You may find it easiest to use physics with joints. You can spawn each rope section where you want it, and pin the joints together in a single function call.
It depends how detailed you want these ropes to be, and how many you want to have on-screen at once... but you should easily be able to have quite a few ropes doing it just with physics. If you want to try IK chains, that's a fair bit more difficult - but there are tutorials on the forums for IK solvers.
~Sol