. There is a guy on here selling the exact same brand.

01-18-2014, 09:14 AM
I had an atlas 10x56 also with babbit bearings. At the time I thought every lathe after can only be better. Then I got a 7x14...

01-18-2014, 10:07 AM
That would be enough to make anyone miss their Atlas!:(

01-18-2014, 11:24 AM
Thanks for all the help. So to summarize: 16tpi lead screw bad. I will need a screw that is evenly divisible into 100 to avoid confusion and headaches.

Paul, You right math is great, it just makes ME feel stupid... sometimes :confused: