Caption: An animation dynamically illustrating Archimedes' screw---which is a rotating helical ramp in a tube used to raise/lower water over low grades. Power goes in/out to raise/lower.
Features:
The ball rolls to stay at a minimum location in the rotating frame of the screw as that mimimum location changes place in the rotating frame, but does NOT change place in the azimuthal direction of the outside frame, but does change place in the axial direction of the outside frame.
But Archimedes' screw was certainly invented empirically by people just playing around with screws and pipes perhaps after an observation of an accidental Archimedes' screw.