Say you're a prisoner (or kidnapee)... what methods could you use to manufacture makeshift rope in such limited/constrained circumstances?

Rope is useful for improvised weapons (the rope extends one's reach, making a longer lever arm; see meteor hammer, sling) and for traversing walls. Well, okay, and then there's that.

e — a cable, made of three hawsers
g — a hawser, made of three strands
h — a strand, made of three yarns
a — a yarn, made of individual fibers

NOTE that each layer is twisted in the opposite direction from the layer below

starting materials

You can make rope out of a lot of different materials:

preparing wool/cotton for yarn-making

[1] [2] [3]

creating yarns

rope-making — by hand

[1] [2a] [2b] [3] [4] [5] [6] [7]

rope-walk machines — simplified (3 pins + 2 boards)

[1] [2] [3] [4] [5]

rope-walk machines — with gears or belts

[1] [2] [pdf] [3] [4]