An undercarriage leg including a strut assembly in which a rod carrying in its lower portion one or more wheels is mounted to slide and free to turn about a pivot axis (Z), the undercarriage leg including an orientation control for selectively orienting the wheel or wheels by causing the sliding rod to pivot, the orientation control including a rotating member rotatably mounted on the strut assembly that includes a toothed sector forming a pinion and is rotationally coupled to the sliding rod, as well as a rack mounted to slide on the strut assembly along a sliding axis perpendicular to the pivot axis to mesh with the pinion in a meshing area, the rack being moved by drive means, wherein the drive means includes a rotary drive inside the rack adapted to turn about the sliding axis and to cooperate via a helicoidal coupling with the rack, the rotary drive being immobilized axially by two opposite axial thrust bearings allowing angular tilting of the rotary drive, the thrust bearings being carried by at least one elongate support inside the rack having a proximal end fixed to an end of a cylinder in which the rack slides.