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

[G Jones]

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

 

[Lo-Fi]

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?

 

[RJSakowski]

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.

 

[G Jones]

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

 

[G Jones]

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

 

[G Jones]

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

 

[G Jones]

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.

 

[Norppu]

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

 

[Optic Eyes]

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

 

[hman]

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.