# Prime number division without gearing?



## British Steel (Sep 23, 2017)

Some While Ago, I saw a YouTube video describing a way to divide by "awkward" numbers by using different hole circles - as well as the usual quadrant and fingers, there was a second setup on the rear face of the dividing plate, and the plate was stepped with each move of the worm - I can't find it again, or any formulae and I don't really fancy sitting and puzzling for hours over how it's done and how to work out which plates and circles I'd have to use  - can anyone with a better memory (not difficult nor rare...) who's seen anything relevant point me to it?

Having rescued a BIG rotary table (with dividing plates etc.) on its way to the skip, I'd like to see whether I can turn my old 6" with dividing gubbins into something that can index e.g. 127 tooth (or any other random) gears...

Thanks,
Dave H. (the other one)


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## Bob Korves (Sep 23, 2017)

Sure you can, Dave, as long as you arrange a mounting system for the plates.  Dividing itself is really pretty simple, just need to know how many turns for a complete rotation of the table and how big of increments you are trying to make, and use simple arithmetic division to determine what plate and how many turns and divisions are required.  We can help you with understanding the math if you can get the RT set up for indexing.  There are always some divisions that are not possible without a compound indexing arrangement to reach or very closely approximate (for mere mortals) the division you are looking for.


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## British Steel (Sep 23, 2017)

Thanks Bob, I've already managed dividing with the plates, working out turns/holes for the various numbers is well within my capabilities, simple multiplication and er... division 

What I'm trying to find is how to do prime number (compound) division without a prime-numbered (e.g. 127) hole plate or gearing - I know there's a method, as I saw that YouTube video years ago, then lost the bookmark with an old HD...

As I say, the principle I remember as being rotating the division plate with each set of handle-cranking, so the worm rotated slightly more or less than the "by the holes" division, the final hole being rotated into a new position each time...

My guess is the mechanical side will be pretty easy - take out the three screws holding the plate, put another index pin on the RT/DH body to locate either the plate in use or another mounted behind it (using the three mounting holes to lock 'em together), possibly a new pair of sector arms for the rear of the plate(s) - it's the maths confusing me, e.g. which holes circles, how many holes to rotate the handle vs how many to rotate the plate and which circles to choose...

What stuck in my mind was that to e.g. divide by 127 you set up to divide by 120, and the plate rotated back so you had to make 7 extra turns on the 120 setting to get back to the starting point - but I can't see how you do that without the 127 creeping back in! I suspect the maths is similar to calculating gearing on an universal dividing head - I think most of that's done by looking it up in Machinery's / Brown & Sharpe, but I'd like to get the principle then I could write a natty program to do it, or a spreadsheet?

Dave H. (the other one)


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## Wreck™Wreck (Sep 23, 2017)

I have never seen a rotary table that would not resolve to Deg., Minutes by using the dial.
In a production environment dividing plates simply make it faster and anyone may be trained to turn the handle X number of times then place the pin in THIS hole every time.

If you are a hobbyist making a part once or twice just divide the circle and use the dials in degrees, minutes. This is why they are there, this can be a laborious process for a circle with many divisions and is impractical in production, for one off parts you do not need dividing plates.


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## Bob Korves (Sep 23, 2017)

https://groups.google.com/forum/#!topic/rec.crafts.metalworking/SRT2z1mIzHI


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## British Steel (Sep 24, 2017)

Thanks Bob, that may be the one I'm looking for - I've emailed, although it was some years ago and his address may not be reachable...

Dave H. (the other one)


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## Karl_T (Sep 24, 2017)

Machinery's handbook has a ten page discussion on simple and compound indexing. just what you need to know.


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## British Steel (Sep 24, 2017)

Thanks Karl, I had Machinery's at my elbow - it has tables for 40:1 (the RT I want to use is a 90:1), describes the calculations and process - I had though it only described differential indexing, my bad!

The process isn't too difficult, but it only gives exact divisions for a few of the unusual numbers, there's no rule-of-thumb for those that don't give exact results (the process, as you've probably noticed, involves cancelling factors in the desired division and the plates - so a 127 plate would be needed anyway for exact divisions...), I *think* that I'd have to multiply hole counts etc. by the 90:40 ratio, tricky when it's using e.g.  2+23/39 and 12/49 turns on crank and plate...

Dave H. (the other one)


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## benmychree (Sep 24, 2017)

Wreck™Wreck said:


> I have never seen a rotary table that would not resolve to Deg., Minutes by using the dial.
> In a production environment dividing plates simply make it faster and anyone may be trained to turn the handle X number of times then place the pin in THIS hole every time.
> 
> If you are a hobbyist making a part once or twice just divide the circle and use the dials in degrees, minutes. This is why they are there, this can be a laborious process for a circle with many divisions and is impractical in production, for one off parts you do not need dividing plates.


It is extremely difficult to do this without making mistakes.


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## hman (Sep 25, 2017)

I have a 90:1 rotab.  As others have stated, there's NO exact way to divide by a prime number except to use a the same prime number divider plate.

That said, I did some playing around with approximate solutions using the plates I have.  The best I could find uses the 62 hole dividing plate.  The basic advance is 44 holes per tooth, but you reduce this to 43 holes 8 times, evenly spaced around the gear - ie, every 16th tooth.  The maximum error for any given tooth introduced by this procedure is 0.065º (360º÷90÷62), which may well be acceptable ... probably less than other errors inherent in the machine tool.

Yes, it's laborious ... but not as difficult as calculating the degree positions of each tooth.

I suppose if I wanted to make more than one 127 tooth gear, I'd use this procedure to make a 127 hole dividing plate, then use the plate repeatedly for the gears.


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## 4GSR (Sep 26, 2017)

I do have a Cincinnati high number dividing plate I scored off of eBay years back that has a row of 127 holes.  Haven't mounted it to my rotary table yet.

It would be nice to get someone here to offer to make a 127 hole plates for their dividing head using their CNC mill.  Any offers?


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## Bob Korves (Sep 26, 2017)

4gsr said:


> I do have a Cincinnati high number dividing plate I scored off of eBay years back that has a row of 127 holes.  Haven't mounted it to my rotary table yet.
> 
> It would be nice to get someone here to offer to make a 127 hole plates for their dividing head using their CNC mill.  Any offers?


That is a good idea, Ken.  Keith Rucker had a set of plates made on a CNC machine for his K&T horizontal mill.  A friend of Keith who is a manager in a machine shop did the work for him.  I am not much into CNC in home shops (old fart), but for making stuff like dividing plates, it is the only way to go!  You could spend most of a lifetime doing it manually, even with using a DRO for the hole locations.  Without any electronic assistance, the job is likely to end in mistakes and failure.


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## Karl_T (Sep 26, 2017)

Tell ya what. If somebody will give all the holes in an X#.###  Y#.### format, one hole per line, with the center of the plate at X0.000 Y0.000  I will run it.

karl


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## 4GSR (Sep 26, 2017)

Karl_T said:


> Tell ya what. If somebody will give all the holes in an X#.###  Y#.### format, one hole per line, with the center of the plate at X0.000 Y0.000  I will run it.
> 
> karl


I guess I could take the plate I have and overlay it as a template on top of a new plate and drill those holes by hand.  Ooh! 127 holes to drill by hand!  I'm going to think on that!
On CNC mill, there's got to be a subroutine that could be plugged into the programming to locate 127 holes on a circle, without hand cranking coordinates and programming.


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## benmychree (Sep 26, 2017)

4gsr said:


> I guess I could take the plate I have and overlay it as a template on top of a new plate and drill those holes by hand.  Ooh! 127 holes to drill by hand!  I'm going to think on that!
> On CNC mill, there's got to be a subroutine that could be plugged into the programming to locate 127 holes on a circle, without hand cranking coordinates and programming.


Aren't the Cincinnati plates drilled on both sides? Could complicate that approach.
I made a 127 tooth by differential indexing with my B&S dividing head, of a pitch that fits my automatic gear cutter, then cut a gear of a pitch to fit my 19" Regal Leblond that requires a gear of a smaller numbered pitch; the dividing head would not accommodate a gear that large of diameter without raising blocks, which I do not have, besides which, the larger the blank the more tendency to chatter; the gear cutter has a back rest to address the tendency.


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## Karl_T (Sep 26, 2017)

4gsr said:


> On CNC mill, there's got to be a subroutine that could be plugged into the programming to locate 127 holes on a circle, without hand cranking coordinates and programming.



Nope, CNCs are not that smart. you have to tell it exactly what to do.


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## RJSakowski (Sep 26, 2017)

A few decades back, I wrote some g-code to scribe 360 degree marks on a disk.  I believe that I did it with the conditional programming.  It cut four 9 mm lines  for degree positions, 12mm lines for five degree positions, and  a 15mm line at every degree position.  

It was actually my first attempt at writing g-code.  I used polar coordinates and left it to the machinist finish filling out the code. We had a CNC machine but the machinist had never written any code.  He only used conversational programming or some simple routines that came with the controller.  I don't recall what the machine was or how this would relate to other machines.
Here is the code:



Other than that, it would be a simple matter to create the model in SolidWorks or Fusion and let the CAM program write the code.


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## 4GSR (Sep 26, 2017)

Karl_T said:


> Nope, CNCs are not that smart. you have to tell it exactly what to do.


I'll check with my brother. I bet he has something in his bag of tricks that would work without having to calculate and type out every coordinate point.  Of course, it may require buying a half million dollar machine to do it on too.


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## Bob Korves (Sep 26, 2017)

A dividing plate is just a series of bolt circles, basically, just multiple circles.  That is a very common task for both manual and CNC equipment.  I am certainly not a CNC programmer, but cannot believe it is that difficult to drill multiple bolt circles on a flat plate.  I think doing it manually would be the challenge (drudgery caused mistakes), but suppose lots of them were done that way, at least the templates for the production runs.


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## chips&more (Sep 26, 2017)

Yes, I know it could be a new and challenging frontier for some. It kinda was for me. But, I now have stepper motors on my dividing head and Levin lathes. I can now punch in any divisions I want. And no more turning that handle. And easy to run, hard to make a mistake, I just push the button. I do have a very minor error on some divisions, but it’s very small…Dave.


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## RJSakowski (Sep 26, 2017)

My version of PathPilot doesn't have a conversational program for bolt circles but I believe that the later versions do. If I recall correctly, Mach 3 had a wizard that did bolt circle patterns.

My Grizzly DRO has a bolt circle routine that would do a 127 hole pattern.  Even though it is a manual operation, it is fairly well fool proof.  You pick a hole and the DRO shows how far you are from the position.  You just adjust the x and y axis for a 0,0 reading and drill.  Hit the up or down arrow to go to the next hole.


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## 4GSR (Sep 26, 2017)

RJSakowski said:


> ............
> Other than that, it would be a simple matter to create the model in SolidWorks or Fusion and let the CAM program write the code.


My brother said this is the way he would do it.  He also said he had a macro somewhere in his stuff that could be used too.  He mentioned the macro may not run on all brands or age of controllers.


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## talvare (Sep 26, 2017)

I have a two axis BP CNC mill that will do this. One of the things that needs to be considered is the diameter of the dividing plate. For instance, if we assume a single row of .125 dia. holes on a 4.00" radius (approx. 8.25 dia. plate) it will leave about .073 of material between holes. If we assume a 3.00" radius (approx. 6.25 dia. plate) it will leave about .023 of material between holes and that's getting  pretty thin.

Ted


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## Karl_T (Sep 27, 2017)

guys, he has a 90:1 index head. the need is for 127 holes over 90 turns. To do this right, IMHO, the holes should be laid out in a spiral. if i were to do this, I'd use Excel, then print out the X Y values to a file.  Do the work in polar coordinates, then convert to Cartesian.

Of course, may ways to skin the cat.


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## 4GSR (Sep 27, 2017)

Karl_T said:


> guys, he has a 90:1 index head. the need is for 127 holes over 90 turns. To do this right, IMHO, the holes should be laid out in a spiral. if i were to do this, I'd use Excel, then print out the X Y values to a file.  Do the work in polar coordinates, then convert to Cartesian.
> 
> Of course, may ways to skin the cat.



That would be kind of hard to index on when the spring plunger is on a fixed circle diameter.


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## RJSakowski (Sep 27, 2017)

Karl_T said:


> guys, he has a 90:1 index head. the need is for 127 holes over 90 turns. To do this right, IMHO, the holes should be laid out in a spiral. if i were to do this, I'd use Excel, then print out the X Y values to a file.  Do the work in polar coordinates, then convert to Cartesian.
> 
> Of course, may ways to skin the cat.


I laid out in SolidWorks a plate that should work.   For a 90:1 head, the spacing would be 360 x 90/127 or 255.1181º.  If that spacing is laid out with each successive hole being 255.12º from the last, you end up with 127 holes spaced at 360/127 or 2.8346º.  The problem is that this spacing would result in intersecting holes. 

126 is highly factorable; 2 x 3 x 3 x 7.  What I did was break up the pattern into three sets of 42 holes spaced 3 x 2.8346 or 8.5039º apart and on radii. 35" apart  Each set of holes was offset by the 255.12º  This gave me 126 holes.  The last hole was created at 2.8346º before the first hole, giving me the required 127 holes equally spaced in angle.  My Grizzly DRO bolt circle function will easily make the hole pattern.  

However, I can see that using the plate will present some problems.When a hole is made, the plate has to be rotated 255.12º or dropping down one circle and skipping to the 30th hole.  This could quickly become confusing.  To resolve that problem, I would make a template disk with two radial slots angled 255.12º apart and central pivot hole.  When the hole was made, I would line up the slot with that hole which will expose the next hole to be made.  The disk could be whole or a half disk as depicted  to allow removal from the plate once a new hole was located.


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## Karl_T (Sep 28, 2017)

Just a concept here, using the spirial out idea. If you start at  radius  1.5" and increase each point by 0.020, ending at  radius  4.0, this is what the plate would look like. closest hole is 0.200 apart. Advantage here is not getting lost in your indexer. disadvantage is sliding the pin out 0.02 every move. Also make sure you can handle an 8" diameter.  i could re do this with known min and max diameters
	

		
			
		

		
	



	

		
			
		

		
	
 on the pin.


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## RJSakowski (Sep 28, 2017)

Karl_T said:


> Just a concept here, using the spirial out idea. If you start at  radius  1.5" and increase each point by 0.020, ending at  radius  4.0, this is what the plate would look like. closest hole is 0.200 apart. Advantage here is not getting lost in your indexer. disadvantage is sliding the pin out 0.02 every move. Also make sure you can handle an 8" diameter.  i could re do this with known min and max diameters
> 
> 
> 
> ...


Karl,  if you start at the innermost hole on one spiral, your next hole  has to be at 255.12º from the previous one (for 90:1 gearing).  Which hole will that be on your plate?


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## talvare (Sep 28, 2017)

Gentlemen,
I am truly quite ignorant when it comes to the complexities of dividing heads so if I'm not understanding something here I would appreciate a little education. It seems to me that in this particular case where we are dealing with a prime number that the easiest and simplest dividing plate would be one with a single row of  127 holes. I don't understand how the ratio of the dividing head even comes into play. It seems to me that the pin would just be advanced to the next hole on the plate in succession until all 127 equally spaced cuts had been performed. What am I missing ?

Thanks

Ted


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## RJSakowski (Sep 28, 2017)

With 90:1 gearing, the plate needs to rotate through 255.12º in order to turn the table 255.12/90 = 2.8346º = 360/127.  Just moving to the next hole will only rotate the table by .0315º.


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## talvare (Sep 28, 2017)

Thanks RJ. I think the light bulb just came on !

Ted


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## RJSakowski (Sep 28, 2017)

If you assume a 50% of hole diameter space between holes, the bolt circle for a 127 hole pattern would be about 60 x the hole diameter.  For a 1/4" hole, that would require a 15" bolt circle.  That's the reason for multiple rows or the spirals.


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## Bob Korves (Sep 28, 2017)

Deleted


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## markba633csi (Sep 28, 2017)

What you are missing Ted is the gear ratio of the head itself usually 40:1 but sometimes a different ratio like 72 or 90 to 1
Mark


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## talvare (Sep 28, 2017)

Bob Korves said:


> Ted, that requires a plate with the 127 holes and an indexing setup to engage them.  That would be "plain indexing."  It would work fine, but the plate has to be available (which they are not) or shop made, which you might be able to do on your CNC BP, but most of us cannot.  One of the issues is the size of the dividing plate with a single row of 127 holes and the 1/8" hole size that people here are suggesting, along with a relatively large space between holes.  I have no idea why a 1/16" hole size could not be used, or a pin tapered to a cone point.  There is not much rotary stress on the plate when drilling a hole or cutting a gear, and the spindle should be locked anyway for each cut.  But again, all of that would need to be fabricated.  I do not think the spaces between holes need to really be large, there only needs to be enough meat there to keep the dividing plate from being fragile if dropped.



Bob,

Ya, my brain wasn't working very well this morning (nothing new for me). My theory would work fine if the dividing head was a 1:1 ratio .  I figured that a single row of 127 holes could be done with 1/8" holes on a 8" diameter plate with about .070 of material between holes. The dividing plates I have only use 1/8" holes. I agree that there really shouldn't be any stress on the pin if the spindle is locked.

Ted


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## Karl_T (Sep 28, 2017)

RJSakowski said:


> Karl,  if you start at the innermost hole on one spiral, your next hole  has to be at 255.12º from the previous one (for 90:1 gearing).  Which hole will that be on your plate?



There are five spirals, move four each time, or one less than current position each time. I'd suggest a magic marker to keep track of the hole that was already used. wipe it clean when done.

Talvare: A dividing head is geared down. This one 90 times. So, you go around 90 times on the crank to move the head one revolution. This is so you can move very accurate small amounts.


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## British Steel (Sep 28, 2017)

talvare said:


> Gentlemen,
> I am truly quite ignorant when it comes to the complexities of dividing heads so if I'm not understanding something here I would appreciate a little education. It seems to me that in this particular case where we are dealing with a prime number that the easiest and simplest dividing plate would be one with a single row of  127 holes. I don't understand how the ratio of the dividing head even comes into play. It seems to me that the pin would just be advanced to the next hole on the plate in succession until all 127 equally spaced cuts had been performed. What am I missing ?
> 
> Thanks
> ...



Not ignorant, you have an enquiring mind, that's the opposite of ignorant 

A 127-hole plate would be simplest IF you had one - they have to be pretty big, as the holes can't overlap... It's not standard provision with dividing heads/rotary tables, probably for that reason?

The worm ratio dictates how many holes you have to go each time around the plate - simply put, if you did have a 127-hole, you'd step around the ratio-number of spaces and you'd get a perfect 127 division - so 40 spaces on a 40:1, 90 on a 90:1 etc.

If that seems illogical, for a full turn of the workpiece you need [ratio] turns around the plate, if you have [divisions] holes then for that full turn of the workpiece you have [ratio] x [divisions] spaces to pass, to dividing by [divisions] you get [ratio] hole spaces - if you wanted 2 x [divisions] (e.g. cutting a 254 tooth gear), you'd have to pass [ratio] divided by 2 spaces, so 45 on a 90:1 dividing head, 20 on a 40:1.

I hope that makes sense, rather than confuses!

Dave H. (the other one)


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## 4GSR (Sep 28, 2017)

The high number plate I have with the 127 hole pattern is on a 6.875" dia hole circle.  Hole diameter is .093" and the web between holes is approximately .080".  That's a lot of holes!


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## benmychree (Sep 28, 2017)

4gsr said:


> The high number plate I have with the 127 hole pattern is on a 6.875" dia hole circle.  Hole diameter is .093" and the web between holes is approximately .080".  That's a lot of holes!


Yes, a lot of holes, and how to divide them for drilling?????  It's the old one about the chicken and the egg; which came first?  The probable answer is differential indexing likely came first and with it, the ability to divide prime numbers.


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## Bob Korves (Sep 28, 2017)

talvare said:


> Bob,
> 
> Ya, my brain wasn't working very well this morning (nothing new for me). My theory would work fine if the dividing head was a 1:1 ratio .  I figured that a single row of 127 holes could be done with 1/8" holes on a 8" diameter plate with about .070 of material between holes. The dividing plates I have only use 1/8" holes. I agree that there really shouldn't be any stress on the pin if the spindle is locked.
> 
> Ted


I actually deleted the post you responded to, Ted,  because I also realized that we would not likely be using a 1:1 ratio setup, and if we were, it would not be so accurate.  The 40 or 90 or whatever to 1 is where the potential accuracy comes from.  You were too quick to read my post...


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## talvare (Sep 28, 2017)

Gentlemen,

Thanks for all the replies. The flaw in my thinking became obvious pretty quickly.

Ted


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## silence dogood (Sep 28, 2017)

Look up Clickspring Antikythera fragment #2.  He will show you how to make a single plate with your 127 holes.  He did  for 223 gear teeth.  Just substitute holes for teeth.


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## Asm109 (Sep 29, 2017)

In the village press book "The Shop Wisdom of Rudy K", He describes a method of making dividing head wheels from scratch.
He gave 3 options depending on the machinery in your shop. 1. Rotary table, 2. Drill Press with circular table, 3. Plywood cut round to sit on drill press.
You also need some old fashioned drafting equipment like T square and triangles. and a long meter ruler.
You get a roll of adding machine paper and wrap it around your rotary table and cut it at the over lap so it fits perfect.
Lay that out on your drafting table and draw vertical lines up from each end.
Now pick a length on the meter stick for each division of your wheel.  For a 127 tooth I would go with 5mm.  10 would be simpler but you would need a ruler 1.27 meters long.
127*5=635mm
Lay the meter stick on the table at an angle with 0 on one end of the paper strip and 635 intersecting with the vertical line drawn at the opposite end of the strip.
Now put a tick mark on the table every 5 mm on the meter stick.
Using the T square and triangle drop a vertical from every tick to the strip and make a line.
Wrap this around the rotary table and tap. 
Make something to act as a point and rotate the table from line to line and drill.
If this is not clear, buy the book it is all clearly photographed and explained. Plus there is lots of other great stuff in there.


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## RJSakowski (Sep 29, 2017)

Asm109 said:


> In the village press book "The Shop Wisdom of Rudy K", He describes a method of making dividing head wheels from scratch.
> He gave 3 options depending on the machinery in your shop. 1. Rotary table, 2. Drill Press with circular table, 3. Plywood cut round to sit on drill press.
> You also need some old fashioned drafting equipment like T square and triangles. and a long meter ruler.
> You get a roll of adding machine paper and wrap it around your rotary table and cut it at the over lap so it fits perfect.
> ...


A dividing plate would normally be made to much greater precision than the method you describe.  Rudy may be much more adept then I am but I would find it difficult to scribe a line to better than .01" accuracy. Additionally, there will be error associated properly intersecting a vertical line with the scribe line and with lining the pointer up with the vertical lines.  If he is marking with a pencil, add another .02" for the line width.  It isn't unrealistic to have the stacked error be as much as .05".  On a 10" disk, this would be .6º.  My RT will resolve to 5 seconds of arc which is .0014º and better than 400 x better.

This method might work for making something visual but I definitely wouldn't use the plate made by this method for making a gear.


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## Bob Korves (Sep 29, 2017)

There are dividing heads and Dividing Heads.  If you need to make a hex bolt head or a nut, there is plenty of latitude for slight and even more than slight errors.  To make gears and other precision tooling, good accuracy is critical, and makeshift methods will not be able to do the job.  In the beginning, of course, there was no accuracy, it needed to be created from crude resources.  The study of how tools and tooling became more accurate over time is an interesting study.  Sorry, I do not have a link to a single book or article that chronicles that evolution, but maybe someone else here does.
https://www.amazon.com/Foundations-mechanical-accuracy-Wayne-Moore/dp/B0006CAKT8  This is a good one that mostly explores the higher end of it, Wayne's father Richard F. Moore also wrote books on the subject.  Moore tools is in the stratosphere of making precision tools.


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## RJSakowski (Sep 29, 2017)

A process come to mind where a person could make a custom dividing plate without precision measuring equipment.  Make a plate as described in post #33.  It won't be accurate but if used on a 40:1 dividing head, it can produce a second plate with 40 x better accuracy. At that point, other errors associated with machining will probably outweigh the errors in the plate.  The only precision tool required is the dividing head.


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## British Steel (Sep 29, 2017)

RJSakowski said:


> A process come to mind where a person could make a custom dividing plate without precision measuring equipment.  Make a plate as described in post #33.  It won't be accurate but if used on a 40:1 dividing head, it can produce a second plate with 40 x better accuracy. At that point, other errors associated with machining will probably outweigh the errors in the plate.  The only precision tool required is the dividing head.



I've always heard that is how the first proto-dividing-plates were made, by layout on a circle with actual ( > ) dividers - as long as the worm and wheel are accurate, a 1-degree error will be reduced to an (e.g.) 1/40th or 1/90th (or on my big rotary table 1/120th) of a degree on the first generation, second generation 1/1600th, 1/8100th (or 1/14400th, a quarter-second of arc - this is probably beyond the accuracy of most worms and wheels...). A third generation would probably be unnecessary.

I may just print a 127-hole circle from TurboCAD, stick it to an old freebie CD-ROM and use it as a plate with a pointer, locking the table each set of steps, and generate a more accurate plate in steel (with tiny-tiny holes!) - after the reduction in the little 6" RT I'll be looking at (assuming a 1-degree printed error - which would be obvious on the print-out) still better accuracy, it should theoretically produce work with 4/9ths of a second error or less...?

Then I'll have to work out how I can cut this 127-tooth 48 DP internal gear 

(I'm thinking at the moment that I'll make an indexing plate to attach to the lathe chuck, and a slotter attachment to sit on the topslide - at least I won't have hefty cuts to make, just lots of 'em)

Dave H. (the other one)


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## mathsquid (Oct 1, 2017)

Karl_T said:


> Tell ya what. If somebody will give all the holes in an X#.###  Y#.### format, one hole per line, with the center of the plate at X0.000 Y0.000  I will run it.
> karl



That's trivial using trigonometry. If you want it let me know the radius you'd want for the circle.


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## Wreck™Wreck (Oct 1, 2017)

mathsquid said:


> That's trivial using trigonometry. If you want it let me know the radius you'd want for the circle.


What he said, simple trig easily done with a calculator.


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## EPAIII (Oct 2, 2017)

I have been preaching this on other boards for some time. A dividing head (a worm gear) is an accuracy amplifier. So if you use a 40:1 worm to make a plate with the same number of holes as your original plate, then the errors on that second generation plate will be just 1/40th of those in the original. This can be shown with a rigorous mathematical proof. It is not just an assumption or a rough approximation. It is mathematically exact. The error is reduced (divided) by the worm ratio. 

If you need a 127 hole plate, you can make a first generation plate using any method you want to lay it out. Just for Ss & Gs, lets say your first plate has the holes located +/- 1 degree. Then, when you make a second generation plate with it, your error will be just 1/40 degree or about 1.5 seconds. If you use that second generation plate then your work with it will be 1/40th of that or about 2.25 seconds. That is down to 25% of the error spec of my RT. So, if you are going to use the plate with your dividing head or rotary table, then a second generation plate will probably give you greater accuracy than the specs of that DH or RT. You can stop there. If you want to use the plate for direct indexing, then you may want to make a third generation plate which would have that +/-2.25 second accuracy. 

This method does not require any math. Your first plate can have a lot of error in it. All you have to do is make two or three generations of hole plates. It will work for ANY number of divisions and produce work that is as accurate as your DH or RT is capable of. 

I have read about compound and differential indexing and can only shake my head. I am sure those techniques do work. Sometimes they are exact and sometimes they are only approximate so if you go around a second time the error increases. A third time around and you have three times the original error, etc. I just shake my head. All that math and you still have error. For 127 divisions I would just make the plate. And using my, multiple generation plate method, the error does not increase when you go around a second, or a third, or even a millionth time. You will land on the same point every time around. 





RJSakowski said:


> A process come to mind where a person could make a custom dividing plate without precision measuring equipment.  Make a plate as described in post #33.  It won't be accurate but if used on a 40:1 dividing head, it can produce a second plate with 40 x better accuracy. At that point, other errors associated with machining will probably outweigh the errors in the plate.  The only precision tool required is the dividing head.


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## KBeitz (Sep 25, 2018)

Right now there is a 127 tooth gear for sell on E-bay....Could you make that work ?


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## KBeitz (Sep 25, 2018)

double post... Sorry...


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## benmychree (Sep 25, 2018)

There is nothing inexact about differential indexing, compound indexing may be another matter.  Some dividing heads such as the Cincinnati can do may prime numbers, but others like the B&S, the plates are not large enough to accommodate numbers of holes much larger that the standard plates without modification of the crank and sector arms.
I accept the premise of making inexact plates and repeating the process to diminish error, but I have the dividing head and the gearing, and it takes little time to set it up.  A 127 tooth gear could likely be used to index a dividing plate for drilling, but using that plate may be problematic for many dividing heads that might not be able to make use of a plate that is necessarily that large in diameter.


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