race not shown which is installed at an end of the shaft and having grooves formed therein an inner race 3 b installed in the outer race a plurality of balls not shown for transmitting the rotational power of the outer race to the inner race 3 b and a cage 5 b for supporting the balls here an outer spherical surface of the inner race 3 b have two sections b 21 b and b 22 b having radii ri1 b and ri2 b respectively and centers o 2 b and o 1 b of the radii ri1 b and ri2 b are axially spaced distances f2 b and f1 b apart from a center ob of a radius rc b of an inner spherical surface c 2 b of the cage 5 b and are radially spaced distances f4 b and f3 b apart from the center o b of the radius rc b of the inner spherical surface c 2 b of the cage 5 b the radii ri1 b and ri2 b are smaller than the radius rc b of the inner spherical surface c 2 b of the cage 5 b the center ob of the radius rc b of the inner spherical surface c 2 b of the cage 5 b is spaced a predetermined offset distance apart from a reference line w b.