Complex, dynamic player generated 3d models

I'm just looking for some search terms, references or examples for what I would need to do to have 3d models with moving parts that aren't part of preset animations.  Imagine a tank with 8 legs, a few turrets, a radar dish that moves on its own, maybe a robot arm… and some way for the user to move these things around the model, design their own parts, and maybe even define their behavior.

I'm pretty comfortable with making or finding a model, putting it into the world, and having it scoot around based on user controls. I haven't even tried to animate one yet in a game, but I've worked with 3d animation in Maya. The things I want to do are considerably more complex than this.