change wheel dividing

I need help.I have built a dividing head and footstock between a Harold hall and a Sparey pattern and some of my own ideas .What I now require is to be able to compound divide using only change wheels ,is there a formula for this that has been posted before as my maths are somewhat lacking,and an easy solution is what I'm looking for please.

Frank

Start with some labelling. You will have a detent that fits a tooth space to lock the gear and you count a number of teeth past it - call that T teeth.

The main spindle has a gear with N1 teeth, then you have a gear on a banjo meshed with that with N2 teeth. That gear is on a stud which has a second gear keyed or pinned to the N2 one with N3 teeth.

So with just the first gear the divisions D = N1/T but only if D calculates as a whole number, no fractions allowed.
When you add N2 and put the detent in that gear each tooth passed just passes one on the main gear N1 so you haven't gained anything,
However one whole turn of N2 passes N2 teeth so it is may be an easier way of counting and your divisions are N1/N2 because in this case N2=T.

Now put the detent on the second stud gear N3 so you are passing just a fraction of a whole turn of N2 each time.
Now D=(N3/T)x(N1/N2) but again only works properly if D is a whole number. This means that with a regular set of change wheels only a few divisions numbers are possible.

Add another stud and pair of gears and it goes along the same pattern D=(N5/T)x(N3/N4)x(N1/N2).

Thank you Bazyle. I will now put pen to paper and work out what divisions are possible.

Frank

Or you can do it the easy way and get yourself a ready made chart of gear wheels for compound indexing on such a dividing head. Harold Hall's book "Dividing" has a basic chart in it and GH Thomas's "Workshop Techniques" has a comprehensive table from 2 divisions to 360.

Everything below 16 divisions can be done with a single wheel. Above that, you mostly need a 1:3 or 1:2 ratio added to those same single gears to get multiples thereof. Most commonly, a 20T/60T or 30T/60T combo.

For instance, an 8 division indexing is done using a single 40T wheel, with the detente engaging every 5th tooth to give 8 divisions. A 16 division indexing is done by adding a 30T and 60T keyed on the same stud with the 30T engaged with the original 40T. The detente engages with the 60T and at 5 tooth intervals gives you your 16 divisions as each tooth is working through the 1:2 reduction of the 30T/60T compound gears.

Clear as mud? Good. Get the books and charts!.

PS, one very useful division that GHT includes but HH does not is 125 divisions, used for leadscrew handwheels on 8tpi leadscrews such as Myfrod etc.

125 divisions is done by a 50T wheel on the spindle, with compound gears keyed onto a stud of 30T and 75T. Detente is engaged at 1 tooth intervals to give 125 divisions.

Another couple of points that may be in the books if you don't already realise. The detent is typically a rod with a wedge shape in the end that fits the gear tooth space. If you can arrange to rotate it 90 degrees and make a notch that fits over the tooth then you have instantly doubled the number of positions in your indexing gear.

Since the gear you are putting the detent into does not have to mesh with any other gear it does not have to be from the same set so you can pick up any stray gears you find provided you can make the bore and keyway fit the stud. It is a small hop from there to fitting a regular index plate or even a printed paper disc with divisions set out by a CAD program.

From looking at GHT's chart, a standard set of change gears, 20 to 75 by fives plus a 38T will give you almost every number of divisions up to 100, minus the prime numbers such as 23, 37, 41, 53,62, 67-9, 71, 79, and a similar couple in the 80s and 90s. So a pretty good strike rate for anything you are likely to ever need in real terms. Except of course the metric conversion change gear of 127T, for which you need to make his Versatile Dividing Head with the secondary worm and wheel. But that of course defeats teh object of the simplicity and reliability of the direct indexing by change gears method!,

One advantage of the notched plunger that Bazyle mentions above is that you can use it with a 60T gear to do most of the common number of divisions used. (Without the notched plunger you can't do 8 divisions.)

Of course, using the notched plunger on the end of a compound string of gears probably adds many more possibilites than my head can get around at this time of night.