Hi Alan,
Thanks for the Congratulations.
I see that you left this message in several forums. My previous answer involved scales moreso than screws, but I thought that I should explore more details about your Archimedes screw.
I think that there are details that have been largely overlooked here. First, there is the "pitch" of a screw thread. In the US, most of our screws are pitched such that we turn "right to tighten, or left to loosen", but screws with the opposite pitch can also be manufactured. About 20 years ago, many propane gas cylinder tanks had opposite threads - I guess that the assumption was that you would try to "turn left to loosen", but always tighten instead - until you read all of the safety directions and realized that you didn't know what you were doing. They have since changed propane gas cyclinder threads back to the standard pitch - I guess that you don't want people to accidently loosen a tank while they thought they were tightening it.
Conclusion - By changing the pitch of an Archimedes' screw, you can make it attractive or repulsive.
Another detail is the rotation of the screw. It should be obvious that if we change the rotation of a screw - say from Clockwise to Counter-clockwise, then the direction of the force induced by the Archimedes' screw changes.
Conclusion - By changing the rotation of an Archimedes' screw, you can make it attractive or repulsive.
I think that all of these ideas may tie into CPT symmetry. Perhaps handedness (parity) and antimatter (charge) (4 different permutations) are related to these concepts of pitch and rotation (also 4 different permutations).
Personally, I have no problem modeling a Field line or a String with an Archimedes' screw (with variable thread spacing), but realize that the resultant force could be attractive or repulsive - as is electrostatics.
Now we need to explain why gravity is strictly attractive. Is there more to gravity (say within a Black Hole or in a scale of greater complexergy) such as Quantum Gravity, Holographic Gravity, my WIMP-Gravity (see my book), or Edwin Klingman's GEM Gravity? And we only observe the attractive side? Or is this tied into CPT symmetry such that attractive gravity moves forward in time, and repulsive gravity moves backwards in time (which would look attractive and forward)? I don't know...
I think there is enough that we truly don't understand about the origins of mass and gravity that we shouldn't get too overconfident in our models.
Have Fun!
Dr. Cosmic Ray