A positioning device comprises a moving carriage for supporting members which serve to position a part to be machined and the position of which is determined by an adjustable stop. The device consists of a rotary drum provided with a series of studs of variable length, each stud being moved in turn opposite to a movable bearing member which is coupled with the carriage by means of a motion-reduction mechanism so that the range of motion of the bearing member is smaller than the range of motion of the carriage and in a predetermined ratio.