Unless you want it to actually operate in the game engine, I’d recommend doing it using traditional animation techniques, i.e., get in there & keyframe that sucka!
If you need a “physics look” to some parts, then set up the game engine and bake the physics to keyframes. Or use Soft Body or Cloth or Force Fields, depending on the needs of your Rube’chine. But keyframes give you absolute control – and, it must be admitted, absolute responsibility for getting it right.
The power of keyframes over physics sims is that you’re not limited to what the sim can accomplish, and by no means are any of the Blender sims complete physics solutions. They are good approximations but no more, and help immensely when trying to solve some particularly difficult animation problems (such as Cloth). But their strength is also their weakness – they are only physics sims. In many cases what they can produce lacks that spark of “life” that a competent animator can bring to even mechanical objects using keyframes. Rube Goldberg’s crazy inventions were intended to be humorous, and that requires a deft touch at the animation controls when you’re animating usually inanimate objects. Physics sims may be acceptably accurate for many uses, but they are rarely deft.