Prime number division without gearing?

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)

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.

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)

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.

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)

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

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)

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.

Click to expand...

It is extremely difficult to do this without making mistakes.

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.