I don't think this is true. Archimedes screw is a similarly shaped helix but contained or partially contained in a tube so that it can move substances by rotary

I don't think this is true. Archimedes screw is a similarly shaped helix but contained or partially contained in a tube so that it can move substances by rotary action. Using a helix as a simple machine is an old concept and probably predates writing; that's about as much of a common ancestor as they share.