I'm still leaning toward the camera exposure counting idea - but, as yet, do not have any definitive proof to support my claim. However, I have made some observations that may be of interest. ( I have not read every one of the 894 comments already posted - and apologize if the following topics have already been discussed).
1. Take a close look at the backside photo, and you will notice the two pressed in features that look like two minature golf clubs. These were clearly intended to keep the back of the device away from a flat surface so as to allow the center pivot to spin freely. I suspect the flat surface was metal and not wood. Many of the older, antique type cameras had tin or metal housings.
2. The reason I believe the flat surface was metal is evident by the two mounting prongs at the top that are typical of a design that would have gone through holes and then bent down to secure it in place. Additionally, the two extension flanges at the bottom likely fit into a couple of slots to secure the bottom portion in place.
4. Incidentally, aluminum was invented in 1886.
3. I can see no evidence whatsoever that indicates the device was connected to any other moving part such as a rod or additional wheels, etc. Which leads me to believe it was independent from whatever it was attached to, and that it's sole purpose was for keeping track of something - say, like the number of exposures on an older type of camera.
5. Many of you have probably already done this, but try reducing the zoom level to 50% for a more accurate idea of it's actual size. 60% would be better yet, but most computers jump from 50% to 75%.
Lastly, I admit there are a couple of flaws in my "Counting Device" theory.
A. Most cameras and the accompanying film came in exposures of 12 - 24 - 36.
B. If it was intended for keeping track of something as important as the exposures, you would think it would click and lock in place, as opposed to being so easily bumped/moved out of sinc.
I'm not sure how much my observations will help, but maybe they will trigger further ideas in this never-ending quest for life - liberty, and the pursuit of ... what the heck is that darn thing, anyway?