PURPOSE: To attain high speed rotation by arranging balls between a screw and a raceway ring, and receiving the balls in a ball cage fitted to a nut element.

CONSTITUTION: The outline of an outer half part of a ball race 8 and that of an inner half part of a ball race 9 on the left side are formed of sectors of circles with the center on an axis 11 of a screw 1 and with radii R and (r). A raceway ring 4 therefore has certain freedom of upset motion, so that the raceway ring 4 itself can be accurately conformed to the screw 1. On the right side, another method is shown to obtain the freedom of this motion. A ball race 8 has an ordinary cross-sectional form, and only the ball race 9 has an outline formed of a sector of a circle with the center . One of these is used. A ball cage 21 is fixed to a nut 3 by a support ring 7 through a fitting ring 22 to prevent balls 13 from rolling along with the rotary motion of the screw 1.