A Piezo-Driven Compliant Nanopositioning Stage with Large Stroke for Micro / Nano Manipulation

This paper presents the design, analysis, and testing of a single-axis compliant nanopositioning stage with large stroke driven by piezoelectric actuator for micro/nano manipulation. In the developed stage, a hybrid displacement amplifier integrating two kinds of flexure-based input/output decoupling modules have been developed to achieve a large stroke and precise positioning. The analytical modelling and finite element analysis are given to validate the mechanical performance and a prototype of the proposed stage is fabricated for performance tests. The experimental results show that the developed stage has the travel stroke of 214 μm with a resolution of 8 nm. It is demonstrated that the stage can be adequate for micro/nano manipulation.


Introduction
Recently, compliant nanopositioning stages with a large stroke are frequently required in different fields of micro/nanomanipulation. [1,2] Meanwhile, piezoelectric (PZT) actuators with nanometer resolution, excellent dynamic characteristics, small size, and high driving force have been usually employed in the nanopositioning stages.[3,4] However, the drawback of the piezoelectric actuator is its limited travel range which are not suitable for requiring a large workspace.
Consequently, a lever-type flexure-based displacement amplifier is widely applied to amplify the limited stroke of PZT in many compliant nanopositioning stages.[5] While is can easily induce parasitic motion errors.[6] Another type of commonly used amplifier refers to bridge-type amplifier, which has compact size, symmetric structure and sufficient amplification ratio.[4,7] Unfortunately, the nanopositoning stages based on bridge-type amplifier have relatively poor dynamics.In addition, duo to a lateral displacement at the driving end of the stage increases with the increasing of the input displacement, a decoupling mechanism is needed for protect PZT from the lateral forces and bending torques.[8] Therefore, it is a challenge working to design a compliant nanopisitioning stage possessing both low cross-coupling and large stroke simultaneously.
In this paper, a novel compliant piezo-driven nanopositioning stage with large stroke is proposed.A hybrid amplifier, which is composed of double flexure-based amplifers, is developed to achieve a large stroke.In contrast with the commonly amplifier, the novel amplifier is characterized by compact size with large amplification ratio, high dynamics and low cross-coupling.
Meanwhile, two types of compliant decoupling modules are developed to reduce the input and output couplings.Based on the configration of the stage, the analysis models and experimental tests validate that the developed stage achieved the large stroke with nanoscale resolution, low input coupling and compact size.It is demonstrated that a considerable potentical of the stage for the applications in various micro/nano manipulations.

Mechanical design
The novel compliant nanopositioning stage is shown in Fig. 1.It is composed of a symmetrical flexure-based input decoupling module(ABCD), a hybrid amplifier(EFGH), a flexure-based motion guide module(IJKL), and a PZT actuator.Corner-filleted flexure hinges are used in the stage .The PZT actuator adopted in the developed stage can generate a nominal displacement of up to 38μm at the max mum drive voltage of 100 V, and can provide a maximum driving force of 1000 N.
As shown in Fig. 1(b), a hybrid-type amplifier, which is a combination of lever-type and bridge-type amplifier, has a compact size with a large amplification ratio and high dynamics.Meanwhile, duo to the symmetric configuration, the amplifier can eliminate the lateral offset error of the output end and gurantee a precise linear output.A couple of input decoupling modules are both mounted between two sides of the PZT.It can reduce the lateral movement perpendicular to the PZT, and protect the PZT from lateral forces and bending torques.In addition, a motion guide module is integrated with the  The motion of the nanopositioning stage is described as follows.When the PZT exerts on the stage, it results in the horizontal displacement of the input decoupling module, which is subsequently amplified by the lever-type and bridge-type amplifiers (EFGH) , and in turn, to prompt a precise linear displacement of the moving platform by the motion guide module (IJKL).

Modeling and analysis
According to Eq. ( 7), it can be seen that the stage has a constant amplification radio, which only depends on the geometric parameters of AB l , BC l , OC l and OD l , but has no relations with flexure elements.The static model of the compliant nanopositioning stage is based on the strain energy method.[9]For Castigliano's second theorem, the total strain energy of the developed stage is where E is Young's modulus; A is the cross-section area of the flexure hinges; I is the inertia moment; G is the shear modulus.The normal force For strain energy method, the input displacement in x , output displacement out x , input stiffness of the stage can be obtained as respectively It is known that a piezo actuator is compressed when a force is applied.Hence, the stiffness of the PZT and the stage must be taken into account when deducing the maximum output displacement of the stage and can be expressed as where pzt k is the stiffness of the PZT, pzt x is the maximum nominal displacement of the PZT.Fig. 3 shows the FEA results of the developed stage by commercial software ANSYS.The stage can generate an output displacement of 208 μm with the input displacement of 18 μm as shown in Fig. 3 (a) Thus, it can be deduced that the proposed stage has a displacement amplification ratio of 12.1.And it can be inferred that the input stiffness of the stage is 28.2N/μm and the output stiffness of the stage is 2.45N/μm.In addition, the relevant maximum stress of 52 MPa is much smaller than the yielding stress of the material of aluminum alloy 7075.

Conclusion
A pizeo-driven compliant PZT-driven nanopositioning stage with large stroke is developed in this paper.To design an optimized prototype, we establish the kinematic model and perform the FEA validation.Finally, a prototype of the stage is fabricated to carry out the performance test of the stage.The test results show that the proposed stage with a minimum resolution of 8 nm has a high amplification ratio of 12.1 and a maximum displacement of 214 μm.It demonstrated that the proposed compact stage is capable of utilizing in the field of micro/nano manipulations.

Figure 2 .
Figure 2. Kinematics of the developed compliant stage

S
and bending moment bi M can be expressed by static equilibrium.

Figure 3 .
Figure 3. FEA results of (a) Deformation Behaviour and (b) Mode Shapers from 1st to 3 rd

Fig. 3 (
Fig.3shows the FEA results of the developed stage by commercial software ANSYS.The stage can generate an output displacement of 208 μm with the input displacement of 18 μm as shown in Fig.3(a) Thus, it can be deduced that the proposed stage has a displacement amplification ratio of 12.1.And it can be inferred that the input stiffness of the stage is 28.2N/μm and the output stiffness of the stage is 2.45N/μm.In addition, the relevant maximum stress of 52 MPa is much smaller than the yielding stress of the material of aluminum alloy 7075.Fig.3 (b) demonstrates that the first three natural frequencies of the proposed stage are 202 Hz, 1161 Hz and 1410 Hz, repectively.