Alan:

A couple of simple things you can do to "diagnose" the gear mesh. First
thoroughly clean both rack and pinion. Do not polish, but be sure they are
clean. Then, do a contact pattern check. This is simply applying some sort
of compound to the entire rack and repeatedly running the rack end to end
several times and reviewing the "pattern" left behind. Obviously, don't use
too much or anything that will get into the optics. Any good grease will
do. (On a side note the professional gear guys use colored componds similar
to jewelere's rougue.)

What you should see ( in a correctly functioning gear mesh) is a uniform
pattern on both the rack and pinion through out the entire stroke (all the
way round the pinion and full length of the rack). The pattern should be
centered on both the rack and pinion and should be as wide as the narrowest
member (either the rack or the pinion).

You probably will not see a uniform pattern based on what you wrote. If you
see the pattern move back and forth across the gears, then you have a
misalignment of the pinion shaft (not 90 degrees to the rack). If you see
the pattern move deeper and then shallower in the gears then either the rack
is warped, or the pinion is ecentric, or you have excessive wear. Use a
dial indicator to determine whether you have an alignment problem and deal
with it accordingly if you find one. Alsi check to see if the top of either
the pinion teeth or the rack teeth is contacting in the root of the mating
gear.

Rack wear is simple to check. Use a caliper and measure the pitch between
any two teeth near either end of the rack (just like thread pitch). If two
adjacent teeth are too close for you to measure then simply measure between
any convenient number ot teeth (say three or four). Then repeat this
measurement several times along the length of the rack paying special
attention to the teeth in the middle of the rack. Shorter measurements
indicate wear.

The pinion can be checked for wear similarly. A helpful trick is to get two
short pieces of wire the same diameter (No. 12 copper wire is good enough)
and lay one wire in the root of one tooth pair and the other wire in the
root of another tooth pair as close to 180 degrees as possible from the
first pair. Measure the distance "over the wires". Now repeat this
procedure with sucessive tooth root "pairs" all around the pinion You
should get the same measurement every time (or real close). Smaller
measurements indicate worn teeth.

Hope this helps.

"Allan Adler" wrote in message
...

The telescope I've referred to in recent postings has a pair of knobs
joined by an axis whose center is a pinion that engages a rack on a tube
that holds the eyepiece. This enables one to focus the telescope. The
rack seems to be well-oiled but still moves somewhat unevenly in some
places as one turns the knobs.

When I look at it so that I can see all the teeth below me: |||||||||||
it seems that they have not all worn evenly, that some are apparently
thicker than others, and that some of the valleys between them are
more filled than others. I don't know if the latter condition indicates
there is more oil in some than others or whether it indicates the presence
of more dirt, which contributes to the uneven motion. The person who
loaned
it to me told me it would be ok for me to oil it and maybe that also means
it is ok for me to clean it (e.g. with a toothbrush). But before I do
anything,
I'd like to be sure of what kinds of conditions contribute to this kind
of uneven motion in a rack and pinion. It mostly turns evenly but in some
places it seems more prone to offer some resistance.

Leaving aside whether it would be permissible to make repairs on the
borrowed
scope, I don't know if it is possible to replace the rack. It seems to be
riveted in place. I wouldn't know how to select a replacement rack or two
replacement rivets. Maybe with suitable machines, I could make my own
rack.
That is something I would keep in mind for the future, when I have some
machines and want to modify or build my own telescope.

Continuing with the hypothetical, suppose I want to be really fanatical
about figuring out what exactly is wrong with the rack. Since eyeballing
it suggests some irregularities, suppose I want to measure all of the
heights of the teeth and all of the widths of the peaks and of the
valleys.
Is there any convenient way to do this? One way that occurrs to me
is to take the rack, clean it, ink it and press it against a piece
of paper to make a print of the rack. Then I can photocopy the inked
page with enlargement and measure it. There would still be a lot of
measurements to make, but they wouldn't be so small and easy to mess up.
Also, if the print were faint in some places, that would confirm my
impression that it was badly worn in some places.

There is one other issue related to the rack and pinion. There seems to
be no barrier between the rack and pinion and the interior of the
telescope tube. It occurs to me that this might let vapors from the
oil diffuse into the tube and possibly also coat the inner surface of
the telescope lens at the other end. That sounds undesirable and makes me
wonder whether someone might have made a mistake by oiling the rack and
pinion in the first place. If so, the source of the mistake might have
been that someone noticed the uneven motion and resistance to turning,
didn't realize the role that wear might have played in it, and instead
tried to solve the problem by oiling it without realizing that this
might be bad for the optics.

On the other hand, I don't know anything about scopes or racks and
pinions,
so my 'pinions aren't worth anything. If someone is better informed,
please
inform me. Thanks.
--
Ignorantly,
Allan Adler
* Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions
and
* comments do not reflect in any way on MIT. Also, I am nowhere near
Boston.