Equipment includes bony anchoring members one or two linking rods, intended to be connected to the anchoring members, and parts for connecting the linking rod(s) to the anchoring members, at least one anchoring member including a proximal threaded stud and a clamping element for assembling a connecting part thereon, the connecting part including a clamping element for immobilizing the linking rod with respect thereto. The connecting part includes a rounded section for hugging a linking rod and two parallel branches having holes enabling engagement on the proximal threaded stud of the anchoring member; and the clamping elements may be engaged coaxially on the proximal threaded stud of the anchoring member, a first clamping element enabling the assembly of the connecting part on this proximal threaded stud and the second clamping element enabling to clamp both branches of this connecting part.