I have the bog standard Myford head, but I didn't have the table so I did my own spreadsheet.

With that, I know how many turns on the wormscrew there are to make the head revolve once, and I calculate decimal; whole revs and part revs separately. (Integer and fractional parts). I do that for every division from one to as many as I need. Usually around 125 divisions. You can always do more division just by extending the number of rows down.

Then I have columns which know how many holes there are in the division plate circle. In each cell for the column I calculate how many holes is the closest to the fractional part of the number of divisions for that row. Finally, that cell uses conditional formatting so that it lights up yellow if it is within a given angular tolerance of a single division for that number of divisions.

The beauty of this, is that you can adjust the tolerance as you need. If you only have certain plates, then you can relax and/or tighten the tolerance to find out if you can reach a given number of divisions accurately enough.

What I found with the standard Myford plates is that they must have been fairly clever with their choice of hole circles. If you tighten the tolerances too much, the choices all drop away together. If you loosen the tolerance then you don't get much more benefit unless you can tolerate really gross errors.

There are four Myford plates, and No.1 plate gives the most possibilities with only 7 circles. No. 2 plate gives a lot of repeats and only a few a few more (perhaps half as many again) divisions with more hole circles. By the time you get to plates 3 & 4 you pretty nearly get only one extra division per hole circle (although they're not all primes). The Myford head shipped with No.1 and 2, you could buy 3 & 4 as extra if you needed the hard to get divisions.

**LINK**

Obviously it's a spreadsheet so you can tweak it to your worm and plates.

Edited By Andy Ash on 11/05/2016 18:25:37

John,

If you look at that 'vintage' article of mine, which you recently referenced on another thread, you will find two very small programs … one for CBM BASIC [Commodore 64] and one for the Psion Organiser XP.

They are pimitive by modern standards, but the underlying principle is sound.

If Neil & Diane wish to do so, I would be happy for the two little programs to be published here; as a starting point for development.

MichaelG.

.

Sorry to disappoint you, John, but I think you will have a very long wait … So far as I recall, I made no mention of worm-angling.

MichaelG.

Hi John,

I'm glad you found it useful, and figured out how to customise it for your dividing head.

My current job is developing manufacturing software. Before I did that spreadsheet, I had considered actually writing an application to do the job that the spreadsheet now does. I realised I could get everything I needed out of the spreadsheet so I never bothered with the application.

I read that you wanted an application and not a spreadsheet, and I wasn't going to post. When I then read what you had said about precision, I realised I should post anyway. Obviously, with the variable precision you can compromise if you want.

I would always recommend calculating out any choice that the spreadsheet helps you to find. This is just in case the spreadsheet has an error. As far as I know it's all-right.

If you decide to compromise and use a hole circle that doesn't give an integer result, don't forget that you can distribute the error around the full circle. If you calculate how far short/over 60 revolutions (or whatever for your input and worm) you would be with a hole circle that you know carries an error, then you can drop/add those holes gradually and evenly throughout division of the full revolution.

I'll admit that it's not the easiest of things to keep track of, but you only need to use a notepad and a pencil to keep track. It's perhaps a lot better than having to find/make a plate and hole circle that you only ever use once.

If you do it that way, the errors can be surprisingly small, and you still get what you want without the "correct" plate.

Glad to be of service.

Edited By Andy Ash on 12/05/2016 13:33:32

Andy, your excel file is great for adapting to other worm ratios and plates and giving alternative which might save swapping the plate sometimes. I was interested in your use of the MOD function as I haven't been aware of it.

However it seems to dislike the situations where the target division is a multiple of the plate so I modified it using the TRUNC function.
=IF((($D4*E$3)-TRUNC($D4*E$3))>$B$1,0,$D4*E$3)

This still gave errors due somehow to the calculations not being exact so needed a big error allowance.

Going to this long winded version seems to do the trick. B2 is the worm wheel size. Not sure if this was a variable in your version as I've fiddled around as one does.
=IF((($B$2*E$3)/$A4)-($C4*E$3)-TRUNC((($B$2*E$3)/$A4)-($C4*E$3))>$B$1,0,(($B$2*E$3)/$A4)-($C4*E$3))

Roger that Bazyle.

I certainly think that making the worm an adjustable parameter is a useful thing if you're exploring division possibilities. I only have the one head so it never mattered to me. It would be quite a straightforward change to make.

The spreadsheet isn't actually that complicated mathematically. What's incredible is that the computer can do so many sums, so quickly that it can answer all the separate problems in the blink of an eye.

The worm sets the number of revolutions for a complete circle. The actual rotation of the handle for one division out of however many you want can be expressed as a fraction;

Worm revs / Number of Divisions = Actual rotations of worm for one division.

If you do that sum, then you get a number, say 2.456.

The two whole revs is easy. But you also have to get the 0.456 part. It's just added on, but the holes on the plate help to define it. If a hole circle has 46 holes and you use 35 of them, this too can be expressed as a fraction.

35 / 46 = 0.760…….

That is to say using 35 of 46 holes, you can define 0.760 of a revolution. We actually wanted 0.456 of a revolution and with our 46 hole circle we can ask how many holes makes 0.456 of revolution.

0.456 * 46 = 20.976 holes

Obviously this carries an error. The closest you can actually get is 21 holes. So you're left with an error of 0.024

My spreadsheet simply asks how many holes of each hole circle do I need to use to achieve complete accuracy. On top of that is an algorithm that rounds up or down and decides if the difference (proximity) between that nearest integer is bigger or smaller than the specified limit for the whole sheet of hole circles and divisions. If it is smaller, the results are hilighted, if larger they are zeroed and not hilighted.

NOTE: Watch out. The way the columns are aligned it may not always be evident that decimal values are being returned. If you have any doubts temporarily stretch the cell width. The wider you make it, the more precision you will see.

If you set the proximity bigger, you get more matches, but you will notice that more of the results are actually decimal values. The spreadsheet might say 0 full rotations plus 22.08 holes on the 46 hole circle. Obviously you can't have 22.08 holes. You can have 22 holes. I was aiming to get 125 divisions.

125 * (22 / 46) = 59.782

Over the whole circle I come up short. How short?

60 – 59.782 = 0.217 of a revolution.

So how many holes is that?

0.217 * 46 = 10 exactly.

So if we were to divide a circle into 125 divisions using 22 holes on the 46 circle; we'd get to the end of the 125 divisions and we'd be short of 60 revolutions, by 10 holes. It's still not precise, but you can achieve integral precision. All you do is add the extra ten holes gradually throughout the division operation. If you have 125 divisions you could normally use 22 holes on the 46 circle. Then every 13th division use 23 holes.

The differential precision still has a problem, but the integral precision is now fine.

The only way you can have both, is to use a hole circle that reports an integer number (nothing after the decimal point) on my spreadsheet. These integer numbers are those which are typically only reported by the manufacturers on the table that comes with the dividing head – say Brown and Sharpe.

You can make my spreadsheet so that it only shows the integer numbers, but I find the variable precision is more useful (because I only have a couple of plates) so I do it that way. I can get at things I wouldn't otherwise be able to get.

I have to go make some zeds right now. (I hope my worked example sums were right!!! I'm sure someone will say if not.)

I'll try to analyse your worksheet functions tomorrow Bazyle, and compare them with what I did originally. I'll let you know whatever I think.

Edited By Andy Ash on 17/05/2016 23:27:44

Steve that looks good, I gave it a quick try and it seems to work ok , I dont have time today to play with it much but I will over the next day or two.

good job

Shaun

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