This equipment (1) comprises at least one connecting bar and at least one anchor member (1) of the "tulip" type and of the so-called "polyaxial" type. According to the invention, -the head (3) forms an articulation portion (15)； -the body (2) forms an articulation cavity (8) for receiving said articulation portion (15), defined by a bearing wall (9)； -the anchor member (1) includes a ring (20) bearing against said bearing wall (9)； -the ring (20) and a distal bearing surface of the head (3) comprise inter- engagement means (16, 21) having, in a first angular position of the ring (20), a first inter-engagement position of the ring (20) in which play exists between the ring (20) and said bearing wall (9), and having, in a second angular position of the ring (20), a second inter-engagement position in which said play is eliminated such that the head (3) is made immobile, or substantially immobile, relative to the body (2).
