Method of assembling a constant velocity universal joint

A method of assembling components of a constant velocity universal joint for connecting two shafts, said universal joint comprising a one-piece first shaft and inner race, said inner race having an outer surface of partially spherical configuration, a one-piece second shaft and outer race, said outer race having a closed end and an open end, said outer race having an inner surface of partially spherical configuration with the radius of the outer surface of said inner race being substantially equal to the radius of the inner surface of said outer race, whereby the outer surface of said inner race and the inner surface of said outer race fit closely together in the manner of a ball and socket, said inner race having a plurality of outwardly-facing grooves, said outer race having a plurality of inwardly-facing grooves, a cage having a convex outer surface, bearing balls for the corresponding grooves of said inner and outer races, said bearing balls having diameters slightly less than the diameters of said corresponding grooves, said method comprising placing said cage in said outer race with a portion of the convex outer surface of said cage being in contact with the inner surface of said outer race at the closed end thereof, placing said inner race in said outer race and rotating said inner race to align the grooves thereof with the grooves of said outer race, turning said inner race and first shaft so that a portion of said first shaft is received in an end portion of one of said grooves of said outer race at the open end thereof, and placing one of said bearing balls into corresponding grooves of said races opposite the groove into which said first shaft extends.