I studied Mechanical Engineering and did learn about mechanisms and how to calculate a bunch of these things, but we saw only a let's say "very limited subset" of possible mechanisms, though we studied those in depth. IIRC the most complex gear was a planetary gear.
I am truly marveled when I see the more complex mechanisms and imagine how/where they could be used. You have a lot of repeated ones of course, like linear alt motion to circular or the reverse is a favourite one, but even then it's beautiful seeing many options because each might be more useful for a specific purpose (e.g. high torque, or high speed, or ...).
I remember constructing a digital prototype of a Geneva wheel (really cool mechanism btw) and came to respect the complexity in wrapping your mind around some of these CAD designs in the 3d space, along with the necessary constrains. perhaps even more complicated than producing them in reality.
I am truly marveled when I see the more complex mechanisms and imagine how/where they could be used. You have a lot of repeated ones of course, like linear alt motion to circular or the reverse is a favourite one, but even then it's beautiful seeing many options because each might be more useful for a specific purpose (e.g. high torque, or high speed, or ...).