An X-Y movable stage with rotation is described. A fixed base comprises a magnetic bed with a checkerboard, hexagonal or pseudo-random pattern of alternating north and south poles on a grid. A movable puck moves and rotates on the base. The puck comprises three or more nodes where each node may be energized for a north, south, or off magnetic field, with varying field strength. Methods of mapping node locations, controllers, and applications are described. Embodiments for specific applications are described.