A drive system for operation of a roll top cover for covering a cargo bed of a vehicle enables improved and smoother roll top cover movement. The drive system includes: an elongate housing that defines a longitudinal axis and first and second ends, the housing including an axially extending aperture for receiving the roll top cover therethrough; first and second receiving plates disposed transversely within the housing at the respective first and second ends thereof, the receiving plates comprising opposed spiral-shaped slots extending therethrough, each of the spiral-shaped slots having an open end proximally and a closed end distally; and a drive shaft assembly disposed within the housing and extending axially between the first and second ends thereof; wherein the drive shaft assembly is adapted for being operably connected to a drive chain and driving movement thereof within the spiral-shaped slots during operation of the roll top cover.