Grappling rope

After playing around with the physics joints for a while I've encountered a problem:

I would like to create a grappling rope for the player (a custom rigidbody controller) that allows them to fire the rope to swing onto a surface and use it as a hinge joint to walk up objects vertically.

However, the existing hinge joint for Unity does not allow the length of the joint to change (i.e. the player cannot walk towards the joint location). How can I allow this to happen?