Peaucellier-Lipkin linkage - GIF

[clavius]

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.

I do get what you are saying. I think the point in this instance is what is noted in the description: "converting exact straight-line motion to circular motion,without reference guideways.

I think it's the lack of reference guideways that was the important point of this particular linkage, for an application like the beam engine that Marv K. posted.

To your point, there is are much simpler ways to do this, but until crossheads came along this was one workable (if more complex) way to accomplish that conversion.