Hello,
You should be able to make that mechanism using physics constraints. I’m not sure how you would control it, though. What do you intend to do with it?
From what I can see, each leg of the platform is made of two ball joints (I think. sorry, I’m not an expert in joints) and a crank. So you should be able to control the cranks with a certain function to make the platform tilt however you like.
Have a look at the crankshaft tutorial, that should help you out a lot.
Not sure what you’re asking about the static equilibrium point. The physics constraints and objects act largely like in the real world. So a simple pendulum, if left free, would point in the direction of the gravity.
Have I answered your questions?