Ball screw mechanism and linear displacement device

Ball screw device comprising: is formed of a screw (1) on whose outer peripheral surface thereof a helical circulation recess (3); is formed of a nut (2), in its inner peripheral surface a helical circulation recess (4) corresponding to the helical circulation recess (3) of the screw (1); a helical circulation path, which is defined by the two helical circulation recesses (3, 4); and a plurality of balls (5) are rollably disposed in the helical circulation path, wherein between at least two balls (5) a spacer member (10) with two concave surfaces (11) is arranged corresponding to the respective beads (5) are facing, characterized, in that the concave surfaces (11) of the spacer element (10) are formed in section of two circular arcs whose origins (X) different from each other, so that the shape of a Gothic curvature is achieved.