embodiments of the invention exemplified in the drawings will now be described . first , referring to fig2 a , 2b and 3 , the basic construction of a tripod type constant velocity joint will be described . fig2 a is an end view of a joint shown partly in section . fig2 b is a cross sectional view of a trunnion and a roller assembly . fig3 is a longitudinal sectional view of the joint taking an operating angle θ . as shown , the constant velocity joint comprises an outer joint member 10 and a tripod member 20 , wherein one of the two shafts to be connected is connected to the outer joint member 10 and the other is connected to the tripod member 20 . the outer joint member 10 comprises a bottomed cylindrical mouth section 12 and a stem section 18 , the stem section 18 being in the form of a serrated shaft , through which the outer joint member is connected to one of the two shafts to be connected . axially extending track grooves 14 are formed at three equispaced positions on the circumference of the inner peripheral surface of the mouth section 12 . each track groove 14 has roller guide surfaces 16 formed in the circumferentially opposed side walls thereof . the tripod member 20 comprises a boss 22 and trunnion 26 , the boss 22 being formed with a serrated hole 24 , through which the tripod member is connected to the other of the two shafts to be connected . the trunnions 26 radially project from three equispaced positions on the circumference of the boss 22 . each trunnion 26 carries a roller assembly ( 32 , 34 , 36 ). the roller assemblies are received in the track grooves 14 in the outer joint member 10 . in this embodiment , the outer peripheral surface 26 a of the trunnion 26 , when seen in a cross section ( fig2 b ), is of the shape of an ellipse with its longer diameter crossing the joint axis at right angles , but when seen in a longitudinal section ( fig3 ), it is of straight shape parallel with the trunnion , the cross section remaining the same when taken at any axial position . the cross - sectional shape of the trunnion 26 has a shorter diameter extending axially of the tripod member 20 , and the mutually opposed surfaces are retracted in opposite directions from an imaginary cylindrical surface toward the smaller diameter side . the roller assembly includes a ring 32 , a roller 34 , and rolling elements 36 . the ring 32 is fitted on the trunnion 26 , and the ring 32 and roller 34 are unitized through a plurality of rolling elements 36 to constitute a relatively rotatably roller assembly . that is , the rolling elements 36 are rollably interposed between the cylindrical outer peripheral surface 32 b of the ring 32 and the cylindrical inner peripheral surface of the roller 34 . in this embodiment , stop rings 33 and 34 are fitted in annular grooves formed in the inner peripheral surface of the roller 34 , thereby unitizing the ring 32 and roller 34 , preventing slip - off of the rolling elements 36 . as shown enlarged in fig4 , the inner peripheral surface 32 a of the ring 32 is arcuately convex in section . that is , the inner peripheral surface 32 a has a generatrix in the form of a convex arc . whereas the inner peripheral surface 32 a of the ring 32 may be in the form of a convex arc over substantially the entire length thereof ( see fig2 a ), in this case , the generatrix for the inner peripheral surface 32 a of the ring 32 is a combination of a central arcuate section m and relief sections n on both sides thereof . the relief sections n are portions adapted to avoid interfering with the trunnion 26 when the joint takes a working angle θ as shown in fig3 , and are defined by a straight line or curve which is gradually diametrically expanded from the end of the arc m toward the end of the ring 32 . in this case , the relief section n is exemplified as part of a conical surface with a conical angle α = 50 °. as described above , since the generatrix for the inner peripheral surface 32 a of the ring 32 is a convex arc with a radius r and since the cross - sectional shape of the trunnion 26 is substantially elliptic , with a predetermined clearance defined between the trunnion 26 and the ring 32 , the ring 32 is not only movable axially of the trunnion 26 but also oscillable with respect to the trunnion 26 . further , since the ring 32 and roller 34 are relatively rotatably unitized through the rolling element 36 , as described above , the ring 32 and roller 34 are in oscillable relation to the trunnion 26 as a unit . oscillation in this case means that the axis of the ring 32 and roller 34 is tilted with respect to the axis of the trunnion 26 in a plane containing the axis of the trunnion 26 ( see fig3 ) thus , as a result of the roller 34 being oscillable with respect to the trunnion 26 , the roller 34 will roll on the roller guide surfaces 16 while maintaining its posture which is parallel with the axis of the outer joint member even when torque is transmitted with the joint taking an operating angle . the roller guide surfaces 16 of the outer joint member 10 contacting the outer peripheral surface 34 b of the roller 34 each have an arcuate sectional shape with a radius of curvature r . the generatrix for the outer peripheral surface 34 b of the roller 34 is an arc whose center of curvature is located at a point radially spaced from the axis of the roller 34 . the radius of curvature r of the generatrix for the outer peripheral surface 34 b of the roller 34 is smaller than the radius r of the outer diameter surface of the roller 34 . specifically , the radius of curvature r of the generatrix for the outer peripheral surface 34 b of the roller 34 is such that where r1 and r2 are the minimum and maximum values , respectively , of the radius of curvature of the generatrix for the outer peripheral surface 34 b of the roller within the range where solid contact is effected by elastic deformation of the contact section between the roller 34 and the roller guide surface 16 under the condition that the torque load correspond to not more than a half of the breakage torque for the constant velocity joint with respect to the radius of curvature r of the roller guide surface 16 , it is preferably set in the range r1 ≦ r ≦ r2 . in the above setting , the radius of curvature r of the generatrix for the outer peripheral surface of the roller has its allowable range defined to be up to a value slightly smaller than the radius of curvature r of the roller guide surface 16 . since the roller 34 is of torus shape , an inclination of the roller 34 in the rolling direction results in the same state as the setting r & gt ; r , that is , the area of the roller 34 adjacent its widthwise middle separates from the roller guide surface 16 and instead the areas of the roller adjacent its widthwise opposite ends contact the roller guide surface . this setting makes it possible to provide a contact angle over the entire width of the roller 34 and to increase the recovery couple during torque load . further , the solid contact occurring in the high load region greatly reduces the contact surface pressure , thereby reducing wear of the contact section . in the illustrated embodiment , the widthwise opposite ends of the roller 34 are formed with roundings having radii of curvature r3 and r4 smaller than the radius of curvature r of the generatrix so as to be relieved from the roller guide surfaces . this makes it possible to avoid edge load in the widthwise ends of the roller 34 . fig5 and 6 show other embodiments . in each case , the roller is rotatable and oscillable with respect to the trunnion , the relation between the radius of curvature of the roller guide surface and the radius of curvature of the generatrix for the outer peripheral surface of the roller is almost the same as in the preceding embodiment , the difference being as follows . in the constant velocity joint of fig5 , the roller assembly 130 is composed of a ring 132 and a roller 134 which are relatively rotatable through rolling elements 136 , with the cylindrical inner peripheral surface of the ring 132 being fitted on the spherical outer peripheral surface of the trunnion 126 . in the constant velocity joint of fig6 , the roller assembly 230 is composed of a ring 232 and a roller 234 which are relatively rotatable through rolling elements 236 , with the concavely spherical inner peripheral surface of the ring 232 being fitted on the spherical outer peripheral surface of the trunnion 226 .