Input: yellow engine piston.
The linkage causes the flywheel (in orange) to make two revolutions for each double-stroke of the engine piston. Thus, thanks to high speed the flywheel size can be decreased.
Key factor: there is a dead position when red, green, blue and orange links are in line. Inertia helps the mechanism overcome such position.
Source: US patent 2295, October 11, 1841.