A motorized surgical handpiece (42) with a chuck (60). Internal to the chuck are clamping members (210) that releasably hold clamp the shaft (322) of a cutting accessory (320) to a drive shaft (134) so the cutting accessory rotates upon the actuation of the motor (50). The chuck includes a collar (212) with an opening (236) through which the cutting accessory is inserted. The opening is (236) non-circular in shape. When an accessory shaft with a cross sectional shape that matches the shape of the opening is inserted in the opening, the accessory shaft is appropriate aligned with the chuck clamping members (212).
