The equipment includes at least one connecting bar, at least one flexible ligament, and at least one connector making it possible to connect the ligament to the connecting bar. The connector having a first conduit for engaging the connecting bar, equipped with a device for immobilizing the connector relative to the connecting bar, and a second conduit for receiving at least one strand of the ligament, having an insertion opening for this or these strands and an outlet opening for this or these strands, and equipped with devices for mobilizing the ligament relative to the connector. The second conduit is rectilinear between the insertion opening of the strand(s) of the ligament and the outlet opening. The second conduit has a transverse section adjusted to the transverse section of the strand(s) of the ligament that it is intended to receive, i.e. a transverse section just sufficient to allow sliding of the strand(s) of the ligament in the second conduit, but such that the strand(s) are in close contact with the walls delimiting the second conduit.