The equipment (1) includes 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 the 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) includes 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 the 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).
