fig1 partially illustrates a tripot - type constant - velocity joint 1 intended for a motor vehicle transmission , and essentially comprising the following components : ( 1 ) a male element or tripod 2 , with ternary symmetry with respect to a central axis x - x ( orthogonal to the plane of fig1 ), and which comprises a hub 3 and three radial arms 4 spaced angularly at 120 ° and just one of which is depicted . the end part of each arm 4 forms a spherical bearing surface 5 formed integrally with it and centered on the axis y — y of the corresponding arm 4 . this male element 2 is secured to a first rotating shaft 6 . ( 2 ) a female element or bell housing 8 with ternary symmetry with respect to a central axis x ′- x ′, the latter axis being coincident with the axis x - x when the joint is in the aligned position depicted . on each side of each arm 4 , this bell housing has two tracks 9 a and 9 b facing each other . this female element 8 is secured to a second rotating shaft ( not depicted ). ( 3 ) for each arm 4 , a mechanical transmission member 11 which comprises an external roller 12 of axis of revolution z - z coincident with the axis y — y of the corresponding arm 4 in the position depicted in fig1 . the external roller 12 is intended to roll along one or other of the corresponding tracks 9 a and 9 b . as the three mechanical transmission members 11 are identical , and because of the ternary symmetry of the male element 2 and of the female element 8 , only the part of the joint 1 which is depicted in fig1 will be described . the directrix of the tracks 9 a and 9 b is , for example , a substantially straight line parallel to the axis x ′- x ′. these tracks are symmetric with respect to one another about a longitudinal and radial plane p ( orthogonal to the plane of fig1 ) of the female element 8 . each track 9 a , 9 b has a central region 14 a , 14 b along which the roller 12 rolls and a bearing surface 15 a , 15 b for radially retaining the roller 12 . the central regions 14 a and 14 b each stretch on each side of the mid - plane q ( orthogonal to the plane p ) of the tracks 9 a and 9 b . the transverse profiles , that is to say the profiles as seen in a plane transversal to the axis x ′- x ′, such as the plane of fig1 of the central regions 14 a , 14 b of the tracks 9 a , 9 b are substantially straight and inclined by an angle α with respect to the longitudinal and radial plane p . the transverse profiles of the central regions 14 a and 14 b therefore converge radially towards the inside of the bell housing 8 at an angle substantially equal to 2α . the transverse profiles of the bearing surfaces 15 a and 15 b are substantially straight and orthogonal to the longitudinal and radial plane p . the bearing surfaces 15 a and 15 b are situated radially on the outside of the bell housing 8 , that is to say radially on the diverging side of the transverse profiles of the central region 14 a and 14 b . for each track 9 a , 9 b , the transverse profiles of the central regions 14 a , 14 b and of the bearing surfaces 15 a , 15 b therefore make an acute angle . the bearing surfaces 15 a , 15 b and the central regions 14 a , 14 b of each track 9 a , 9 b are connected by parts which have curved transverse profiles . the mechanical transmission member 11 comprises , on the one hand , an internal ring 18 , of cylindrical overall shape with axis of revolution z - z , and which is arranged inside the external roller 12 and , on the other hand , means 19 of coupling the internal ring 18 and the external roller 12 . these coupling means 19 comprise a needle ring 21 arranged between a cylindrical surface 22 of the ring 18 which is radially external with respect to the axis z - z , and a cylindrical surface 23 of the external roller 12 which is radially internal with respect to the axis z - z . these coupling means 19 further comprise two flat thrust washers 24 and 25 arranged on each side of the ring 18 and of the needle ring 21 . the periphery of each thrust washer 24 , 25 is housed in an annular groove formed in the surface 23 . the washers 24 and 25 hold the needle ring 21 and the internal ring 18 therebetween , with a small clearance c along the axis z - z . the coupling means 19 therefore allow relative pivoting between the roller 12 and the ring 18 about the axis z - z and allow their limited relative translational movement along the axis z - z . the internal ring 18 comprises a surface 27 , radially internal with respect to the axis z - z , which is substantially cylindrical , which delimits an opening to accommodate the arm 4 . the spherical bearing surface 5 of the arm 4 and the surface 27 of the ring 18 allow a swivelling and sliding movement about the axis y — y between the ring 18 and the arm 4 . the external roller 12 has a peripheral surface 30 , radially external with respect to the axis z - z , which has a central region 31 . this roller 12 also has a frontal surface 32 and a rear surface 33 . the central region 31 , extends , in the direction of the axis z - z , on each side of the mid - plane q ′ of the roller 12 . this plane q ′, orthogonal to the axis z - z , is substantially coincident with the plane q in the position depicted in fig1 . the tracks 9 a and 9 b keep the mid - plane q ′ of the roller 12 substantially orthogonal to the plane p . the central region 31 is substantially frustoconical and converges , at an angle substantially equal to 2α , toward the hub 3 of the tripod 2 , that is to say in the same radial direction as the transverse profiles of the central regions 14 a and 14 b of the tracks 9 a and 9 b . the central region 31 of the roller is therefore , in meridian cross section , substantially the conjugate of the central regions 14 a and 14 b of the tracks 9 a and 9 b . the frontal surface 32 is substantially a flat annulus of axis z - z . this surface 32 is situated radially on the divergent side of the region 31 of the external roller 12 . the frontal surface 32 of the roller 12 is therefore , in meridian cross section , substantially the conjugate of the bearing surfaces 15 a and 15 b of the tracks 9 a and 9 b . the rear surface 33 is substantially a flat annulus of axis z - z and is located radially on the inside of the joint 1 . the region 31 of the external roller 12 is connected to the frontal surface 32 and rear surface 33 by parts , the profiles of which are curved in meridian cross section , of the roller 12 . the way in which the joint 1 works is as follows . when , for example , the male element 2 is driven in the counter - clockwise direction in fig1 the roller 12 comes to bear against the track 9 a in order to transmit the torque to the female element 8 . the arm 4 therefore transmits to the corresponding mechanical transmission member 11 a force f parallel to the plane q ′. the point m of application of this force f is the point of contact between the bearing surface 5 and the surface 27 of the ring 18 . for each mechanical transmission member 11 , the central region 14 a of the track 9 a and the central region 31 of the roller 12 bear against each other . the transverse profiles of these central regions means that they press together substantially flat and implies the generation of a reaction force which , because of the inclination of the transverse profiles of these central parts , has a component r directed radially toward the outside of the joint 1 . this radial component r tends to move the roller 12 radially toward the outside of the bell housing 8 until the frontal surface 32 of the roller 12 comes to bear against the bearing surfaces 15 a and 15 b of the tracks 9 a and 9 b . the surface 32 of the roller 12 comes into contact almost at right angles with the bearing surfaces 15 a and 15 b , which presents no risk of jamming . when the joint 1 is operating at an angle of misalignment between the shafts of axes x - x and x ′- x ′, the arm 4 is given a back and forth movement in radial translation with respect to the tracks 9 a and 9 b , in the plane p , because , on the one hand , of the inclination of the arm and , on the other hand , of the orbital movement , known as the offset , of the tripod at a frequency which is three times the rotational speed , as is well known in the art . the amplitude of this movement is greater in the direction directed radially toward the inside of the joint 1 than in the direction directed radially toward the outside of the joint 1 . when , during this back and forth movement , the arm 4 moves radially toward the inside of the joint 1 ( downward in fig1 ), the point m at which the force f is applied moves radially toward the inside of the joint 1 , and so would tend to cause the roller 12 to rock in the clockwise direction in fig1 . in addition , during this movement , the arm 4 through friction exerts a force f 1 on the internal ring 1 along the axis z - z , which force f 1 is oriented radially toward the inside of the bell housing 8 . this force f 1 would also tend to cause the roller 12 to rock in the clockwise direction in fig1 . the flat pressing between the peripheral surface 30 of the roller and the track 9 a at their central regions 14 a and 31 , and the inclination of the transverse profiles of these central parts , make it possible , through the component r , to compensate for the effect of this force f 1 and the movement of the point m , so that the roller 12 remains bearing against the bearing surfaces 15 a and 15 f of the tracks 9 a and 9 b . when the arm 4 moves radially toward the outside of the joint 1 ( upward in fig1 ), the point m of application of the force f moves in the same direction . at the same time , the arm 4 , through friction , exerts a force f 2 on the internal ring 18 along the axis z - z and directed toward the outside of the bell housing 8 . the movement of the point m and the force f 2 tend to keep the external roller 12 bearing against the bearing surfaces 15 a and 15 b of the tracks 9 a and 9 b . thus , the external roller 12 remains stable , without its part facing the central region 14 b of the track 9 b , against which it is not bearing , oscillating . the angle α is determined so that it just compensates for the effects of the force f 1 and of the movement of the point m of application of the force f radially toward the inside of the joint 1 . in this way , the reaction forces f 3 exerted by the bearing surfaces 15 a and 15 b of the tracks 9 a and 9 b on the external roller 12 are limited , regardless of the direction in which the arm 3 moves . the oscillations of the roller 12 and therefore the risks of the latter jamming when the joint 1 is operating at an angle of misalignment , are therefore limited . finally , the curved profiles in the parts connecting the central regions 14 a and 14 b to the bearing surfaces 15 a and 15 b of the tracks 9 a and 9 b make it possible to avoid high pressures at the ends of the bearing between the central region of the external roller 12 and the tracks 9 a and 9 b . it should be noted that these curved profiles are obtained partly by relief - machining the ends of the central region 31 of the bearing surface 30 . in general , the angle α may be between about 1 and 10 ° and preferably between about 3 and 5 °. according to variants , the transverse profiles of the central regions 14 a and 14 b of the tracks 9 a and 9 b converge radially toward the outside of the bell housing 8 . in the latter instances , the central part 31 of the external roller 12 also converges radially toward the outside and the marginal retaining parts of the tracks 9 a and 9 b are situated radially on the inside of the bell housing 8 . fig2 illustrates a second embodiment of a constant - velocity joint 1 according to the invention , which can be distinguished from the one illustrated in fig1 as follows . the internal ring 18 has an annular shoulder 40 of axis z - z on the radially internal surface 27 of this ring 18 . this shoulder 40 is situated radially on the outside of the joint 1 . the length , along the axis z - z , of the surface 22 of the ring 18 is greater than the length of the surface 22 of the joint 1 in fig1 . the surface 23 of the external roller 12 has two annular shoulders 41 of axis z - z , arranged on each side of the needle ring 21 along this axis . the coupling means 19 also do not have thrust washers 24 or 25 . the coupling means 19 thus allow a pivoting movement about the axis z - z and a sliding movement along this axis between the external roller 12 and the internal ring 18 . in addition , the internal ring 18 swivels and slides along the axis z - z about the spherical bearing surface 5 of the arm 4 . the latter sliding movement is , however , limited radially toward the inside of the joint 1 by the shoulder 40 and , toward the outside , by the end 42 of the bell housing , between the bearing surfaces 15 a and 15 b . the shoulders 41 of the external roller 12 allow the needle ring 21 to be held in place with respect to the roller 12 . this second embodiment makes it possible to reduce the forces transmitted by the internal ring 18 to the roller 12 along the axis z - z because the relative movement along this axis between the internal ring 18 and the external roller 12 is provided via the needle ring 21 .