Dividing a circle by 359

[stuartw]

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!

 

[Bob Korves]

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...

 

[stuartw]

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.

 

[markba633csi]

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

 

[BROCKWOOD]

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!!!!!

 

[tcarrington]

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!

 

[stuartw]

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.

 

[stuartw]

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.

 

[MarkM]

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.

 

[Karl_T]

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.