Using Dividing Heads
There are two types of dividing heads, the old and indeed simple type is just a shaft, one end takes the job, the other takes either a dividing plate, which is just a large selection of holes all equally spaced around it, or a change wheel, quite often the very ones used on your lathe, and then an indexer which is just an arm with a pin on the end or for the latter a detent to fit snuggly between the teeth on the change wheel.
The other type is the one with a worm and wheel and dividing plates mounted on the shaft of the worm, this is the more complex type but is capable of just about anything, it also happens that it confuses a lot of people, so that's the one we shall deal with here.
First to even begin to use it you must know the ratio of your worm and wheel, this is usually 40:1 or 60:1  If you don't know, then mark the wheel and with the crank at top dead centre or bottom dead centre it doesn't matter start turning and counting until the mark is back where it started from.
Using it  Maybe you want to make a "square" or a "Triangle" or a "Hexagonal" or quite often a "spur gear" (cog wheel) Taking these in order lets see how we proceed:
Square  Each face or facet is one forth of a full turn (4 sides) so:
40:1 ratio  40/4 = 10 therefore 10 full turns are required for each face.
60:1 ratio  60/4 = 15 therefore 15 full turns again, easy stuff.
Triangle  Each face is one third of a full turn so :
40:1 ratio  40/3 = 13 and one third turns  not so easy we will come back to this one.
60:1 ratio  60/3 = 20 full turns
Hexagonal  Each face is one sixth of a turn so :
40:1 ratio  40/6 = 6 and 4 sixths turns
60:1 ratio  60/6 = 10 full turns
Spur gear  Suppose one with 27 teeth so one 27th of a turn so :
40:1 ratio  40/27 = 1 and 13 twenty sevenths of a turn.
60:1 ratio  60/27 = 2 and 6 twenty sevenths
Right so for anything that works out to "full" turns it's no problem, but for the rest we need the dividing plates. What you need is a dividing plate that has holes in it divisible by the divisor just used, take the triangle first, divisor = 3, therefore we need a plate with holes in it that is dividable by three, lets say we have one with 60 holes in it:
So 60/3 = 20, going back to the original calculation this then gives us on the 40:1 ratio 13 turns and 20 holes more. Don't do this read on
Now the fingers of a normal dividing head are set to encompass the holes and this is where confusion can clobber you. The best analogy is an imaginary fence with posts, so look at figure1
Lets say this is four fence panels surrounding a well, and it would equate to our square that we worked out earlier, so if this was a dividing plate and we wanted one forth, then a forth of four is one, and that's what we need, but using the fingers on a dividing head we need to span that forth, so look at figure2
You can see this with the two fingers spanning "one" quarter, but we are using two holes or fence posts to do it, and again if we needed two parts, look at figure3
For two sides we use three holes, and so it goes on, so every time you do this you add one to it. Going back to our triangle of 13 turns plus 20 holes it becomes 13 turns and 21 holes, always remember this.
Those are the principles, its all quite straightforward, but as it involves counting I would always suggest that you either have a note pad to keep check of your progress or make damn sure you don't get interrupted.
One last point and that's going back to our wonderful spur gear with the very odd number of teeth, I chose this especially, well you may well have a disk with 54 holes in it who knows, then its just a case of halving it. But remember that you could in fact make a disk up, and you don't need to worry that the pitch of your holes is correct to the nearest micron either. The reason being that any small error will be further reduced by the ratio of the worm and wheel.
Well that's it, remember the principles are the same, just substitute your values and off you go.
For my good friend John.
