# Can someone help me wrap my head around all the divisions needed for a diving index?



## G Jones (May 10, 2021)

I'm trying to decide what divisions I reasonably need to be able to make any needed set of divisions, from 2 - ?? (max accuracy of my machines)

im thinking of rings of trhese divisions
5
12
15
a second set of 15 offset by 1/2 
50
another set of 50 with a 1/2 offset

from what my napkin/brain math can figure, I should be about to make any variation of even divisions from 2-400 (or more) with this set of divisions. the 12/15 variations cover all the lower divisions (think base 60 math like the babylonians used (or Mesopotamia? does it matter?)
the two larger groups with the offsets should cover any other combination I could want all the way to 400.

Does this make sense? is there a common pattern used by precision indexes?
I truly appreciate any feedback; I'd really rather not sit down and do the math to make sure I can come up with any gear pattern I need. It sounds like a terrible bore.

Thanks so much! Cheers!
-GJones


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## Lo-Fi (May 10, 2021)

Same calculation with different inputs over and over again? Excel is your friend here! I'll try and rake out a spreadsheet I made a while back if you're interested. 

What will trip you up is primes, of course, but it's not clear what you're trying to do? Direct indexing?


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## RJSakowski (May 10, 2021)

For a simple dividing plate, I would think that you need divisions for each of the prime numbers or multiples of the prime numbers.  For example, if you require 7 divisions, you need a plate with 5, 14, 21, etc. divisions will work.  The prime numbers up to the notorious 127 are 1, 2, 3, 5, 7, 11, 13, 15, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 97, 101, 103, 107, 109, 113, 127.  In order to make any if those divisions, you will require a plate with either those divisions or a multiple of those divisions. 50 = 2 x 5 x 5  so a plate with 50 divisions will do 2, 5, 10, 25, or 50 divisions.  Similarly, 60 = 2 x 2 x 3 x 5 so a 60 division plate will do 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, or 50 divisions.

If your plan was to use two plates with the second offsetting the first, there would be a little more versatility. The spin indexer is an example.  The main disk has 36 divisions, giving 10º increments while the vernier holes are 11º part which effectively provides 1º increments, thus providing 360 angles in 1º increments or the same as a dividing plate with 100 divisions. I set up a spreadsheet to see what possibilities there were with using a 12 hole and a 15 plate in this manner and came up with 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, & 60 as the possible divisions.


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## G Jones (May 10, 2021)

Lo-Fi said:


> Same calculation with different inputs over and over again? Excel is your friend here! I'll try and rake out a spreadsheet I made a while back if you're interested.
> 
> What will trip you up is primes, of course, but it's not clear what you're trying to do? Direct indexing?


Id like to make a smal precision index that I can use to divide not only common gears, but pretty much any radius I really want. Its for dial indicators and eventually watches, so I'm not going to be sweating over primes, but I have this little itch after doing some quick memopad math, that I should be able to hit just about every degree or whatever up to a reasonably usable number with a minimal amount of drilled rings.
The 1./12 and 1/15 divisions should take care of all the smaller number sets, and then by having a larger clever ring or two, as well as an "offset" to slide between the 30 or 50 pin wheels, I feel like there is a way to make a maximum amount of gear patterns with a minimum number of holes.

I worry that this is actually getting into some pretty heavy theoretical maths, I have no Idea if anyone has figured this out before, and I don't know where I'd look to find papers on the subject anyways.

Its just a neat thought experiment. How can I make the maximum amount of variations with the smallest amount of hole sets. The answer lies in being able to offest the rings by fixed amounts to use them for more than one position. I jsut like thinking about this stuff, and its way cooler than spening a week CAREFULLY marking with dividers, drilling 500 holes, then reaming each one perfectly, only to slip up 90% percent of the way through and contemplate baking my head in the oven. (not serious)

EDIT: my dying stiff miserable keyboard is unreliable so I apologize for the constant egregious typos
EDIT NUMERO DOS;  I mistyped radius a bunch as radians. screw radians. I aint got time for that **** and its not applicable to this in any way any how. RADIUS not RADIAN


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## G Jones (May 10, 2021)

I have zero experience with excel. This is the sort of theoretical problem I learned to solve by drawing diagrams, and using some basic precalc operations


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## G Jones (May 10, 2021)

RJSakowski said:


> For a simple dividing plate, I would think that you need divisions for each of the prime numbers or multiples of the prime numbers.  For example, if you require 7 divisions, you need a plate with 5, 14, 21, etc. divisions will work.  The prime numbers up to the notorious 127 are 1, 2, 3, 5, 7, 11, 13, 15, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 97, 101, 103, 107, 109, 113, 127.  In order to make any if those divisions, you will require a plate with either those divisions or a multiple of those divisions. 50 = 2 x 5 x 5  so a plate with 50 divisions will do 2, 5, 10, 25, or 50 divisions.  Similarly, 60 = 2 x 2 x 3 x 5 so a 60 division plate will do 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, or 50 divisions.
> 
> If your plan was to use two plates with the second offsetting the first, there would be a little more versatility. The spin indexer is an example.  The main disk has 26 divisions, giving 10º increments while the vernier holes are 11º part which effectively provides 1º increments, thus providing 360 angles in 1º increments or the same as a dividing plate with 100 divisions. I set up a spreadsheet to see what possibilities there were with using a 12 hole and a 15 plate in this manner and came up with 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, & 60 as the possible divisions.


I hadnt thought of a second plate, but that makes a lot of sense, I was considering some extra holes to allow me to accurately offset a basic group. say 50, to allow me to slightly move the pattern, allowing much more versatility with some well thought out movement operations


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## G Jones (May 11, 2021)

RJSakowski said:


> For a simple dividing plate, I would think that you need divisions for each of the prime numbers or multiples of the prime numbers.  For example, if you require 7 divisions, you need a plate with 5, 14, 21, etc. divisions will work.  The prime numbers up to the notorious 127 are 1, 2, 3, 5, 7, 11, 13, 15, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 97, 101, 103, 107, 109, 113, 127.  In order to make any if those divisions, you will require a plate with either those divisions or a multiple of those divisions. 50 = 2 x 5 x 5  so a plate with 50 divisions will do 2, 5, 10, 25, or 50 divisions.  Similarly, 60 = 2 x 2 x 3 x 5 so a 60 division plate will do 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, or 50 divisions.
> 
> If your plan was to use two plates with the second offsetting the first, there would be a little more versatility. The spin indexer is an example.  The main disk has 26 divisions, giving 10º increments while the vernier holes are 11º part which effectively provides 1º increments, thus providing 360 angles in 1º increments or the same as a dividing plate with 100 divisions. I set up a spreadsheet to see what possibilities there were with using a 12 hole and a 15 plate in this manner and came up with 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, & 60 as the possible divisions.



I've been thinking pretty hard about this - I'm not sure a situation would ever come up where I abslutely would need a prime number of gear teeth either in indexing tools (simple 1-1000 ratios etc depending on resolution), or even more complicated geartrain sued in watches. I may simply be able to get away with some of the more used gear sizes.

EDIT- the only thing I could think of for prime gears is movements in automata that require trains of many, many different sizes and shapes.


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## Norppu (May 21, 2021)

You can also use the BS0 calculator I created for Excel.
You can easily modify it to suit Your dividing head.


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## Optic Eyes (Jul 3, 2021)

Just buy a Chinous copy of a B&S, they work and when you have one, you might never use it, look it as a kind of insurance, like buying a lathe with a steady and 
follower rest, having them means the job never shows up, same for faceplates.
Amateurs worry about things real machinists NEVER DO


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## hman (Jul 4, 2021)

G Jones said:


> EDIT- the only thing I could think of for prime gears is movements in automata that require trains of many, many different sizes and shapes.


About the only "useful" prime I can think of is 127.  That's the number of teeth on an english<->metric transposing gear for a lathe - to make metric threads on a inch lathe with an inchleadscrew, and vise versa.  The inch is now legally defined as 25.4 millimeters exactly.  A transposing gear could have 254 teeth, but 127 is smaller and much more useful.


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## Optic Eyes (Jul 4, 2021)

It's indexing with a 40:1 or 60:1 worm gear, you are doing unecessary thinking


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## jaded13640 (Jul 9, 2021)

I have no idea how I made the Dean's list and got awards for being smart....I feel like a kindergartener among you guys! The old saying, "if you don't use it you'll loose it" is for sure true. I couldn't pass a pre-algebra class now. I know that for a fact, I got out my old books because I was trying to figure something out and couldn't remember how to do it. I don't only couldn't do it, I couldn't even do some of the basics. When I was finished up with college and working in the field nobody wanted us to do algebra. They wanted us to draw the stuff and the computer would do the math and determine angles and sine bar heights. So, as it turned out, I only used algebra or trig ONCE in the years I worked in the field and the only reason I did it by hand then was because we didn't have a good piece of CAD software yet. Once we did it never happened again. 

I just thought I'd drop that in there. Just because you're pretty sure you're never going to use higher math "in real life" there could very well come a time you wished you had kept up with it and could still use it. Some people just remember all that stuff. One of the first things I learned in engineering was NOT remember stuff that could be looked up. Now I wish I had remembered that stuff. 

Wayne


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## chatter chatter cut cut (Sep 6, 2021)

G Jones said:


> Id like to make a smal precision index that I can use to divide not only common gears, but pretty much any radius I really want. Its for dial indicators and eventually watches, so I'm not going to be sweating over primes, but I have this little itch after doing some quick memopad math, that I should be able to hit just about every degree or whatever up to a reasonably usable number with a minimal amount of drilled rings.
> The 1./12 and 1/15 divisions should take care of all the smaller number sets, and then by having a larger clever ring or two, as well as an "offset" to slide between the 30 or 50 pin wheels, I feel like there is a way to make a maximum amount of gear patterns with a minimum number of holes.
> 
> I worry that this is actually getting into some pretty heavy theoretical maths, I have no Idea if anyone has figured this out before, and I don't know where I'd look to find papers on the subject anyways.
> ...


the easy is to buy a saw blade for vinyl siding 120 teeth that look like this vvvvv with a spring loaded indexer. no work with measuring or drilling. all it it needs is teeth counting and labeling


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## hman (Sep 6, 2021)

An additional solution worth looking at is one of the pre-made indexing plates from Alisam Engineering.  They're designed to jam between the lathe spindle and chuck of a woodturning lathe.  Pretty easy to adapt to a metal lathe - just enlarge the hole as needed, maybe mount to the outboard end of the spindle.  They have one ring of 72 holes and another of 20. This will cover a wide range of divisions.





						Alisam Engineering Universal Indexing Systems
					

Model WIS-1.0 and WIS-.75 Complete universal system for indexing on most 7 to 12 inch wood lathes



					alisam.com


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## chatter chatter cut cut (Sep 7, 2021)

hman said:


> hman said:
> 
> 
> > An additional solution worth looking at is one of the pre-made indexing plates from Alisam Engineering.  They're designed to jam between the lathe spindle and chuck of a woodturning lathe.  Pretty easy to adapt to a metal lathe - just enlarge the hole as needed, maybe mount to the outboard end of the spindle.  They have one ring of 72 holes and another of 20. This will cover a wide range of divisions.
> ...





chatter chatter cut cut said:


> the easy is to buy a saw blade for vinyl siding 120 teeth that look like this vvvvv with a spring loaded indexer. no work with measuring or drilling. all it it needs is teeth counting and labeling


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## chatter chatter cut cut (Sep 7, 2021)

more on the saw blade for dividing head. made a internal expanding shaft to fit quill, mounted outboard with saw blade attached and spring loaded latch to hold. the different divisions are marked with different colored inkmarker. if you want a pic i will post one  or private email.


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## Larry$ (Sep 7, 2021)

I had a math minor in college, 4 semesters of calc. All long since washed overboard. I still use basic trig. Spread sheets are great for a lot of things.


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## Brento (Sep 7, 2021)

Norppu said:


> You can also use the BS0 calculator I created for Excel.
> You can easily modify it to suit Your dividing head.


Thanks for the excel spread sheet! Is that able to be edited?


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## Bi11Hudson (Sep 7, 2021)

My father was a "book keeper", not to be confused with an accountant. When I was in grammar school struggling with fractions, he taught me to convert to decimals, do the calculations and then grab an answer close to the decimal solution. I didn't learn fractions very well, but got by on the tests. I finally learned fractions on a B&S index head, where decimals wouldn't work. It had to be fractions. Although I never did fractions, I did understand trigonometry, both for electrical and celestial navigation. And used them repeatedly as I aged. If I had gone to high school, I would probably still be confused.

In answer to the original question, a dividing head is the nominal answer. I have a couple of rotary tables that would be small enough for many smaller projects. Nominal size 3 inch table. One has fraction plates so can be used as a dividing head. With a ratio of 72 rather than 40, many odd numbers can be acheived. Excepting primes, as noted above.

A smaller yet version can be, and has been, built using a small worm and wheel. A lot of work but then that's what we specialize at. Making tools to make yet more tools. I have not built a small dividing head but have seen many uTube videos of such being built. One specifically by an amateur watch builder, by the way. If a suitable worm wheel could be found, fraction plates can be easily developed by hand, with sufficient accuracy to be usable the first generation. Second generation plates have sufficient accuracy for any but NBS use. Mr Pete 222 goes into considerable detail on this subject.

*EDIT:* Added one of many links: 




Fraction plates can be developed for most any prime number, again by hand. Although the higher numbers would make the fraction plate so large as to be essentially useless. All that is necessary is basic geometry and primitive drafting equipment. And a lot of time. . .

.


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## Downunder Bob (Sep 7, 2021)

A couple of years ago when I first bought my lathe I also bought a small divider. It has  a ratio of 90:1. I didn't know at the time that 40:1 is more common. So I'm not sure how useful the 90:1 will be. Any one know if it's good, bad or doesn't matter?


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## pontiac428 (Sep 7, 2021)

On a direct drive system (an indexer with no 4:1 divider), you need only the multipliers and the primes.  If you want 60:1 options, that makes the list very short (easy to attain).

Why would you want prime numbered gears if you only design gear trains with simple ratios?  The answer is a wear-dividing function called hunting teeth.  If I made a 4:1 system with 32t and 8t gears, each tooth on the 8t gear would repeatedly contact the same 4 teeth on the 32t, propagating a wear pattern.  If I instead made a 4.11 system using 17t/70t, it would take 17 revs before any one tooth engaged the same tooth twice.  That 4.11 number should be familiar for long-wearing gears we've seen, and this is why.


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## hman (Sep 7, 2021)

Have you heard this story of the Hot Rod race
When Fords and Lincolns was settin' the pace
That story is true, I'm here to say
I was drivin' that Model A

It's got a Lincoln motor and it's really souped up
That Model A body makes it look like a pup
It's got eight cylinders; uses them all
It's got overdrive, just won't stall

With a 4-barrel carb and a dual exhaust
With 4.11 gears you can really get lost
It's got safety tubes, but I ain't scared
The brakes are good, tires fair


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## Bi11Hudson (Sep 7, 2021)

Downunder Bob said:


> A couple of years ago when I first bought my lathe I also bought a small divider. It has  a ratio of 90:1. I didn't know at the time that 40:1 is more common. So I'm not sure how useful the 90:1 will be. Any one know if it's good, bad or doesn't matter?


I have a couple at 40:1, I don't know where the B&S-0 is so bought an old B&S that isn't "standard". Then have a 72:1 and a potential 90:1. It's set up as a rotary table but I have fraction plates and indexer to make a dividing head. The ratio is as much about size and speed as anything. Using a larger ratio takes longer to make one revolution.

With a Brown & Sharpes Nr-0 as reference, at a 40:1 ratio, the smaller devices I have, at 72:1 and 90:1 are 3-1/2 and 3 inches respectively. A 40:1 and 90:1 does a count of 5 directly, a 72;1 does not. (I think) Just as a rotary indexer(?) will not at 24 divisions. A B&S-0 weighs in at several(!!) times the weight of a 90:1. And costs several times what a smaller 90:1 does.

Essentially, it is about cost and physical size. If your 90:1 will fit the work and divide what you need, it is sufficient. In a much smaller package. . . MrPete222 mentions a 4:1 in his video. It does what he needs and is considered a "quick acting" device. I'm sure there are other ratios out there that I haven't encountered. It doesn't mean they are lesser or greater devices, it just means that I've never seen one.

In a nutshell, if it works for you it doesn't matter. We, the group, are mostly hobbyists. Time is of secondary concern. It comes down to the old saying about mind over matter. If you don't mind, it don't matter.

.


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## brino (Sep 9, 2021)

Downunder Bob said:


> A couple of years ago when I first bought my lathe I also bought a small divider. It has a ratio of 90:1. I didn't know at the time that 40:1 is more common. So I'm not sure how useful the 90:1 will be. Any one know if it's good, bad or doesn't matter?



My Troyke Model U9 rotary table has a 90:1 ratio.

Other than having a different output rotation for a single turn of the input handle, it doesn't matter.
Just get and use the proper tables for the gear ratio you have and it's all good.

Here are links to replies in a thread that offer a couple options for 90:1 tables:
https://www.hobby-machinist.com/threads/looking-for-90-1-dividing-head-chart.35820/post-304583
https://www.hobby-machinist.com/threads/looking-for-90-1-dividing-head-chart.35820/post-304888
other posts in that thread offer other links and tools too.

Sure you need to crank the input handle around 90 times to get one full revolution of the output table, but theoretically, the 90:1 could offer better precision. Say for whatever reason you cannot control the input handle better than 1 degree. (parallax, bad light, bad eyes, etc.)
On a 40:1 table that results in an error on the output shaft of 0.025 degrees (360/40 * 1/360).
On a 90:1 table that results in an error on the output shaft of 0.011 degrees (360/90 * 1/360).
However this really only applies when you are NOT using the index plates, but instead the handle markings in degrees to produce soome odd output spacing.

-brino


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## chips&more (Sep 9, 2021)

Maybe think about using a stepper motor to drive a dividing head. You won’t need any hole plates. And can get any division you need. Just push the button! That is what I have and I won’t go back.


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