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.