Constant velocity joint of the type comprising - a male element having multiple arms, - a female element having a female element central axis (X'-X') and defining, for each arm, a pair of opposed tracks (18, 20) which are arranged on either side of said arm and which are symmetrical in relation to a radial longitudinal plane of the female element, and, mounted on each arm, a mechanical transmission unit comprising an outer roller which is mounted so as to plunge and slide in relation to the arm and which is designed to roll on one or other of the corresponding two tracks (18, 20) via a peripheral rolling surface, the female element furthermore comprising at least one bearing surface (60, 62) which prevents or limits the rotation of the outer roller around an axis perpendicular to the female element central axis (X'-X') and to the axis of the arm, characterized in that in respect of each arm: - the cross-section profile of each track (18, 20) comprises either two circular arcs having centers of radii offset one from another or one single circular arc extending over a female element median plane (Q-Q), - the rolling surface has as part spherical shape or a part torical shape, and each track (18, 20) and the rolling surface are capable of contacting each other at a first and second contact points (Z1, Z2) spaced radially from one another; characterised in that in case the rolling surface has a part spherical shape its cross profile, taken along a plane comprising a revolution axis (Z-Z) of the outer roller, is circular with the center of a circle (C-C), defining the spherical shape of the surface, being arranged on the central axis (Z-Z); wherein in case the rolling surface has a part torical shape the degree of toricity T = RT2/RT1 is between 0,8 and 1; wherein the dimension RT1 is the radius of the rolling surface which is the distance between the central axis (Z-Z) taken in a median plane (Q'-Q') of the outer roller and the rolling surface, and the dimension RT2 is the radius of the rolling surface taken in a plane containing the central axis (Z-Z). - a male element having multiple arms, - a female element having a female element central axis (X'-X') and defining, for each arm, a pair of opposed tracks (18, 20) which are arranged on either side of said arm and which are symmetrical in relation to a radial longitudinal plane of the female element, and, mounted on each arm, a mechanical transmission unit comprising an outer roller which is mounted so as to plunge and slide in relation to the arm and which is designed to roll on one or other of the corresponding two tracks (18, 20) via a peripheral rolling surface, the female element furthermore comprising at least one bearing surface (60, 62) which prevents or limits the rotation of the outer roller around an axis perpendicular to the female element central axis (X'-X') and to the axis of the arm, characterized in that in respect of each arm: - the cross-section profile of each track (18, 20) comprises either two circular arcs having centers of radii offset one from another or one single circular arc extending over a female element median plane (Q-Q), - the rolling surface has as part spherical shape or a part torical shape, and each track (18, 20) and the rolling surface are capable of contacting each other at a first and second contact points (Z1, Z2) spaced radially from one another; characterised in that in case the rolling surface has a part spherical shape its cross profile, taken along a plane comprising a revolution axis (Z-Z) of the outer roller, is circular with the center of a circle (C-C), defining the spherical shape of the surface, being arranged on the central axis (Z-Z); wherein in case the rolling surface has a part torical shape the degree of toricity T = RT2/RT1 is between 0,8 and 1; wherein the dimension RT1 is the radius of the rolling surface which is the distance between the central axis (Z-Z) taken in a median plane (Q'-Q') of the outer roller and the rolling surface, and the dimension RT2 is the radius of the rolling surface taken in a plane containing the central axis (Z-Z).