My apologies in advance to our more experienced club members if this amounts to teaching granma to suck eggs.  Some of our less experienced members may
find it useful.

I'd heard and read about this for years.  Basically, the premise is:

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On a self-centering three jaw chuck, there's one particular pinion (the
so-called master pinion), which, if used to tighten the stock being held, will
center it with better accuracy than would be the case using any of the other
pinions.
---

So, I'm futzing around in the shop today, not wanting to start another project
before going to MMM, and I decide to test this out.

Now, understand, I do not consider the 3jaw chuck a precision tool.  Its real
advantage, if it has any, is its ease of use and wide range.  If I'm turning
something where all the cuts can be made with a single chucking, thus
guaranteeing coaxial features, fine, I'll use it.  If the work requires several
chuckings and/or reasonable accuracy, I'll use collets or the four jaw.

The premise goes on to say that good chucks will have the master pinion marked.
My Bison (Polish) 6" 3jaw has a small '0' (zero) stamped next to one of the
pinion sockets so, if this is all a myth, it's one that's permeated as far as
the Katyn forest.

So, select a piece of 5/8" stainless shafting that mikes the same all round,
shove in the 3jaw and tighten down using one of the unmarked pinion sockets.
Set up the DI and read 0.002" TIR (i.e., peak-to-peak) error in one
revolution.  Pretty good for a 3jaw but proof of my wisdom in using
collets for anything important.  Loosen chuck and retighten using other
unmarked pinion socket.  TIR still comes in at 0.002". 

Ok, now repeat the experiment using the manufacturer-marked pinion hole.  Lo
and behold, now the TIR is down to 0.001".  I'll be damned.  Being the
untrusting soul that I am, I chalk it up to a fluke.  Try the experiment again
varying the pinion-tightening sequence... master-x-x, x-master-x, etc. as well
as rotating the shaft slightly between each clamping.  Same results each time.
Much as it annoys me, there seems to be some truth to the premise.

I'll leave it as a puzzle for our experienced members to explain *why* there
is a master pinion in the first place.  I don't have a clue nor do I have the
patience to research it.  Offhand, my guess would be that the master is the
pinion used to preload the jaws when they were ground on the ID but that's
just a SWAG.

Those of you who are trying to squeeze the last thou of accuracy out of your
3jaw might want to try this with your own chuck.  According to the premise,
even if your chuck doesn't have a master pinion marked, there is one pinion
that will provide better centering accuracy - your de facto master.  Once you
identify it, you may want to consider marking its location for future
reference.  If you don't want to stamp marks into the chuck, get one of those
paint pens (like a Sharpie, but filled with bright colored paint), clean the
metal with brake cleaner and paint a spot/line, whatever.

One side note here.  The books tell us, if chucking a heavy piece, to tighten
the 3jaw using ALL THREE pinions.  This raises the quandry ... Do we tighten
the master pinion first or last?  Personally, I don't care.  I'd use the 4jaw
if I was worried about the part slipping or coming loose.

Marv Klotz