Software seems like overkill for mechanism. I were doing this I’d model the mechanism part manually, maybe a scaled-down mock-up out of foamboard, pins, tape, glue etc. if you’re unsure about a certain connection prototype it with scrap wood.

For the dimensioning, Rhino or Sketchup. Really any 3d cad. You probably can get by with grid paper though.

If I really wanted to geek out on the mechanism in a cad modeller I’d probably do it in Grasshopper which is a plug-in for rhino.