Obviously, you could animate something like this by hand but is there any software on Linux meant to simulate this kind of mechanism?
I don't know about installed software, but Open Constructor is a recreation of the Soda Constructor, which is what that animation makes me think of: https://peterfidelman.github.io/constructor/
And here's another SodaPlay inspired tool as well: https://panoramx.ift.uni.wroc.pl/~maq/constructor/
Hope it helps!