Precision division plates

I have been thinking a lot about making division plates. Simple, make an approximate plate, bolt it onto your indexing head and use it to make a more accurate one. Thanks to the magic of the 40:1 ratio your new plate is 40 times more accurate. Repeat for evermore accurate plates.

But...

How do you make the accurate worm wheel in the indexing head? Any error in that will be directly copied to the plate you make.

Yesterday while enjoying the sunshine and watching a shadow move across the floor, I had an idea. Accurate clocks are easy to get, If you know time elapsed you can calculate how far the sun has moved across the sky.

This got me to thinking, if I had a telescopic sight, welders goggles, milling machine and a large contraption so I could mount it all on the altazimuth plane. All I would have to do is line up on the sun and cut a tooth, and repeat every N seconds.

N = 86400 / (teeth on gear)

N for 40 = 2160s = 36mins

As the gear is symmetrical you could rotate it 90, 180 and 270 degrees and cut the other teeth.

Six hours, of uninterrupted sunshine might be a little hard to get in the UK, but 6 hrs to cut an accurate gear is a win!

Could be a good holiday project. The better half roasting on the beach, you amazing the locals with a huge machine.

I suppose if you can’t get a sunny day you could use the moon at night.

OK I'll bite

1. The sun is not a point object so you have to assess the centre of the disc.

2. You are still essentially measuring angles when you really want to measure distance of arc.

Suggestion 1

Ditch the sun and use a star

Suggestion 2

Ditch the astronomy and reduce to movements you can measure directly such as.

Fit a mirror to the centre of the plate and bounce a laser beam off it so that the beam is projected onto a distant wall. Make a mark.

Measure the distance to the wall from the mirror. Calculate how far you need the spot to move to give you your required angle. Make a second mark on the wall at that distanceTurn the plate so that the spot falls on the new mark. Drill your hole or cut your tooth. adjust the mirror so that the spot falls on the first mark again and repeat.

Or you may like to think that you could make a second worm wheel from your supposedly inaccurate head which by the logic of your first paragraph is going to be 40 times as good as the old one.

regards Martin

Hi Martin,

Yes the sun is a disk, but you dont have to find the centre, an edge would do, or have double cross hairs that bracket both sides of the sun.

Trouble with the laser/mirror method is any error would be cumulative. I had considered using a sine bar, but discounted it because of the cumulative error..

Making the second worm wheel would not reduce the error. The error in the indexing worm wheel is copied 1:1 to the output. i.e the error is on the output of the indexing head. The plate error is on the input so is divided by 40.

This whole problem really does highlight how clever our forefathers were in creating precision machines.

Ball bearings are held to a pretty tight tolerance so select the number required and machine a circular groove to take them fully crowded,make a detent to pick up each ball. You have just made a very accurate division plate

Mike

Mike Poole, stack the balls on top of each other and you have got the basis of the Microball height gauge, if you could fit 36 into a groove as you describe you would have a very accurate ten degrees between them.

Do dividing plates need to be any more accurate? seems like angels dancing on the head of a pin to me, but what you say about play in the gear train is very valid. I have an old Brown and Sharpe dividing head, which is really too big for my mill, but I manage. The clearance between the worm and pinion is adjustable by turning a handle, and clearance can be almost totally eliminated. I think that for 99% of work this is near enough, and I dont know if the more modern dividing heads have this adjustment. I can understand that if you were,say, dividing a scale for an astronomical instrument, you would be entirely dependent on the finest accuracy you could obtain. My dividing head only has one plate, and I was considering making some more, when I was tipped off about a local cnc shop which would cut and drill for me at a cost that could not be argued with!

It wasn’t my idea here is where I read it.

Fair comment Adrian regarding gear, shows I wasn't really thinking about that bit.

But back to your sun. The edge is not sharply defined. The telescope you use will have a limit to it's resolution. You have atmospheric distortion to consider. The rotaion of the earth is not constant. You have stabilty effects. The angular size of the sun is about 0.5 degrees so you need to fix the edge or the centre to better than 0.05 % of the disc to get an accuracy of 1 arc sec (if my maths is right) and the distortion in the atmosphere is going to be worse than that when the sun's out . Far better off using a big disc with graduations round the edge or ball bearings as has been suggested.

At least with the mirror and the wall you can put the wall as far away as you like to get the accuracy you want.

)

Martin

Nice one Mike.

Back in the19century when it was all new dividing engines were made but used linear measurements to sub divide the angles. I've seen one in a museum somewhere based on a circular table some 8ft in diameter as far as I recall.

On a slightly different method I would try something based on marking a linear scale on a stable substrate, or one at a stable temperature, and wrapping it round a disc. This should remove cumulative errors but might still be inaccurate at the finer divisions depending on method.

Recommened 'background reading' **LINK**

http://fer3.com/arc/m2.aspx/Jesse-Ramsdens-Circular-Dividing-Engine-commentary-Morris-aug-2010-g13701

MichaelG.

If you want perfection, the sun isn't as accurate as you might want (google analemma) accelerating and slowing down over the year. You also need to get your polar alignment accurate. I'd use a star, but remember to work using a sidereal clock, not a solar one.

In practice, it's worth remembering that division plate errors are reduced by the worm ratio. If you can mark out a division plate by hand to an accuracy of half a degree (easy) so the maximum error is 0.25 of a degree then with a 60:1 worm wheel the maximum error will be 15 seconds of arc.

That's an angular error of 0.02mm in 300m, or about a thou in a foot.

I doubt anyone needs to cut two-foot diameter gears with an accuracy greater than a thou.

So unless you are the NPL, you are probably OK marking out your disks with a protractor and drilling them by hand.

Neil

Hmm good to see I have got the brain cells working

I must admit I had forgotten about the ball bearing method, read it in a MEW back issue.

Maybe I had not made the issue I was exploring clear enough. No matter how accurate the division plate you have and how well you adjust the index head. You will always have the error from the worm and wheel.

It is so easy to take for granted accuracy, but when you start to think how do I get accuracy without buying it it becomes quite a interesting problem.

Interesting

So the base accuracy of dividing head is matching of worm and wheel...

This first needs two threaded parts. .of the same pitch and diameter.

One is made into a tap...

The other becomes your worm.

The tap is used to cut the worm... choosing the pitch/circumference ratio desired...which regardless of the pitch will be known...we now have accurate reduction drive.

Now let's think about how you without a screw cutting lathe could generate a screw thread if CONSISTANT pitch?...

Chase a long screw thread...as fine as you can file the chaser

Now arrange to hold many pitches of this thread ( two flat plates) ..you now have a CONSISTANT but weak thread...use this to drive screw cutting for stronger thread also accurate....now make the screw thread required above....

For a laugh...Google Watt micrometer for

There is a technique for making an accurate leadscrew from scratch. When you draw wire through a die you can get long lengths with a very consistent diameter. The die will eventually wear, but for the sort of length we need we can get a very consistent diameter. So then you turn a long mandrel parallel, and close wind the wire around it to form a thread. Because the wire is constant diameter and the mandrel is parallel, this will give a constant pitch screw, with the pitch being the diameter of the wire. Now you cast a lead nut around the wire thread and break it free...coating the wire with graphite first will help. Now you have a nice accurate leadscrew, so you can set up and cut a worm, or probably first, cut a more lasting type of leadscrew for your lathe.

So the worm is not an impossible problem, however to make the worm wheel, you need accurate dividing equipment....so you need an accurate worm and wheel.

I've tried the technique where you use a tap to form a worm wheel. It works, but there is no guarantee that you will end up with the number of teeth that you planned for, quite often you will get one more or one less. Presumably the teeth can also be out of position by a small amount, but how will you check?

John

I googled anal emma by mistake. Got some very interesting results....

Edited By Pete Rimmer on 06/03/2019 20:32:14

Yep, been there, done that, works well for non-critical worm wheels:

For a specific number of teeth I've also pregashed a worm wheel and then used a home made free running hob to clean up the teeth:

Commercially worm wheels are hobbed in a similar way to spur gears with a gear train between the hob and worm wheel blank. So you don't need an accurate worm wheel to cut an accurate worm wheel.......

The notes for my Elliott dividing head say the worm wheels are hobbed on a single purpose hobbing machine, with pitch correction, and the worms are ground on a precision thread grinder. Total error is quoted as a maximum of 1' 30".

I'm not sure about the need for pitch correction. The only thing I can think of is for any given worm and worm wheel the worm linear pitch and worm wheel diametric pitch are connected by pi. Since pi is an irrational number any gear train used in hobbing will have an error. Rather than use large, or multiple, gear sets it may be easier to add a small correction, a bit like differential indexing.

Andrew

.

It would be interesting to know just what they mean by that ^^^

... Is there any more detail in the notes ?

MichaelG.

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For the obsessives:

https://sextantbook.com/category/chasing-tenths-of-an-arcminute/

Edited By Michael Gilligan on 06/03/2019 22:19:21

Or doing it directly using a digital readout (which most seem to have these days) on the mill. If the drilling is carefully done that should be pretty accurate in its own right. Might take a little longer but it's not going to be a short job anyway.