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From: Robert Bastow <>
Newsgroups: rec.crafts.metalworking
Subject: Re: Precision Indexing
Date: Sun, 03 Jan 1999 01:41:49 GMT

One of the beauties of a worm and wheel indexing or dividing system is that it
inherently produces results more accurate than itself.

Any error on the index plate is divided by the gear ration of the head.

This can be used to generate very accurate index plates.  For example..I just
finished building a dividing head based on a 5C spin indexer and a 40:1 worm and
wheel from Boston gear.

To produce the division plates I first made a "slave" plate to fit the dividing
head.  This was divided by whatever means available...Direct from the indexer's
36 hole plate available odd gears, or by careful manipulation of dividers and

With the "slave" plate mounted on the crank end of the dividing head and the
soon-to-be-master plate blank on the spindle end, I was able to generate rings
of holes with 1/40th of the error of my slave plate.  Henceforward, each time I
use the master plate to produce a job, any error will again be reduced by a
factor of 40:1

Let us suppose I was a massive 0.040" out in the position of one of my hand
divided holes on the slave plate. This would produce a hole on my shiny new
master plate that is 0.001" out of position..Which is closer than I can
consistantly drill anyway.  But this error will be reduced to 0.000025" on any
job I make on that head!!

Professor Chaddock, (Quorn) once remarked that one could produce accurate index
plates with a school protractor and a large sheet of paper!!

Robert Bastow wrote:

> I'm interested in knowing how the great machine tool builderss achieved the
> accuracy in their dividing heads (indexing heads)
> It seems to me that just setting up a commercial hobbing machine is not good
> enough because all the gears in the various gear trains would have to be of
> similar or greater accuracy.
> I seem to recall tha B & S advertised their index heads with a positional
> accuracy of .001" at a 10" radius.
> Quite an achievement 40 or so years ago!
> I would appreciate hearing from people who made a career out of achieving
> these results.
> Thank you very much for your efforts.

From: Robert Bastow <>
Newsgroups: rec.crafts.metalworking
Subject: Re: Precision worm gear hobbing
Date: Tue, 05 Jan 1999 17:01:26 GMT

>I am just interested in knowing how the tool companies achieved those
>remarkable indexing accuracies.

Just like the rest of us....VERY carefully!!  By which I mean that "Accuracy"
doesn't just "happen"..It is the result of careful, methodical, attention to
extreme detail.  An "ANALists" delight!

Lindsay has a reprint of "Modern Toolmaking" (of which I have an original)  I
recommend this as a primer on how to achieve extreme accuracy in dividing etc.,
working from basics.

Here's how it was done in the "Old Days"

Let us suppose you want a division plate with a prime number of divisions..Say

First make 31 "toolmakers buttons"...Say, 1/2" dia x 1/2" long, each with an
axial hole of 1/4" dia.  The buttons must be hardened, ground and lapped to as
close to the same diameters as Human Endevour can make them. The ends must be
lapped dead square with the axis and parallel to each other.

Next, calculate the EXACT diameter of circle that will be contained by the 31
buttons when they are placed in a circle, in radial contact with each other, and
in contact with the "master circle". Let us call this diameter "X"

On a VERY accurate lathe, face up a circular blank of "X" + 1" diameter

Turn a 1/4" spigot to PRECISELY "X" dimension and at the same setup, bore the
center hole, accurately, to fit your dividing head, gear cutter, or whatever.

Now, arrange the "buttons" around the master circle, drill and tap for 8-32
screws and fasten the buttons in place, arranged so that they are ALL touching
the master diameter AND each other.

You now have a VERY accurate Master Division Plate for 31 divisions...Repeat as

Robert Bastow

From: Robert Bastow <>
Newsgroups: rec.crafts.metalworking
Subject: Re: Precision worm gear hobbing
Date: Wed, 06 Jan 1999 06:18:56 GMT

Fitch R. Williams wrote:

> Robert,
> You have the dividing part done to a "T".  He has a reasonably good
> one too - not as good as the buttons but not bad either.
> I think he is looking for hobbing or cutting techniques that will
> preserve the accuracy of the circle of tool makers buttons (or his
> ball bearings) during the machining process.   He's gashing the gear a
> bit first, but then with the worm cutter letting it rotate which it
> apparently doing non-uniformly.  He thinks his major source of error
> is in the machining process - the fact that the cutter rotates the
> worm gear being cut less than accurately, or cuts each tooth slightly
> unsymmetrically.
> The only way I could see to improve the machining was to force the
> gear being cut to rotate by driving it with a gear.  Several people
> suggested the same thing.
> Are there some tricks in the machining that are being missed here?

I think not Fitch.  In "Professional Practice" the wheel blank would be
positively driven by a very precise gear train...that could probably trace its
ancestry back to a "Master Plate" of one kind or another.

Wolfgang's method of having the hob drive the gashed blank does work quite well
in practice..I have done it myself.  However he mentions that once he reaches
full depth any further running degrades the accuracy because the "Hob" starts to
cut on one side or the other, and unevenly at that.

I think that "Aye and there's the rub"!!..Actually the lack of it!!  ;^)

Firstly this form of cutting SHOULD NOT be attempted with a conventional hob!!
That is, one with relief formed or ground on the teeth.  This will only work
with a non form relieved tool which CANNOT cut on its flanks.  A tap or a
screwcut worm, with simple gashed teeth, works best.

Secondly, it is advised that, to even out prior inaccuracies in the gashing of
the wheel blank, the hob be withdrawn and re-engaged a part of a turn round,
several times during the hobbing process.

I have produced several wormwheels that met all MY requirements..ranging from a
63 tooth wheel (For my Howitzer) that was produced from a blank gashed with a
hacksaw!! and an 8-32 a 90 tooth wheel cut with a 1/2"-10 ACME hand tap.
(For a rotary table)

I would not however, rely on the above methods to produce a worm and wheel to
National Physics Lab Standards...or even, with predictable consistancy, to meet
the standards of a $40.00 set from Boston Gear.

Do however, bear in mind, that when using, even "crudely" produced worms and
wheels in a dividing application..that the error is divided and subdivided into
"smidgins" that are beyond the measuring capabilities of most HSM'

Robert Bastow

From: Robert Bastow <>
Newsgroups: rec.crafts.metalworking
Subject: Re: The search for precision
Date: Thu, 07 Jan 1999 03:27:37 GMT

Hi Wolfgang,

I have absolutely no problem with you taking issue on this or any other point.
That's what this is all about.

Two things spring to mind though:

Firstly, that while I agree that in THEORY, the use of balls would be just as
accurate as using rollers...there is a snag.  With rollers you have line
contact, with balls you have point contact.  Consider the effect of two balls,
resting on a common base and varying in diameter by
say, 20 millions.  Now you not only have two different diameters in contact but
one dia is further from the base line than the other (by 10 millionths).  The
point of contact is no longer on the median diameter of the ring of balls in
your indexing device.

Secondly, I did mention that the buttons or rollers should be as "CLOSE IN
DIAMETER AS HUMAN ENDEAVOUR CAN MAKE THEM"  (Remember we are searching for
EXTREME accuracy here)   I am afraid that 20 millionths isn't in the right ball
park for definitive, primary, reference work.

HOWEVER, for HSM purposes, your ring of balls is an excellent
choice..Personally, I would choose to use reference grade Roller bearings for
the above reasons.


Robert Bastow wrote:

> However, I would take issue with your statement that the indexing accuracy
> of, say 40 toolmaker's buttons assembled around a spigot, is greater, or
> better, than 40 selected ball bearing balls arranged in a similar circle
> (always assuming, of course, that the buttons or the balls touch each other.
> I suppose it depends on the workmanship, and on the accuracy of the
> toolmaker's buttons.  The bearing balls, on the other hand, are selected to
> be all of a diameter within 20 millionths of an inch of each other.

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