Diamagnetically levitated nanopositioners with large-range and multiple degrees of freedom.

Precision positioning stages are often central to science and technology at the micrometer and nanometer length scales. Compact, multi-degree-of-freedom stages with large dynamic range are especially desirable, since they help to improve the throughput and versatility in manipulation without introducing spatial constraints. Here, we report compact diamagnetically levitated stages, which employ dual-sided actuation to achieve large-range, six degrees-of-freedom positioning. Dual-sided actuation is demonstrated to enable trapping a magnet array in 3D, with independent control of the trap stiffness about two axes, independent control of forces in 3D and torque about 2 axes. A simplified model is proposed to directly relate these physical quantities to the necessary actuation currents. Experimentally, we demonstrate six degrees-of-freedom positioning with low cross-axis motion, large range and nanometer-scale resolution. In particular, here we show linear motion range of 5 mm with positioning precision better than 1.88 nm, and angular motion range of 1.1 radian with a resolution of 50 micro-radian. With the volume of the stage being between 10-20 cm, its utility as a compact nano-positioner is showcased by using it to automatically replace the tip of an atomic force microscope probe.