Armed Mine is a creature I created for Doom 3 that uses procedural animation to drive motor-controlled physics joints. Animation-driven physics gives a lot of flexibility, but can be difficult to get right. Especially when the engine doesn't support this out of the box. Read how the Doom 3 physics engine was extended and the Armed Mine was implemented.
Find out how the horse's tail physics simulation for W!Games' game 'My Horse & Me' was developed from prototype to final product, going from a many-strand technique to a more optimized skin-and-bone skeletal animation system.
One way to simulate physics constraints and collisions is to use springs. It might not be the most stable solution for all applications, but it can be stable and fast enough for a lot of them. Like my (abstract looking) quad vehicle, for example, of which its traction and skidding behaviour are implicit consequences of the simulated springs in the soft-body tires.