The application discloses a parallelogram type of drive wheel suspension system for a motorcycle and employs only a single swing arm at each side of the drive wheel, with the swing arms being torsionally interconnected through the axle structure of the wheel. An adjustable torsion bar is also disclosed for shock absorption; and there is still further disclosed a chain slack take-up device comprising adjustable means for eccentrically shifting the position of a swing arm pivot axis between different fixed positions.