The invention concerns a motor vehicle flexible axle comprising two longitudinal arms connected by a cross bracing with open cross-section whereof the flanks, have each an edge, extending between docking zones with the ends of said cross bracing. The housing defines an interior chamber, a lower opening, and a receiver. Consequently, even if the diameters of these driven external gears 66 are made large up to the very limit, these driven external gears 66 do not interfere with each other. The adjustable abutment assembly may be secured to an anchoring implant bored into the bones within the mouth.