To do a drawbridge with physics would be fairly easy as long as the wall is tall and thick enough to hide the chain, the length of it wouldn't need to change. The chain would only have to look like a chain, in physics terms it could be a solid box if the chain is always taught. The drawbridge and chains would all 3 boxes joined by 2 hinges.

I suspect might be easier to have the drawbridge rotate and push the chain up, rather than the chains pulling too. But it depends a bit on how realistic it needs to be. That's the way I'd probably do it anyway.