Piezo-actuated, flexure hinge-based compliant mechanisms have been frequently used in precision engineering in the last few decades. There have been a considerable number of publications on modeling the displacement amplification behavior of rhombus-type and bridge-type compliant mechanisms. However, due to an unclear geometric approximation and mechanical assumption between these two flexures, it is very difficult to obtain an exact description of the kinematic performance using previous analytical models, especially when the designed angle of the compliant mechanisms is small. Therefore, enhanced theoretical models of the displacement amplification ratio for rhombus-type and bridge-type compliant mechanisms are proposed to improve the prediction accuracy based on the distinct force analysis between these two flexures. The energy conservation law and the elastic beam theory are employed for modeling with consideration of the translational and rotational stiffness. Theoretical and finite elemental results show that the prediction errors of the displacement amplification ratio will be enlarged if the bridge-type flexure is simplified as a rhombic structure to perform mechanical modeling. More importantly, the proposed models exhibit better performance than the previous models, which is further verified by experiments.

https://iopscience.iop.org/article/10.1088/0964-1726/25/7/075022/pdf

Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms

\n Flexure-based compliant mechanisms are becoming increasingly promising in precision engineering, robotics, and other applications due to the excellent advantages of no friction, no backlash, no wear, and minimal requirement of assembly. Because compliant mechanisms have inherent coupling of kinematic-mechanical behaviors with large deflections and/or complex serial-parallel configurations, the kinetostatic and dynamic analyses are challenging in comparison to their rigid-body counterparts. To address these challenges, a variety of techniques have been reported in a growing stream of publications. This paper surveys and compares the conceptual ideas, key advances, and applicable scopes, and open problems of the state-of-the-art kinetostatic and dynamic modeling methods for compliant mechanisms in terms of small and large deflections. Future challenges are discussed and new opportunities for extended study are highlighted as well. The presented review provides a guide on how to select suitable modeling approaches for those engaged in the field of compliant mechanisms.

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Kinetostatic and Dynamic Modeling of Flexure-Based Compliant Mechanisms: A Survey

This paper presents a novel actuator-internal two degree-of-freedom (2-DOF) micro/nano positioning stage actuated by piezoelectric (PZT) actuators, which can be used as a fine actuation part in dual-stage system. To compensate the positioning error of coarse stage and achieve a large motion stroke, a symmetrical structure with an arch-shape bridge-type amplifier based on single notch circular flexure hinges is proposed and utilized in the positioning stage. Due to the compound bridge arm configuration and compact flexure hinge structure, the amplification mechanism can realize high lateral stiffness and compact structure simultaneously, which is of great importance to protect PZT actuators. The amplification mechanism is integrated into the decoupling mechanism to improve compactness, and to produce decoupled motion in X - and Y -axes. An analytical model is established to explore the static and dynamic characteristics, and the geometric parameters are optimized. The performance of the positioning stage is evaluated through finite element analysis and experimental test. The results indicate that the stage can implement 2-DOF decoupled motion with a travel range of 55.4 × 53.2 μm2, and the motion resolution is 8 nm. The stage can be used in probe tip-based micro/nano scratching.

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A Novel Actuator-Internal Micro/Nano Positioning Stage With an Arch-Shape Bridge-Type Amplifier

A new model analysis approach for bridge-type amplifiers supporting nano-stage design

Optimal design of a piezo-actuated 2-DOF millimeter-range monolithic flexure mechanism with a pseudo-static model

Design and trajectory tracking control of a piezoelectric nano-manipulator with actuator saturations

In this paper, we consider the design and analysis of an X–Y parallel piezoelectric-actuator-driven nanopositioner with a novel two-stage amplifying mechanism, where the mechanical design is optimized to achieve a large stroke and high-natural frequency for the purpose of high-performance servomechanism. The parallel kinematic X–Y flexure mechanism provides good geometric decoupling. The kinematic and dynamic analysis shows that the proposed design has a large work space and high bandwidth, which is further verified by finite-element analysis. The analysis results demonstrate that the designed nanopositioner has a large workspace more than 200 µm and a high-natural frequency at about 760 Hz. Furthermore, the dynamical model of the nanopositioner, including the dynamics of the PZT actuators, is also generated from the perspective of input/output transfer functions, and the parameters are identified by frequency-response experiments, which can be used for nano precision servomechanism.

Design and analysis of an X–Y parallel nanopositioner supporting large-stroke servomechanism

In this paper, a novel X – Y parallel piezoelectric-actuator driven nanopositioner is studied from the perspectives of design optimization, dynamical modeling, as well as controller synthesis for high precision positioning. FEM (Finite Element Method) and dynamical modeling are provided to analyze the mechatronic structure of the proposed two-dimensional nano-stage, where the system model, including the hysteresis loop, is derived analytically and further verified experimentally. A robust control architecture incorporating an H ∞ controller and an anti-windup compensator is then developed to deal with the hysteresis and saturation nonlinearities of the piezoelectric actuators. Real time experiments on the nano-stage platform demonstrate good robustness, high precision positioning and tracking performance, as well as recovery speed in the presence of saturation.

Modeling and control of a novel X-Y parallel piezoelectric-actuator driven nanopositioner.

In this paper, a novel piezoelectric actuator driven nano-stage with bridge type mechanism is studied from the perspectives of design optimization, dynamical modeling, as well as controller synthesis for high precision manipulation purposes. FEM (Finite Element Method) analysis and dynamical modeling are provided to derive the system model including the hysteresis nonlinearity. Considering the complexities of dynamical uncertainties and hysteresis nonlinearity, an active disturbance rejection controller is developed consisting of extended state observer (ESO), state feedback controller and profile generator. With the proposed algorithm, the nonlinear dynamics, system uncertainties and external disturbances can be treated as part of the “total disturbances”, such that the extended state observer can be used to estimate and suppress the effects of these complex dynamics. The proposed control algorithm is deployed in real time implementations on the designed nano-stage, where experimental results demonstrate good control performance in terms of high precision positioning, hysteresis compensation and disturbance rejection.

Pengbo Liu

Papers

A new model analysis approach for bridge-type amplifiers supporting nano-stage design

Design and trajectory tracking control of a piezoelectric nano-manipulator with actuator saturations

Design and analysis of an X–Y parallel nanopositioner supporting large-stroke servomechanism

Modeling and control of a novel X-Y parallel piezoelectric-actuator driven nanopositioner.

Flexure-hinges guided nano-stage for precision manipulations: Design, modeling and control