The positioning and measuring system includes a coordinate positioning machine comprising a movable spindle (60) movable relative to a reference surface 30, a rotor (100) rotatably connected with the movable spindle, an actuator (500) for driving the rotor (100) in rotation around a rotation axis (65), and a coordinate probe (150, 190) detachably connectable to the rotor (100) for measuring coordinate of points (350) of a workpiece (200, 201, 250) along a path resulting from the composition of a translation movement of the spindle (60) and a rotation of the rotor (100). The points (350) are offset (r) with respect to the rotation axis (65) of the rotor (100).