A tidal stabilized tether is called a "skyhook" since it appears to be "hooked onto the sky". They are also called "hypersonic tethers" because the tip nearest the earth travels about Mach-12 in typical designs. Longer tethers would travel more slowly. A grapple system attached to the tip of the tether can thus reach down below the facility and rendezvous with a payload moving in a slower, suborbital trajectory. The grapple would then capture the payload and pull it into orbit along with the tether system. Later, it could release the payload at the top of the swing, tossing it into a higher orbit
The net benefit of the Tether Launch Assist is that it can significantly reduce ΔV that a launch system such as a reusable launch vehicle (RLV) must provide to the payload. Mach 8-12 instead Mach 25 (orbital velocity), so the energy needed is 4-8 times less.
Electro-Dynamic Orbital Accelerator concept has a large vehicle in orbit with a trailing conductive tether. Instead of trying to meet up with a point hook, a vehicle would meet up with the long trailing tether.
The launch vehicle must provide only enough energy to reach OX altitude, thus allowing 30% or more of lift-off weight to be payload, as compared to ~3% for conventional rockets. The result is an enormous reduction in the cost to reach orbit. Payload increases by ten times.
Instead of a meeting an almost point like hook, a sub-orbital vehicle would connect anywhere along a long tether.
NOTE: the tether is unstable and the design would need to be modeled in detail and means to stabilize it found. I was thinking that small sensors and small segments of the tether could have some means of propulsion OR a small towed could be on the end which also flies to stabilize the tether or to pull it taught before rendezvous.