I'm interested in learning about gears & mechanisms that translate linear motion to rotational motion. Specifically, I need to translate the motion of straight-line linear motion (essentially straight up and straight down) into rotation, but rotation that is perpendicular to the linear motion.
Imagine a pencil that is inserted through a doughnut. I want to move the pencil up and down. I want the doughnut to rotate in one direction when the pencil moves up & and the opposite way when the pencil moves down.
Apologies for the crude description; I hope it makes sense.

I've seen it done, with hydraulic cylinders backdriving ballscrews.  I think they may have been multiple- start ballscrews, specifically engineered to be backdriven.

Following up on the the post by itascot you need to get hold of a "Scripto Mechanical Pencil" and look at the mechanism. Also if you can find a cutaway of an "Stockham Wedgeplug Valve" there is a very compact mechanism that raises and rotates the taper plug.

Anecdotal:
The mechanism for the Scripto Pencil and the Wedgeplug Valve were designed by the same person. I got to work with him when I started to school under the CO-OP plan, a long time ago.

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