An apparatus for magnetically positioning a movable X-Y stage with respect to X and Y horizontal axes and a Z vertical axis that comprises:
- an overall magnet array, attached to said movable X-Y stage, defining an X-Y-Z coordinate system with each axis perpendicular to each other axis, each magnet having a predetermined magnetic field orientation with each magnet sized and shaped substantially the same as every other magnet and each magnet having substantially the same field strength, said overall magnet array comprising:
- a first column of magnets in an X-Y plane aligned parallel to said Y-axis, said first column of magnets being a first Halbach magnet array having:
- a first magnet oriented with said magnetic field extending vertically upward therefrom parallel to said Z-axis;
- a second magnet adjacent said first magnet with said magnetic field extending horizontally toward said first magnet parallel to said Y-axis;
- and
- a third magnet adjacent said second magnet with said magnetic field extending vertically downward therefrom parallel to said Z-axis;
- a second column of magnets in the same X-Y plane as said first column, aligned parallel to said Y-axis and located adjacent to said first column, said second column of magnets having:
- a fourth magnet adjacent to said first magnet with said magnetic field extending horizontally toward said first magnet parallel to said X-axis;
- and
- a fifth magnet adjacent to said third magnet with said magnetic field extending horizontally away from said third magnet parallel to said X-axis;
- a third column of magnets in the same X-Y plane as said first and second columns, aligned parallel to said Y-axis adjacent said second column, spaced apart from said first column a width of a single magnet in the direction of the X-axis, said third column of magnets being a second Halbach magnet array having:
- a sixth magnet adjacent to said fourth magnet with said magnetic field extending vertically downward therefrom parallel to said Z-axis;
- a seventh magnet adjacent said sixth magnet and aligned opposite and spaced apart from said second magnet in said first column a width of single magnet with said magnetic field extending horizontally away from said sixth magnet parallel to said Y-axis;
- and
- an eighth magnet adjacent said fifth and seventh magnets with said magnetic field extending vertically upward therefrom parallel to said Z-axis;
- wherein:
- each of said magnets has an upper and a lower lateral extent in reference to said Y-axis with the upper and lower lateral extent of each magnet being aligned with the upper and lower lateral extent of each other magnet within the same column and each other column;
- said overall magnet array has three columns and three rows with:
- a first row having therein said first, fourth and sixth magnets adjacent each other in that order parallel to said X axis and having the same magnetic field orientations relative to said X axis as said first, second and third magnets, respectively, have relative to said Y axis, and said first row is a Halbach magnet array;
- a second row having therein said second and seventh magnets in that order parallel to said X axis and spaced apart from each other by the width of a single magnet with each of said second and seventh magnets having the same magnet field orientations relative to said X axis as said fourth and fifth magnets, respectively, relative to said Y axis;
- and
- a third row having therein said third, fifth and eighth magnets adjacent each other in that order parallel to said X axis and having the same magnetic field orientations relative to said X axis as said sixth,
- seventh and eighth magnets, respectively, have relative to said Y axis, and said third row is a Halbach magnet array;
- and
- said overall magnet array has the same magnetic field orientation of the magnets when viewed parallel to either said X or Y axis;
- a platen having a top surface disposed opposite said overall magnet array;
- four layers of wire coils on said top surface of said platen positioned to translate said X-Y stage in six degrees of freedom when individual coils are energized, said layers include:
- in one layer, a first set of a plurality of flat stationary electromagnetic coils of wire on said platen that lie in a first horizontal X-Y plane angularly offset in said first horizontal X-Y plane by plus a first oblique angle with respect to said X axis;
- in a second layer, a second set of a plurality of flat stationary electromagnetic coils of wire that lie in a second horizontal X-Y plane angularly offset in said second horizontal X-Y plane by minus said first oblique angle with respect to said X axis;
- in a third layer, a third set of a plurality of flat stationary electromagnetic coils of wire on said platen that lie in a third horizontal X-Y plane substantially parallel to said Y axis;
- and
- in a fourth layer, a fourth set of a plurality of flat stationary electromagnetic coils of wire that lie in a fourth horizontal X-Y plane substantially parallel to said X axis;
- and
- means for individually energizing each coil of wire in each of said first, second, third and fourth layers to interact selectively with said magnets of said overall magnet array to translate said X-Y stage in six degrees of freedom in relation to said X-Y-Z axes.