Well, this is not exactly an Archimedes screw, not exactly an automobile, not your usual snowmobile, and not patented that I know of, but wouldn't it be a fun vehicle? These are Russian screw vehicles, which seems to be an area in which they did some development.
If you ever wondered who designed the DeLorean automobile, it was Giorgetto Giugiaro. The DeLorean was designed with a great look, and off the shelf engine and parts. The body was stainless steel, so it should last forever. About 9000 of the cars were manufactured at the DeLorean plant in Ireland before John DeLorean was busted in a drug selling sting. DeLorean got off from the drug bust for entrapment, and served no jail time. He did create one beautiful car! These figures are from U.S. Design Patents 283882, and 257834.