A nano-positioning system based on an optimal two-stage linear displacement amplifier

Nano-positioning systems with large motion ranges often employ displacement amplifiers with poor linearity and a large footprint. Here, we propose a compact nano-positioning system comprising an optimally designed two-stage displacement amplifier with linear input-output relationship over a large motion range. The first stage is a truncated bridge amplifier whose size is 25% of a conventional bridge amplifier, while the second stage is a modified lever-type displacement amplifier whose amplified motion direction can be chosen as desired. It is proposed to exploit the compliance of the structure to improve its linearity by operating the truncated bridge amplifier at a specific optimal angle. A simple reduced-order model is proposed and is shown to agree with finite element analysis to within 1%. Further, the variation in the amplification ratio at various payloads are analysed as function of input displacement. Subsequently, a two-stage amplifier with amplification 28 demonstrating a linear range of 940 µm is fabricated using acrylic. This amplifier's nonlinearity is less than 5.2%, representing about 10-fold improvement compared to a conventional bridge amplifier. Lastly, a nano-positioner employing an optimal amplifier is fabricated using spring steel and demonstrated to possess nonlinearity less than 1.5% over a range of 360 µm and a natural frequency of 210 Hz with a footprint of 21 cm2, which represents a substantial improvement in range-to-footprint ratio compared to other amplifiers of similar natural frequencies.