A ball screw and nut mechanism has a screw in cooperation with a nut via balls that can circulate in a raceway formed by the opposing threads of the screw and nut. The nut has a recirculation insert passing therethrough from the outer face to the thread, the recirculation insert having a first end with a ball transfer groove turned towards the screw. The mechanism has a holding body for holding the recirculation insert in the housing, the recirculation insert having a second end with a shoulder bearing on the nut, the second end of the recirculation insert having an orientation lug having an angular position predetermined and fixed relative to the ball transfer groove, the orientation lug cooperating with a guide relief of the holding body to fix an orientation of the recirculation insert such that the transfer groove is adjusted to the raceway.