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I've been looking for the name of the wheel of which a few are visible on this picture (not the object itself, but the wheels that are used on it!):

Gadget that looks like the mechanical display mechanism of an odometer

I've been looking for terms like "counter wheel", "counter reel", and so on - but can't seem to find anything that names the actual wheels themselves.

I know that these wheels have a name as I've seen it before, but I can't recall what it was. If I had to describe it, "a numbered wheel that represents a counted digit, either stand-alone or as part of a larger number".

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But that's just it - wheels is the word – Adel May 13 '12 at 20:51
Combinations, counters, digit keys, number wheels - it can depend on the context. – Resquiens Nov 2 '14 at 20:04

If they were oriented to face you axle-on, they would be called dials, of course. As they're not, the best I can think of is digit wheel. I can't find an official definition page, but Alibaba has a category page for that term, and everything on it looks like what you're talking about...

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According to alibaba: it's a counter digit wheel. Nice link! – J.R. May 13 '12 at 19:25
That sounds like something I'd attempt to use if you attacked me with a digit wheel. ;-) – Jim May 13 '12 at 22:42
Yes, Counter digital wheels; here's some Google images; also includes some distance measuring tools – Bill Lefurgy May 22 '12 at 0:08

Due to their cylindrical shape the wheels in a mechanical counter like this might be referred to as barrels or drums.

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To be pedantic, they don't have to be cylinders, they could be decagons. – smci May 13 '12 at 22:58

I've always called them rotors. (The caption of the first picture at that link starts off with "A series of three rotors...") However, the aforementioned barrel, drum, wheel terms are more common than rotor in discussions of mechanical counters, where the term counter wheel often is used. Two other terms used are disc and ring; a wikipedia row counter article refers to knurled number rings in its "Pendant knitting counters" section and to number discs (or disks) in other sections. However, the disc terms are specific to flat counters with rotating discs, instead of to cylindrical parts as contained in those Veeder-Root-style mechanical counters.

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You can also find odometer wheel

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An odometer is an instrument that measure distances. The device represented in the picture is just a mechanical counter that can be used as an indicator for an odometer, but not necessarily. – Massimo Ortolano Nov 2 '14 at 18:58

Personally, I would call them dials despite the orientation - to me, a dial is a disc with numbers on that is rotated, and is an appropriate word to use for any such disc used in a safe, combination lock or analogue number counter such as the one pictured.

However, it does seem from a quick Google that the distinction that MT_Head is making is potentially a technically accurate1 one. So, if you reject dials on grounds of pedantry, I would suggest using something like rotating discs or number discs. (Discs is what the Wikipedia page on combination locks uses under several pictures of these types of number dials). These sound more natural - to me - than the phrases with wheels in.

1 I've judged this by usage only.

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