Peaucellier-Lipkin linkage - GIF

[mklotz]

I'm not disagreeing with you but there's a much simpler way to do it. Think of a steam locomotive. If you spin the drive wheel the piston rod will make a nice linear move.

Yes the piston rod moves linearly. However, it drives a slider in the crosshead which also moves linearly. The link driving the rotating wheels connects to the slider, not the piston rod. The forces perpendicular to the motion of the piston are absorbed by the slider pushing against the crosshead. There is essentially no perpendicular force on the piston rod.

It was the invention of the crosshead that allowed the piston to drive the crankshaft/loco wheel directly that eliminated the need for the overhead beam and the various linkages, Peaucellier included.