# Dividing the number 60 and Amateur Questions...



## JAndrew (Sep 10, 2013)

This is my first post here though I've been reading these threads for quite a while. You folks are one talented and helpful group!

Here's something I figured out that I found kind of interesting before I get into my questions. (You experienced guys probably already know this).

I'm cleaning up an Atlas 10H lathe I found locally from a guy who was selling everything and buying a sailboat. The bull gear of this lathe has 60 evenly spaced holes on it's chuck-side face and a small pin you can move in to index a work with these 60 divisions. I didn't know about this feature until I started cleaning up the machine. This opens up a whole bunch of useful purposes from dividing to stamping graduations on thread dials etc.

This got me thinking, "Well what can't I do with 60 index holes?" and "Why 60?"

Here's all the numbers that sixty can be divided evenly by:
1,2,3,4,5,6,10,12,15,20,30 and finally 60.

60 is one powerful number!  If there was 100 divisions instead there would only be 8 possible even divisions but with 60 there are 12 possible!

Why would I ever need to divide by 7 or 9 anyway?

I suppose the globe being divided into 360 lines of longitude and latititude has something to do with the versatility of the number 60.

On to the questions:

How would one use this dividing feature most effectively? Somehow a small milling head must be rigidly attached to the cross-slide, toolpost or carriage. But how is this done best and how was it done on the machine originally?

I've seen one posting here by a smart guy named WheelTapper where he had fabricated a small drill spindle with a pulley and mounted it to this cross-slide. In this setup he had an electric motor hanging from a slide track above the lathe to drive the pulley. Pretty ingenoius. At the bottom of the page on this thread: http://www.homemodelenginemachinist.com/f25/basic-dividing-chester-comet-lathe-9081/

I had considered mounting some kind of spindle directly to the Atlas milling attachment. This gives you the vesatility of being able to adjust the height of the milling bit. My concern with this is that it would not be rigid enough and would chatter like crazy (not the the Atlas lathe is known for rigidity anyway).

Another consideration is if you mount the spindle to the toolpost or milling attachment, you can use your compoundrest angle for things like dividing bevel gears. Again my concern with this is wouldn't it be too loosey-goosey?

Any pictures or advice you guys can offer, I would be extremely grateful. I did a little work on a South Bend lathe with a Dumore Versa-Mil setup when I was in the submarine navy but I still have a lot to learn before I get started.

Thanks in advance!
-J.Andrew


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## Mainer (Sep 10, 2013)

That's why the Babylonian number system was based on 60! That's why I used a 60-tooth gear in my homemade dividing head.

You won't achieve a lot of rigidity in an auxilliary spindle, the best you can do.  You might pick up a copy of "The Amateur's Lathe" By L.H.Sparey. I think he discusses such things. Another option is a filing rest, two hardened steel rollers that can be adjusted for height around the work to control filing depth. Typically used to file 6 flats when making a nut, for example.


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## JAndrew (Sep 11, 2013)

Mainer,

Thanks for the reply. I will check out that book as the original Atlas manual leaves a little to be desired. Is your homemade dividing head posted on here? I will look for it.  I guess I should just start saving my pennies to buy a mill instead of trying to exceed the capabilities of this lathe.

Thanks again,
-J.Andrew


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## Henry (Sep 11, 2013)

It is so good that we still using that number every day.
Is because that that one hour is 60 minutes and the
 minute divisions are also 60 seconds.
And the division of the circumference in 360 degrees is the same and add more divisors.


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## JAndrew (Sep 13, 2013)

Henry,

Thanks for the post. And it make so much sense too. What better way to divide a day (or a year) than to use a base 60 system. A day's length is determined by a rotating circular object (globe) anyway.

Pretty thought provoking. Smarter fellers than I were able to figure this stuff out long ago!

-J.Andrew


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## MachineTom (Sep 13, 2013)

Most dividing heads use a 40:1 ratio in the gearing, My rotab is 72:1 with a crank dial divided into 50 tic's, yielding 1/10 degree or 6 minutes of arc per tic.

Most arc's today are stated in degree's and tenths and hundreds of a degree, not the old style of degrees, minutes, seconds. So the need of using 60 is not that strong as your thoughts make it seem. 

A dividing head of 40:1 will do almost all gear teeth counts in use except some of the higher prime numbers like 127 with only 3 index plates. A compound dividing head will do any number of divisions.


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## Mainer (Sep 13, 2013)

I made my dividing head out of a South Bend 10K headstock so the spindle nose and collets match my lathe...very handy. I used a 60:1 gear ratio because, if you figure out the index plates, you can get by with drilling slightly fewer index plate holes for a 60:1 ratio vs. a 40:1 ratio. In practice, I've never made any index plates -- I picked up an index plate at a used tool place and have gotten by with just that. The smaller diameter of a 40:1 gear would have been advantageous in getting everything to fit, too. If I were to do it again I'd probably design for 40:1.


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## petertha (Sep 13, 2013)

JAndrew said:


> Why would I ever need to divide by 7 or 9 anyway?


 
One biggy I can think of - radial engines extending from their crankcase. 5,7,9.. are magical numbers related to that application, probably related to efficient packing of displacement volume & ignition timing.


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## JAndrew (Sep 14, 2013)

MachineTom and Mainer,

Thanks for opening my eyes on the 40:1 dividing heads and for the pictures. I'm still trying wrap my head around the math behind a 40:1 ratio. I'm curious how many rings of how many holes there are on the plates?

Petertha,

Good point about the radials. I forgot about the odd numbers required to have every other cylinder fire.

Thanks all,
-J.Andrew


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## JAndrew (Sep 14, 2013)

Mainer,

Got looking at your pictures there and I'm wondering what the other two black levers are all about. The bigger one looks like a spindle clamp? The smaller one looks like it interacts with an index ring like I was talking about on my Atlas. Are you double indexing?

Thanks,
-J.Andrew


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## Tin Falcon (Sep 14, 2013)

> It is so good that we still using that number every day.
> Is because that that one hour is 60 minutes and the
> minute divisions are also 60 seconds.
> And the division of the circumference in 360 degrees is the same and add more divisors.



Good point


And the 127 gear that is mentioned is a metric transposition gear. 25.4 x 5 =127



> A dividing head of 40:1 will do almost all gear teeth counts in use except some of the higher prime numbers like 127 with only 3 index plates. A compound dividing head will do any number of divisions.


Also a very good point
Tin


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## Mainer (Sep 14, 2013)

The larger black handle is indeed a spindle lock. It tightens a split cotter and even mild tightening is enough to lock it up like the hinges of hell. The smaller handle lets you adjust the position of the direct indexing pin. The pin can slide forward or backward just over 1 hole spacing, or it can swing out of the way. There are 24 holes around the former bull gear. The worm can drop out of engagement with the wormgear so the spindle will turn freely for direct indexing using the 24 holes. 

The particular index plate I happen to have has hole circles of 15, 16, 17, 18, 19, and 20. That gives me factors of 2, 3, 4, 5, 6, 8, 9, 10, 15, 16, 17, 18, 19, and 20. Those factors cover a lot of possible divisions.

The math is pretty simple. Say you have a 60:1 ratio and you want 45 divisions. Divide the gear ratio by the number of divisions = 60/45 = 4/3 or 1 full turn plus 1/3 of a turn. For a 40:1 ratio, 40/45 = 8/9 of a turn.  So for the first case you'd need an index plate with a factor of 3 (e.g. 1/3 would be 5 holes on my 15-hole circle), and for the second case you'd need an index plate with a factor of 9  (e.g. 8/9 would be 16 holes on my 18-hole circle).

For a 72:1 gear ratio, it would be 72/45 or 8/5 or 1 full turn plus 3/5 of a turn.


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## JAndrew (Sep 15, 2013)

Mainer,

Thank you sir for the explanation and the time it took. It's starting to become clearer. Based on your text I will start sourcing a 40:1 worm gear set to someday build an index head being that it's a bit more compact. I'll peruse the forums to find the number of holes needed on the plates for a 40:1.

HMEM is an incredible learning tool!

Thanks again!
-J.Andrew


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## GailInNM (Sep 15, 2013)

If it helps any, my very old commercial Ellis dividing head, which has a 40:1 gear ratio, has the following holes in the plates.

Plate #1
15, 16, 17, 18, 19, 20

Plate #2
21, 23, 27, 29, 31, 33

Plate #3
37, 39, 41, 43, 47, 49

Gail in NM


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## JAndrew (Sep 15, 2013)

GailinNM,

Thank you it does help! I'll store this info away for that project. Looks like I would be able to get away with just making plate #1 to begin with and could make the other plates down the road.

Thanks again!
-J.Andrew


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## Mainer (Sep 16, 2013)

I suspect you will never need plate 3 and will probably never need plate 2. Make one or the other, if and when.


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