The mechanism is comprised of a swivelling arm (1) hinged at one end to a wheel (2) and hinged at the other end to the frame of the vehicle, and is comprised of a power gear (20) and of a driven gear (21) in the axis of the driving wheel, both gears being associated by a chain. The mechanism is characterized in that the swivelling arm (1) is arranged parallel to the "antisquat" direction defined by the distance between the axes (8, 10) of the wheels (2, 4) and the gravity center of the vehicle. The runs (28, 29) of the chain (22) are parallel to the swivelling arm (1). The effects of the driving wheel (2) and of the chain (22) on the swivelling arm (1), which tend to open and close said swivelling arm, are reduced.