An insertion endpiece for connecting a part carrying the endpiece with another part provided with a bore for receiving the endpiece. The endpiece is provided with an outer groove in which there is received a cylindrical ring, that is free to turn and to slide. The ring has teeth projecting from its outside surface, the ends of the teeth being contained, in the free state, in a substantially cylindrical envelope of diameter that is greater than the diameter of the bore. The ring is received in the groove while being free to turn and to slide. The axial width (L) of the groove is greater than the axial width (L1) of the ring. When the ring is in abutment against a flank of the groove, the teeth are in register with a secondary groove formed in the bottom of the groove receiving the ring, and into which secondary groove the teeth are capable of penetrating elastically.