Universal joints for constant velocity transmission of rotational motion between two shafts able to run at an angle comprising two main parts each mounted on one of the shafts and power transmitting members formed as rollers or balls operatively therebetween. These members have two guiding paths formed by pairs of grooves, one on each of the main parts, in the case of balls, and spindles on one of the main parts and spherical surfaces on the other of the main part, when the members are rollers. The guiding paths on a main part make an angle .alpha. with the axis of the shaft on which the part is mounted. Guiding paths of one of the main parts cut guiding paths on the other main part at an angle 2.alpha.. The points of intersection of the guiding paths on one of the main parts for a given pair of members with a plane perpendicular to the longitudinal axis of the shaft associated with the main part is located on a straight line passing through the longitudinal axis and equidistant from the point of intersection of the straight line with the longitudinal axis. The guiding paths associated with a pair of members on a given main part are parallel to one another. When the guiding paths are part-circular, the tangents to the guiding paths of one main part at opposed points along a straight line passing through the center of the joint make the angle .alpha. with the axis on which the part is mounted.