# Dividing a circle by 359



## stuartw (Jun 17, 2018)

To recap the method I'm familiar with - I have a rotary table with a ratio of 90:1 and a collection of standard dividing plates and assuming for a moment, I want to divide a circle by 7, with a reduction of 90:1, I would divide 90 by 7, writing the remainder as a fraction. which in this case would be 12 and 6/7, multiplying the fraction by 7, we get 42 / 49. or, 12 turns on the wheel and 42 positions on a 49 hole dividing plate.

But what about a number of divisions that's much larger, in this case 359? as I understand it I would need a dividing plate that's a multiple of 359. Further looking at what I have, if we take the 1 degree and and divide it by 30 (30 degrees of hand wheel movement per degree on the table) you end up with .033 degrees of movement per degree on the hand wheel, which gives us 348.387 which doesn't work. Does anyone have any suggestions as to how to divide a circle in 359 even parts?

EDIT: I realize that 359 is prime. which means there will be no ratio that will perfectly divide the circle, but I'm looking for help to get close enough. One possible solution is to gash it very lightly, make a hob and hob the gear, if the size of the blank is correct I should end up with the required number of teeth. but anyway, I would appreciate your input.

Thanks!


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## Bob Korves (Jun 17, 2018)

You are correct about every thing you stated.  The best way to attack that is with a computer as an interface.  You can use a DRO with a bolt circle function (don't know if it will go to that many divisions) or use CNC machinery.  Stepper motors will get you close enough for most real life work.  I am  not a CNC guy, so I will stop here...


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## stuartw (Jun 18, 2018)

Bob Korves said:


> You are correct about every thing you stated.  The best way to attack that is with a computer as an interface.  You can use a DRO with a bolt circle function (don't know if it will go to that many divisions) or use CNC machinery.  Stepper motors will get you close enough for most real life work.  I am  not a CNC guy, so I will stop here...



Thanks. I have an available 4th axis driver (10 uS) or 2000ppr a dividing head and stepper but, on its' own 360/2000 = .18, which is too big by a factor of 100. So, to do 359 divisions, one would need 18:1 reduction (36,000) positions, or, 9:1 / 18,000 and accept around 1% calculated error (i think my math is correct), doable but the timing wheel will be pretty big in either case! it might be more practical to find a worm gear pair or a gearbox but that creates other issues and buying a 4th axis that can do this is not even remotely affordable. (servos for this application solves a bunch of these issues but I do not have a servos or drivers, so at this point it's also a non-starter)

^^ oops, I failed a bit, 360/359 = 1.00278551532. to use a stepper motor (2000 ppr) to approximate the required positions: 360/2000 = 0.18, so a reduction of 100 is required, to get to .0018 which is pretty darn close, but I don't think you can find a 100:1 timing wheel (94 inches?) HEH. so really, planetary/worm gear reducer is required or some other solution.

the bolt circle, might be the ticket? dividing a circle by 359 in software is trivial, but I'm wondering about the overall error? it's a lot of holes. I know nothing will be error free (especially in the hobby realm) but these gears are for mechanically tracking sidereal time (telescope mount), so, accuracy matters. Maybe i just need to do it and see what happens.


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## markba633csi (Jun 18, 2018)

Yeah, you need an electronic dividing head AKA 4th axis, which is on my list of projects to build
Mark


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## BROCKWOOD (Jun 18, 2018)

If 359 on a given diameter is correct:  why not scale that said diameter up or down to give a more easily attainable gear that can accomplish the same resulting turn ratio / torque factor? Sure, the drive or driven gear would also need to change IF the torque / ratio Must be the constant you seek - but well worth doing the math!!!!!


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## tcarrington (Jun 18, 2018)

If you put 359 holes around a dividing plate using the usual 0.125 stylus, just the holes would be a pitch circle over 14 inches in diameter. That might be OK, but I think it will still be difficult to place that many holes with the precision required (save CNC). The compound dividing heads might be able to do that though. That is the old school approach to the 127 tooth gear. Using the vernier and running a table of 359 positions might not be such a crazy idea as it is a fraction over a degree and you manage the fraction from position to position. Good luck!


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## stuartw (Jun 18, 2018)

tcarrington said:


> If you put 359 holes around a dividing plate using the usual 0.125 stylus, just the holes would be a pitch circle over 14 inches in diameter. That might be OK, but I think it will still be difficult to place that many holes with the precision required (save CNC). The compound dividing heads might be able to do that though. That is the old school approach to the 127 tooth gear. Using the vernier and running a table of 359 positions might not be such a crazy idea as it is a fraction over a degree and you manage the fraction from position to position. Good luck!



14 inches is just too big, it would need to be almost half that in order for me to be able to drill the entire plate without moving it. Thanks for the tip about the vernier, I'm gong to see what I can dig up, it sounds like a practical solution.


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## stuartw (Jun 18, 2018)

BROCKWOOD said:


> If 359 on a given diameter is correct:  why not scale that said diameter up or down to give a more easily attainable gear that can accomplish the same resulting turn ratio / torque factor? Sure, the drive or driven gear would also need to change IF the torque / ratio Must be the constant you seek - but well worth doing the math!!!!!



Well, changing the diameter will have a direct consequence on the size of the motor required (smaller is better) but it's becoming clear to me that changing the number of teeth is and using a motor that spins a bit faster (or slower) to compensate as you've suggested is probably sensible.


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## MarkM (Jun 18, 2018)

If your patient and want to work it out on paper.  Your x cordinates will be radius times cosine of the angle of each hole.  Your y cordinates will be radius times sine of each hole angle.  I usually start my bolt circles on my radius and add the angle from there.  You ll end up with four quadrants. +,- x, and +, - y.  You ll see what I mean. Example top right quadrant is x+,y+, and top left is x-,y+.  718 calculations.


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## Karl_T (Jun 18, 2018)

To do this in the days before CNC, you have to make the part that makes the part.

Make a special dividing plate.

a 90 turn head moves  90 * 360 degrees to go around.
divide that into 359 parts or 90.25 degrees and change.

set your yoke to that space. drill the first four holes in your dividing plate. Move in a  large enough amount so hole five is separate from hole one, probably 0.150"   Do four more.

Now the errors will start adding up. So once every two rounds do the exact math on where that hole should be. It is no big deal for the holes in the plate to be slightly off as there is a 90 times improvement in accuracy on the final part.

Doing this makes the spiral you see on the plates. you can see this will form four spirals.  when you are half done, move out and start four more spirals.  I will leave it to you to figure how large the plate has to be. 


Now you got the plate, making the part is a piece of cake now.


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## Karl_T (Jun 18, 2018)

I played with this just a bit in excel. Here's what the spiral plate  would look like if you started at 6" radius, worked your way in, then pulled back every 90 holes. obviously this is too big a plate.  If you really want to do this, make two plates, one for the first 180 holes, then one for the last 179 holes. then you could get the size down.

change the file extension from .txt to .xlsx to open in excel


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## Bi11Hudson (Jun 18, 2018)

This sounds like a "hypothetical" problem to me. For anything short of "Babbage's engine" I would be looking into staged / multiple gearing. From a practical perspective, I do most of my work from a BC (before computer) perspective. But then, I am a hobbyest in the purest sense. The above looks like the optimum solution. With any prime number, a dividing plate will need to be generated. (above 97) I would use, but not recommend, stepping it off with a dividers and keep plugging away until it was within reason. 

That's the hard way so I don't recommend it. The next step would be to use a piece of drafting / graph paper. Measure off 10 spaces, divide by 10, and then extrapolate that number to get diameter. Then, using the graph paper, mark each point and draw a line to center. Determine the hole spacing desired and draw a circle. Punch each intersection and there it is.


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## Smithdoor (Jun 18, 2018)

stuartw said:


> To recap the method I'm familiar with - I have a rotary table with a ratio of 90:1 and a collection of standard dividing plates and assuming for a moment, I want to divide a circle by 7, with a reduction of 90:1, I would divide 90 by 7, writing the remainder as a fraction. which in this case would be 12 and 6/7, multiplying the fraction by 7, we get 42 / 49. or, 12 turns on the wheel and 42 positions on a 49 hole dividing plate.
> 
> But what about a number of divisions that's much larger, in this case 359? as I understand it I would need a dividing plate that's a multiple of 359. Further looking at what I have, if we take the 1 degree and and divide it by 30 (30 degrees of hand wheel movement per degree on the table) you end up with .033 degrees of movement per degree on the hand wheel, which gives us 348.387 which doesn't work. Does anyone have any suggestions as to how to divide a circle in 359 even parts?
> 
> ...


E
Why 359 t


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## stuartw (Jun 18, 2018)

It could be viewed as theoretical. When the table was calculated, 359 offers a solution which is the most accurate (smallest error) there are other possibilities, I have attached a screenshot and the working excel file. I don't think I'll be creating a babbage engine though 

After finding the attached solution, I set out seeing how others' deal with dividing a circle where you have a large prime # (or a number that doesn't work out on the standard plates) which brings me to my original post. 

362 and 365 t would be the next choices, I think. these too would require a new dividing plate with a multiple of 181 and 73. I'm not sure this is any less work than 359 and the same goes for 356.

From a purely execution standpoint, 360 t is dead simple and 365 t (73 hole dividing plate is a lot more manageable than having multiple or a really large dividing plate.


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## Bi11Hudson (Jun 19, 2018)

Sorry, I got called away for a _minor_ emergency. To continue:

I got my hands on a set of fraction plates a few years ago (misidentified, not stolen) with prime numbers up to 97. They are well over a foot(16") in diameter and my indexer is 4 inch diameter. I leave the results to your imagination. It ain't pretty *.... * For any large number like you are describing, keeping track of minutes and seconds would be a real PITA. One missed second on tooth 345 and the job is botched and ready to start over. 

Once you figure out the desired ratio of two gears, it would be like a clock mechanism. Multiple stages if applicable. A damn fine tooth if multiple stages won't work. That's where the hand derived plate comes in. Figure 359 ticks, like 1cm on a yardmeter stick..... Naw, thats only a hundred. Make it 1 mm per. So every 10 mm, mark a reference, and then divide by ten to get an accurate 1 mm.(0.03937) Now from that calculate the diameter of a circle. With a circumference of 359 mm, the diameter would be around 5 inches. Make a sunburst pattern, scribing out to a usable size and draw your circle. When you're ready to cut, each gear is marked. After making a half dozen teeth, set up an indexer for the rest. Simple but exhausting. But it can be done. Just have a *big* coffee pot. I would start with a hacksaw and a fresh pack of smokes, and a clear ashtray. For a larger gear, a cutter.

Once the first one, a master, is made, the rest are a piece of cake. The first concept to grab here is that an indexer or rotary table is not vital. As in, how was the first ever gear ever made? What* is *vital is to think through the problem and determine the simplest way to accomplish the end result. I play with model trains. They use a worm and pinion gear for the drive mechanism. I understood a worm and pinion when I was a kid. Simply a small indexer when you come dowm to it. Not really relevant, I had to plug the models. An indexer is fine for a production shop. But for *one off* gears with an odd number of teeth, as much time is spent figuring out how to make tham as the making. *KISS*

Bill Hudson​


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## tcarrington (Jun 19, 2018)

Keeping it simple would be the best... but if you really need a 359 division plate, I think it can be done in a 6 inch diameter. If you run six tracks with 60 holes, 59 on the last and drill the holes so that each track was the position of every fifth hole (5 degrees and 50.14 arcseconds, it will fit! The trick is you turn one full turn plus a little over 90 degrees (angular distance of five "teeth" on dividing plate which makes the correct amount for five "teeth" on the gear. The sector arms are set to the 90 plus a fraction. When you get ready to do the 61st position, you will have to move the stylus to the next track. If you want the excel sheet with the coordinates, etc, let me know.


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## Smithdoor (Jun 19, 2018)

I would use compound indexing
Simple to use and use your rotay table or indexing head. With indexing plates.

It machine gear with higher tolenent that CNC 

Dave



stuartw said:


> To recap the method I'm familiar with - I have a rotary table with a ratio of 90:1 and a collection of standard dividing plates and assuming for a moment, I want to divide a circle by 7, with a reduction of 90:1, I would divide 90 by 7, writing the remainder as a fraction. which in this case would be 12 and 6/7, multiplying the fraction by 7, we get 42 / 49. or, 12 turns on the wheel and 42 positions on a 49 hole dividing plate.
> 
> But what about a number of divisions that's much larger, in this case 359? as I understand it I would need a dividing plate that's a multiple of 359. Further looking at what I have, if we take the 1 degree and and divide it by 30 (30 degrees of hand wheel movement per degree on the table) you end up with .033 degrees of movement per degree on the hand wheel, which gives us 348.387 which doesn't work. Does anyone have any suggestions as to how to divide a circle in 359 even parts?
> 
> ...


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## stuartw (Jun 19, 2018)

That's awesome, thank you. I hadn't considered compound solution at all. 



tcarrington said:


> Keeping it simple would be the best... but if you really need a 359 division plate, I think it can be done in a 6 inch diameter. If you run six tracks with 60 holes, 59 on the last and drill the holes so that each track was the position of every fifth hole (5 degrees and 50.14 arcseconds, it will fit! The trick is you turn one full turn plus a little over 90 degrees (angular distance of five "teeth" on dividing plate which makes the correct amount for five "teeth" on the gear. The sector arms are set to the 90 plus a fraction. When you get ready to do the 61st position, you will have to move the stylus to the next track. If you want the excel sheet with the coordinates, etc, let me know.


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## stuartw (Jun 19, 2018)

Maybe this will be helpful to everyone wondering why 359 t?

I am interested in tracking celestial object and taking pictures of them. In Astronomy, sidereal time is used to locate objects in the night sky & a general explanation can be found here. To track an object in the night sky for long periods of time (over a few minutes), we need to be able to match the rotation of the earth vs the stars. In order to do that we need to find a ratio that will allow a motor to spin at a constant speed and enable us to cancel out the rotation of the earth.

There's a few avenues to go, one is to buy a commercial mount (prices here to rotate 30lb of gear are easily north of 2000$ CAD, but the popular mounts are easily 4k) as well as auto-guiding systems (mounting a scope on top of a scope with an additional camera and the images are fed into some software to compute drift, that in turn is used to adjust the speed of the motors.) 

For the diy crowed, there's options here as well, from retrofitting an existing mount with commercially made gears like these and these and finally and of course, if you like pain (or just enjoy the process), you can try your hand at doing it yourself. This approach is unlikely to be any cheaper than buying off the shelf parts, but, where's the fun in that? And, after reading the linked the post, I think it's very achievable to do in your own shop.

Coming back to the 359t gear, when we look at the number of seconds (rounded) in a day, the 359 t gear offers the least cumulative error per tooth than any other gear with a reasonable number of teeth and diameter. By extension, the less error at this stage, the less reliance on other solutions like auto-guiding.

Thanks everyone for your input so far!


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## Karl_T (Jun 20, 2018)

So, you want a worm drive with Zero backlash??

There is a method to use a worm cutter to hob out the large gear and then replace the worm with an identical one. You make both worms at the same time so they are the same. The large gear is allowed to spin free while cutting so the home shop machinist can easily do this.  I remember reading about this and have seen pics of others doing it, but have no actual experience.

I'd suggest you research this idea a bit.


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## stuartw (Jun 20, 2018)

Karl_T,

I have not read any information where someone was successful or even to tried to directly hob a blank without gashing it first. It seems like it would not work very well and not the direction I want to go even if one can do it.

The last link 'doing it yourself' links to another site where the guy does just that, hobs a gear in a lathe in the method you've described, but even he gashes it first. Here's the link to the site documenting the worm drive used in the previous article if you're curious.

I found information on hobbyists making 360t gears& worm drives but only professional companies selling 359t gears (for good reason, perhaps) but there you have it, I want to do something I wasn't able figure out on my own by just searching the internet.


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## Karl_T (Jun 20, 2018)

Like I said, I've not done this. For sure, I can see gashing it first would greatly improve the job. The big advantage is getting zero backlash.


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## vtcnc (Jun 20, 2018)

stuartw said:


> But what about a number of divisions that's much larger, in this case 359?



What material thickness, type of material and hole diameter are you looking for? I would just laser cut this...if you want I could help you with that...let me know!


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## stuartw (Jun 22, 2018)

this is a silly question, maybe someone has an answer for, I find the occasional reference to tables in the machinery's handbook, but, I can't seem to find a table anywhere that relates to compound indexing. It feels like some kind of private joke when people say you should check this book, I have it but can find no tables that relate to dividing. I have an ebook of the most recent ed. Anyone know what section it might be found in? compound indexing, dividing are not found in the index and there is no section under measuring and marking that I can see.


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## RandyM (Jun 22, 2018)

Would an online calculator help?

http://www.bilar.co.uk/cgi-bin/division-calculator.pl

Here is a PDF with a chart.

https://littlemachineshop.com/images/gallery/instructions/1811DividingPlates.pdf


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## Smithdoor (Jun 22, 2018)

stuartw said:


> Karl_T,
> 
> I have not read any information where someone was successful or even to tried to directly hob a blank without gashing it first. It seems like it would not work very well and not the direction I want to go even if one can do it.
> 
> ...


I have chart to 250 
I will look for my Excel work sheet for 359
Cincinnati's milling machine has chart for compound indexing to 1,000

Dave

Sent from my SAMSUNG-SM-J320A using Tapatalk


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## Bi11Hudson (Jun 22, 2018)

After reading your explanation a couple of times, I am starting to grasp the concept of what you're doing. I'm not into astronomy, a couple of steel mills too close. Light polution*........ *It seems to me you don't need to go all the way around, simply a quadrant would suffice. That could be driven by a couple of stages of worm and pinion, adjusted to a clock. As in move "x" degrees in "y" minutes. Final speed adjustment would be as simple as a servo motor with a good power supply. The other possibility is that I am so far off the track that I just want to answer and can't really help.


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## Smithdoor (Jun 22, 2018)

For 90 tooth worn for 359 teeth
Plate B
Use 33 and 27 
It will take 11 turns 

If your ratory table or indexing head is not 90 teeth let know it on takes a minute for any other number

Dave

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## Smithdoor (Jun 22, 2018)

Compound infexing is found in books dating back to 1900

You find this old machinest Hand book as late as the 1950's

Some milling company use on there dividing head as late as 1970

Dave





Bi11Hudson said:


> After reading your explanation a couple of times, I am starting to grasp the concept of what you're doing. I'm not into astronomy, a couple of steel mills too close. Light polution*........ *It seems to me you don't need to go all the way around, simply a quadrant would suffice. That could be driven by a couple of stages of worm and pinion, adjusted to a clock. As in move "x" degrees in "y" minutes. Final speed adjustment would be as simple as a servo motor with a good power supply. The other possibility is that I am so far off the track that I just want to answer and can't really help.



Sent from my SAMSUNG-SM-J320A using Tapatalk


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## Smithdoor (Jun 23, 2018)

The hard part of compound indexing
Is when you find index number is not found on the chart .
I use a Excel spreadsheet witch fast to the plate and holes need and number of turns need
Then just use calculator to find the spacing

Dave





Bi11Hudson said:


> After reading your explanation a couple of times, I am starting to grasp the concept of what you're doing. I'm not into astronomy, a couple of steel mills too close. Light polution*........ *It seems to me you don't need to go all the way around, simply a quadrant would suffice. That could be driven by a couple of stages of worm and pinion, adjusted to a clock. As in move "x" degrees in "y" minutes. Final speed adjustment would be as simple as a servo motor with a good power supply. The other possibility is that I am so far off the track that I just want to answer and can't really help.



Sent from my SAMSUNG-SM-J320A using Tapatalk


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## stuartw (Jun 24, 2018)

Smithdoor said:


> The hard part of compound indexing
> Is when you find index number is not found on the chart .



yes, thankfully forums like this exist to point people in the right direction. I had not even considered compound indexing, and in truth, I've never had to divide a circle before now using a dividing plate. I didn't know what to even search for. the book i found on the subject didn't mention it (or i missed it)



Smithdoor said:


> Compound infexing is found in books dating back to 1900
> You find this old machinest Hand book as late as the 1950's



perfect, thanks. I am going to try to find a copy along with the treatise of gear wheels and a couple others. It seems the old timers methods are still applicable today for the hobby user, even if it's not as relevant to current industry.


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## stuartw (Jun 24, 2018)

Bi11Hudson said:


> After reading your explanation a couple of times, I am starting to grasp the concept of what you're doing. I'm not into astronomy, a couple of steel mills too close. Light polution*........ *It seems to me you don't need to go all the way around, simply a quadrant would suffice. That could be driven by a couple of stages of worm and pinion, adjusted to a clock. As in move "x" degrees in "y" minutes. Final speed adjustment would be as simple as a servo motor with a good power supply. The other possibility is that I am so far off the track that I just want to answer and can't really help.



The solution is pretty much just as you've described, a worm and pinion: a low speed motor connected to the worm, and the x, y connected to the pinions and a feedback loop that adjusts the rpm as needed. In terms of tracking an object, from the position you found it, you probably would never go past 180 degrees. I think some commercial work as you've described with a more limited range of motion since you can't track objects past the horizon.


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## stuartw (Jun 24, 2018)

vtcnc sent me a sample using a couple of tracks and it gave me some inspiration to apply the information learned here in a similar manor. the standard dividing plates on the rotary table are about 100mm/4" in diameter. I used that as a constraint and came up with this:

Each group A-F is spaced 90.25 degrees apart. So, starting at A-1, rotate left through 270.75 degrees, after you get to the last position for A-1, when you come back up to 0, you use the next track, A-2, this repeats until you hit A-15 @ 270.75 degrees, at this point you come back up to B-1 and repeat the sequence until you get to F-15, stopping one rotation short for 359 divisions. You can see with the blue lines that what would be A-16 lines up with B-1.

EDIT:

I have attached the original rhino3d + dwg and dfx in the dplate.zip file if in case anyone would like to take a look.


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## Karl_T (Jun 24, 2018)

Looks like you got a great plan.

This is such a neat project, I'll make you an offer.

Make and send me a blank plate. Give me a listing of all the holes in this format:
(X0.000 Y0.000 is center of plate)
X#.###  Y#.###
X#.###  Y#.###
X#.###  Y#.###
...

I'll center drill then drill them on my CNC. I am not offering much, this is trivial on a CNC mill.


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## Smithdoor (Jun 24, 2018)

stuartw said:


> Smithdoor said:
> 
> 
> > The hard part of compound indexing
> ...


It found very old book by Brown and Sharp in early 1900's

I do have draws on the settings up on compound indexing

Dave

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## stuartw (Jun 24, 2018)

Karl_T said:


> Make and send me a blank plate. Give me a listing of all the holes in this format:
> (X0.000 Y0.000 is center of plate)



Thank's for the offer, for the now, I would like to try to do the layout myself and vtcnc has offered to laser cut the disc. If anything changes, would you be okay if I messaged you then?


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## Smithdoor (Jun 24, 2018)

stuartw said:


> Karl_T said:
> 
> 
> > Make and send me a blank plate. Give me a listing of all the holes in this format:
> ...


Good luck
Dave

Sent from my SAMSUNG-SM-J320A using Tapatalk


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## Karl_T (Jun 24, 2018)

no problem


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## vtcnc (Jun 26, 2018)

Stuart,

Here ya go! It cut beautifully on the laser...

View media item 97331
And here is the finished product:













Stuart's Dividing Head Plate



__ vtcnc
__ Jun 26, 2018
__
dividing head
laser cutting




						359 spacing - 4" O.D., 430 SS, 16 ga., Laser Cut on 3kw laser cutting machine (Trumpf 2030)
					




PM me your address and I'll drop it in the mail tomorrow


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## Smithdoor (Jun 26, 2018)

vtcnc said:


> Stuart,
> 
> Here ya go! It cut beautifully on the laser...
> 
> ...


The link did not work

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## vtcnc (Jun 26, 2018)

Smithdoor said:


> The link did not work
> 
> Sent from my SAMSUNG-SM-J320A using Tapatalk



@Smithdoor - I reported my post to the staff. I can see the links fine on a desktop web browser (Chrome). However, I cannot view the media on my iPhone using Tapatalk. I think Tapatalk may be the problem.

Anybody else have problems seeing the media files?


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## HMF (Jun 26, 2018)

Tapatalk may be the issue- it is pretty unstable.

Can these be uploaded to our own video library?


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## brino (Jun 26, 2018)

vtcnc said:


> Anybody else have problems seeing the media files?



It looks great from here. (win7 PC and firefox browser)
That is one cool machine!

-brino


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## stuartw (Jun 26, 2018)

wow.. impressive laser setup and the cur disc looks great!! I pm'd you my address.


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## vtcnc (Jun 26, 2018)

Nelson said:


> Tapatalk may be the issue- it is pretty unstable.
> 
> Can these be uploaded to our own video library?



I uploaded the photo to our library. The video was too large - I received an error stating that. YouTube was the path of least resistance for the video.


Sent from my iPhone using Tapatalk


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## vtcnc (Jun 26, 2018)

vtcnc said:


> It is pretty hard to describe how many ways that machine has helped us and our customers - with little to zero downside.  This is the unit we have had for about 4 years now...
> 
> One thing to consider is that Stuart's dividing head was programmed in about 5 minutes. It took me longer to walk down to the laser and talk to the operator about running it. The run time was a little over 6 minutes. Imagine being able to prototype parts out of scrap sheets that quickly...
> 
> Trumpf 2030 Fiber Laser


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## Canuck75 (Jul 3, 2018)

Late to the party but Brown & Sharpe calls this requirement "Differential Indexing" in which the appropriate indexing plate is moved by gearing at the same time the indexing handle is turned. Apparently any number of divisions is possible. The reference I have is an old "Burghardt & Axelrod Machine Tool Operation" book, circa 1954.

Cheers


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## benmychree (Jul 4, 2018)

Canuck75 said:


> Late to the party but Brown & Sharpe calls this requirement "Differential Indexing" in which the appropriate indexing plate is moved by gearing at the same time the indexing handle is turned. Apparently any number of divisions is possible. The reference I have is an old "Burghardt & Axelrod Machine Tool Operation" book, circa 1954.
> 
> Cheers


Actually, the Brown & Sharpe dividing head will index 359 divisions without resorting to differential indexing; their book "Practical Treatise on Milling and Milling machines" lists 359 divisions as being 5 holes on a 43 hole plate; Cincinnati does not list 359 divisions on their tables, but being as they have a 43 hole plate listed, it would also be possible on their dividing head, or any other 40:1 dividing head with a 43 hole plate.
I have done differential indexing on my B&S dividing head, notably for 127 tooth gears for metric transposing; the usual candidates for differential indexing are prime numbers, which 127 is.


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## brino (Jul 4, 2018)

benmychree said:


> Actually, the Brown & Sharpe dividing head will index 359 divisions without resorting to differential indexing; their book "Practical Treatise on Milling and Milling machines" lists 359 divisions as being 5 holes on a 43 hole plate



Hi John, I started playing with the math to see for myself how that'd work.......but I don't think it does.......

A 40:1 worm will give 360/40 = 9 degrees per full revolution.
To divide a circle by 359 means that each of the 359 steps has to be: 360/359 = 1.002785515 degrees apart.
5/43 * 9 degrees = 1.046511628
Dividing a circle by 1.046511628 gives 344 divisions.

However, I did find a copy of that Brown and Sharpe book in my library.
At the top of the table it shows:


then for the 359 line this:


So four gears mounted in the chain for differential indexing.
However, I have NOT worked out the math on that one....

-brino

Oh, I also see in their table for 344 divisions they use plain indexing and 5 holes on the 43 plate:


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## benmychree (Jul 5, 2018)

I stand corrected; the dividing for 359 does require differential indexing; I did not look far enough to the right  on the page to see the change gears; MY BAD!  "The book" was one of my apprenticeship textbooks; it has the front cover missing now, but the contents are intact, so no excuses, except old age and lack of attention!


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## Smithdoor (Jul 5, 2018)

benmychree said:


> I stand corrected; the dividing for 359 does require differential indexing; I did not look far enough to the right on the page to see the change gears; MY BAD! "The book" was one of my apprenticeship textbooks; it has the front cover missing now, but the contents are intact, so no excuses, except old age and lack of attention!


There is compound indexing as works
You do need to do calculating
I just use a Excel work sheet for calc
This also found in old books

Most B & S charts go to 230 teeth or 250
But in this case he using  a rotating table.  
Most are 90 tooth worm
Eather calc or use 20 & 30 gears to the B &S charts 


Dave


Sent from my SAMSUNG-SM-J320A usi


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## stuartw (Jul 6, 2018)

@vtcnc it arrived and looks better than it does in your photo. It looks great!


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