Reading this kind of stuff always makes me admire Victorian engineers even more, who had to do all the math by hand, to say nothing of the machine designs to cut and create these types of gears and mechanical systems.

I suppose they learned a lot from prior tech, like clockmaking, but even there it would seem that fundamental problems would have needed solutions from scratch (eg shear failure probably isnt much of a worry in most clocks but would be catastrophic in a steam engine).