This is a "Universal Stock Ticker", made around 1880. My father tinkered with it a long time ago and it's been on the shelf since. I've poked at it a few times, but this week I decided it would make a fun project.
The operation of the printer is fairly simple. Letters and numbers are raised around two "character" disks. To print, a small metal cylinder presses the paper against one of the disks. The cylinder is shifted between the disks by a small cam, which lines up with special pins. The disks are nominally inked by one or two rollers, presumably of felt or rubber, but we're missing these. The rotation of the disks are advanced by an escapement (left). The rotation of the disks can be reset to a known place by advancing through two full rotations, after which the lever resting in the worm gear (which is reset every print) stops further rotation.
The machine has two solenoids. One advances the disks, and other prints and advances the paper.