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.