# Compound indexing for 127 Using a BS-0



## SmithDoor (Jan 18, 2015)

Has any one else use compound indexing for making gear like the 127 tooth gear or 157 tooth gear using a BS-0. 
I just working some drawing and have not seen any one even taking about compound indexing, hard to find any data today.

Dave​


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## Ken I (Jan 18, 2015)

I assume you mean differential indexing - using the gear train to drive the indexing plate.

I last did that over 40 years ago - I could probably bend my mind around it again if I needed to but WTH that what the internet is for.

Here's a link to a handbook *.pdf with tables.

http://www.micro-machine-shop.com/Bemato_dividing_head_manual.pdf

I Hope this helps.

Regards,
             Ken


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## SmithDoor (Jan 18, 2015)

Compound indexing Not differential indexing
no gear train


Ken I said:


> I assume you mean differential indexing - using the gear train to drive the indexing plate.





Ken I said:


> I last did that over 40 years ago - I could probably bend my mind around it again if I needed to but WTH that what the internet is for.
> 
> Here's a link to a handbook *.pdf with tables.
> 
> ...


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## tornitore45 (Jan 18, 2015)

127 and 157 are prime numbers and can not be indexed with a compound indexing.


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## kiwi2 (Jan 19, 2015)

I had to cut a 107 tooth gear which the plates on my dividing head didn't cover so I used my rotary table as it has a vernier degrees scale. The scale is in degrees - minutes - seconds so I had to convert the list of decimal degrees to DMS - not an easy process.
I found it useful to cross each angle off as it was cut so I didn't lose track of where I was at. 
It was laborious, but doable.
Regards,
Alan


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## SmithDoor (Jan 19, 2015)

Yes it use two index circles making 
here is part of a chart it when up to 250
Had the dividing head sold it back in the 70's

Dave
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tornitore45 said:


> 127 and 157 are prime numbers and can not be indexed with a compound indexing.


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## tornitore45 (Jan 23, 2015)

Lets pick a number like the 61 for example...
If I read the table correctly it tells to turn the handle 3 turns plus 42/47th of a turn
then add 2/49th of a turn by indexing on the second plate.

Total = 3.95484151107251 turns
Repeating this rotation 61 times should produce a full rotation of the rotary table plate

61 x  3.93443334780721 = 240.000434........  turns of the handle

Dividing such number by the ring gear number of teeth should give a integer number of plate rotation.

Assuming the ring gear has an integer number of teeth, 60 for example then the 61 division would be accomplished in 4 turns minus 0.000434 turns of the handle.

The missing 0.000434 turns represent less than 1/9000th of the spacing between 61 divisions, very acceptable for cutting gears.

The error is on the order of 10^-4   unlikely to result from spreadsheet 16 digits precision rounding.

In conclusion although compound indexing can approximate prime number division it does not allow arithmetically exact solutions.


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## RichD (Jan 23, 2015)

My simple solution would likely be to draw a 127 bolt circle in CAD, print it, glue it on a piece of MDF, drill it, and use it to index.

That's only because the compound thing is too far over my head. Of course if you have a 9x20 lathe, there is a 127 tooth gear available already for indexing.
Rich


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## petertha (Jan 24, 2015)

Its been a while since I looked at this trying to figure out my Vertex dividing head. I wrote an Excel spreadsheet that inputs the gear ratio & plates (hole layout) & it spits out matching indexing solutions if one is available. I recall testing it against the tables & seemed to be functioning correct. 

I punched in 127 & 157 into my particular setup & got 'no solutions found' probably for the reasons outlined. But I'm not sure if different makes of dividing heads have different plates or gear reductions so that other gear/angle permutations are possible? I suspect mine is an offshore clone of something.. but of what?


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## tornitore45 (Jan 24, 2015)

Pete,
from what I can gather from your spreadsheet it is applicable to a plain dividing head/rotary table.
No Compound ( two plates used at the same time).
No Differential (Plate is not fixed but rotate with gear ratio from the handle)

No type of dividing head can divide by a prime number unless it has a plate with the same number of holes.
Compound and Differential can achieve practical approximation much closer that a plain one.

I made a spreadsheet exactly like yours in different format.
On all my spreadsheet I have the same convention of using red characters for User Entered Data.


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## petertha (Jan 24, 2015)

Ah, thanks for the enlightenment tornitore45. 'compound' & 'differential' are not yet in my vocabulary. But I'm intrigued now. Thanks for the heads up.


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## Ken I (Jan 24, 2015)

tornitore45 said:


> No type of dividing head can divide by a prime number unless it has a plate with the same number of holes.


Same rules apply for differential gearing - but most gearsets have a 127T (for imperial / metric conversion).

Regards,
             Ken


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## SmithDoor (Jan 26, 2015)

You are looking at simple indexing on a 49 * 40=1960 spaces or 0.1836 Deg. or 11 Min. .
The compound indexing uses two of the holes in plate
most of the division use 49x47x40= number of spaces is 92,120 or .0039 Deg. or 14 Sec. Using other set of holes give you other spacing . 
FYI on most CNC dividing head give a  Accurate of ± 20 Sec per division 

Dave





petertha said:


> Its been a while since I looked at this trying to figure out my Vertex dividing head. I wrote an Excel spreadsheet that inputs the gear ratio & plates (hole layout) & it spits out matching indexing solutions if one is available. I recall testing it against the tables & seemed to be functioning correct.
> 
> I punched in 127 & 157 into my particular setup & got 'no solutions found' probably for the reasons outlined. But I'm not sure if different makes of dividing heads have different plates or gear reductions so that other gear/angle permutations are possible? I suspect mine is an offshore clone of something.. but of what?


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## SmithDoor (Jan 26, 2015)

FYI to any one looking for compound indexing on your BS-0 
I am working on drawings for setting a  standard BS-0 to do compound indexing 

Thm:

Dave


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