Apparatus and methods for determining an initially unknown commutation position of a member moved by a planar motor

An apparatus for determining an x-y commutation position of a mover of a moving-coil planar motor of which a stator is a checkerboard magnet array extending in an x-y plane, the stator producing a periodic magnetic field having a magnetic-field period of 2π in a u-v coordinate system that is rotated 45° from an x-y coordinate system of the plane, the apparatus comprising:

• a first group of four magnetic-field sensors mounted so as to be movable with the mover, the sensors being situated at integer multiples of π/2 from each other in n- and v-directions of the u-v coordinate system, the sensors producing respective data regarding a respective component of the magnetic field at the respective sensor;
• and
• a processor operably connected to the sensors, the processor being configured to determine, from the data received from the sensors, respective Bz fields at the sensors, convert the Bz data to corresponding u-v coordinates, and convert the u-v coordinates to respective x-y coordinates.

A stage apparatus, comprising:

• a motor comprising a coil array and a magnet array, the magnet array extending in an x-y plane and producing a periodic magnetic field having a magnetic-field period of 2π in a u-v coordinate system that is rotated a predetermined angle from an x-y coordinate system of the plane;
• a stage coupled to one of the coil array and magnetic array so as to generate relative motion between the coil array and the magnet array;
• a position-measurement device, comprising at least a first group of magnetic-field sensors coupled to the stage so as to be movable with the stage, the sensors being situated at integer multiples of π/2 from each other in u- and v-directions of the u-v coordinate system, the sensors producing respective data regarding a respective component of the magnetic field at, and hence the position of, the respective sensor within the period of the magnetic field.