Figure from ROBOT, Moravec, Oxford, 1998, Chapter 5: The Age of Robots, page 160
non-synchronous skyhook

A non-synchronous orbital ``skyhook''
A tapered, spinning cable orbits a planet like two spokes of a giant wheel. Its ends dip into the atmosphere at regular intervals. Because its spin cancels its orbital velocity at those points, and because of its giant scale, from the ground, the cable ends seem to merely decelerate downwards, then accelerate up, at a modest pace.

Here's a 3D animation of a nonsynchronous skyhook.
(this needs a VRML plugin for your browser)