[serjeem]

Is there a general theory or framework for how these kinds of mechanical things get designed and work?

I am always really impressed by the ways mechanical motion can be transformed but I have no idea how people figure out these mechanisms. Is it just 3000 years of trial and error and intuition?

[entrepy123]

It is basically the field of kinematics [0]. I guess you could say machine or mechanical design to be more specific.

[0] https://en.wikipedia.org/wiki/Kinematics

[hackernewds]

Kinematics is a very broad field, akin to subbing "working out" to explain "calisthenics"

There has to be something even niché hopefully