An attachment device (10, 100) obtained by joining three components (12, 14 or 114, 18 or 118), at the end of a tube, comprising: - a conical insert (14, 114) in the form of a truncated cone, the diameter of which narrows in the direction of the end of said tube, the conical insert (14, 114) having an element for receiving a gripping or attachment member, - an internal ring provided with a recess in the form of a truncated cone, the diameter of which narrows in the direction of the center of the tube and the angle of which is equal to or less than the angle of the truncated cone of the conical insert, the external wall of said internal ring being cylindrical with a diameter substantially equal to the internal diameter of the tube, said insert being located in the recess of said internal ring, - an extemal ring (18, 118) comprising a cylindrical portion, the intemal diameter of which is substantially equal to the extemal diameter of said tube, the intemal wall of said cylindrical portion of said extemal ring being intended to come into contact with the cylindrical extemal wall of the tube, said extemal ring comprising a shoulder (28, 128) which partially closes an end of said extemal ring and which has a circular opening (38, 138), said shoulder comprising an annular intemal face (48, 148) intended to abut the end face of the tube and against the transverse end face of the intemal ring located on the side of the end of said tube and an extemal face at the outside and at the end of the extemal ring, characterized in that the conical insert and the extemal ring are sized so that in their assembled position with the intemal ring and the tube: either a smallest-diameter transverse end face of the conical insert abuts the intemal face of the external ring, the circular opening having a sufficient diameter to allow free access to the receiving element and less than the diameter of the transverse face, or the smallest-diameter transverse end face of the conical insert is in the same plane as the external face of the external ring. - a conical insert (14, 114) in the form of a truncated cone, the diameter of which narrows in the direction of the end of said tube, the conical insert (14, 114) having an element for receiving a gripping or attachment member, - an internal ring provided with a recess in the form of a truncated cone, the diameter of which narrows in the direction of the center of the tube and the angle of which is equal to or less than the angle of the truncated cone of the conical insert, the external wall of said internal ring being cylindrical with a diameter substantially equal to the internal diameter of the tube, said insert being located in the recess of said internal ring, - an extemal ring (18, 118) comprising a cylindrical portion, the intemal diameter of which is substantially equal to the extemal diameter of said tube, the intemal wall of said cylindrical portion of said extemal ring being intended to come into contact with the cylindrical extemal wall of the tube, said extemal ring comprising a shoulder (28, 128) which partially closes an end of said extemal ring and which has a circular opening (38, 138), said shoulder comprising an annular intemal face (48, 148) intended to abut the end face of the tube and against the transverse end face of the intemal ring located on the side of the end of said tube and an extemal face at the outside and at the end of the extemal ring, characterized in that the conical insert and the extemal ring are sized so that in their assembled position with the intemal ring and the tube: either a smallest-diameter transverse end face of the conical insert abuts the intemal face of the external ring, the circular opening having a sufficient diameter to allow free access to the receiving element and less than the diameter of the transverse face, or the smallest-diameter transverse end face of the conical insert is in the same plane as the external face of the external ring. either a smallest-diameter transverse end face of the conical insert abuts the intemal face of the external ring, the circular opening having a sufficient diameter to allow free access to the receiving element and less than the diameter of the transverse face, or the smallest-diameter transverse end face of the conical insert is in the same plane as the external face of the external ring.