K'nex Mechanical Computer (2011) [video]
youtube.comA couple of students from Olin College did this back in 2006/2007 with a 4-bit adder, no electricity, no motors: http://knexcomputer.blogspot.com/
It's up in the publicly-accessible library in Needham, MA if you live nearby and want to check it out!
Seems like a slightly more complex (has a binary -> decimal decoder) of this [1] which was made around the same time but is a bit easier to see how it operates (since it isn't made of K'nex)
[1] https://www.youtube.com/watch?v=GcDshWmhF4A
I guess the big difference is the ball-drop adders don't require electricity or motors for one calculation, but you need some method (human or otherwise) to move the balls back to the top. Also you can only carry out calculation downwards, so your CPU might wind up being a few hundred meters tall!
Not to disparage the ball-drop adders at all, just pointing out the differences.
I made that project. The main benefit of balls is that the friction doesn't add up like it does with connected rods and gears.
This is pretty impressive. I can't imagine how much my fingers would hurt after building that thing.
I went to high school with this guy!