There are several editions of 507 Mechanical Movements available on the Internet Archive. I was so impressed with this little book that about a decade ago I downloaded the PDF and turned it into a properly bound book.
I once argued with a colleague that this collection is akin to our software patterns. They are solutions to recurring sub-problems and are a mark of a mature engineering discipline.
39. Sun-and-planet motion. The spur-gear to the right, called the planet-gear, is tied to the center of the other, or sun-gear, by an arm which preserves a constant distance between their centers. This was used as a substitute for the crank in a steam engine by James Watt, after the use of the crank had been patented by another party. Each revolution of the planet-gear, which is rigidly attached to the connecting-rod, gives two to the sun-gear, which is keyed to the fly-wheel shaft.
I'd like to see #29 used in a 3d printer. One spiral driving 3 gears that pull the filament down through the center directly into the hot end. A tiny stepper should do since there is a huge mechanical advantage.
A lot of these sorts of mechanisms have however been made obsolete by modern mechatronics.
For example, washing machines used to have complex gear boxes that made that back and forth motion during washes and also had a second mode for high speed spin cycles. The machine I bought last year has a direct drive BDC motor that simply used electronic control to produce all the motion types. It's just cheaper and in most cases more reliable.
My previous machined died from gearbox failure and replacing it was not economically viable.
It’s not clear from the picture. The belt seen is actually on one of three pulleys. The pulley on the left of the belt drives shaft b, which spins B and turns the output. Likewise, the puller to the rights of the belt will turn a, and therefore A.
The things that are most unclear is that the shaft between b and B is hollow (allowing the shaft from a to A to pass through) and that there are three unconnected pulleys the belt can ride on.
It's confusing because the drawing omits a pulley attached to shaft "a". Shaft "b" is hollow, shaft "a" turns inside shaft "b". As drawn, shaft "b" will rotate and turn bevel gear "B". If the belt were moved to the [undrawn] pulley on shaft "a", bevel gear "A" will rotate, causing "C" to turn in the opposite direction. The topmost pulley presumably slides left or right to engage the different bottom pulleys.
Here's the 1871 edition on the IA:
https://archive.org/details/Mechanical_Movements_507