\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

Piezoelectric-actuator-driven nanopositioning stages, with large stroke and low crosstalk, are quite appealing for fulfilling the through-silicon via lithography etching task. The motivation of this paper is to combine the ability to enable the nanopositioning stage running in a manner of millimeter scale workspace and nanometer scale positioning accuracy. Two pairs of flexure-guided kinematic modules with high displacement amplification ratio are adopted to construct a 4-PP (P is prismatic) XY nanopositioning stage. A new decoupling design is implemented to realize the decoupling behavior between the input actuators and output compliant limbs, respectively. Kinematics modeling including output compliance, input stiffness, displacement amplification ratio modeling, and workspace determination are carried out. After a series of mechanism dimension optimizations via particle swarm optimization algorithm, the performance of the optimized mechanism is analyzed and assessed by using the ANSYS workbench. Then, a repetitive-compensated PID controller and a single-input and single-output closed-loop control strategy are designed. Finally, a series of experimental tests in terms of crosstalk test, frequency characteristic analysis, damping property analysis, dynamic hysteresis nonlinearity characterization, signal trajectory tracking, workspace determination, and Bode diagram plotting are carried out in details. It indicates that the workspace of fabricated prototype has reached to 1.035 mm $\times$ 1.035 mm, the crosstalk ratio is kept within 0.5%, and the closed-loop positioning accuracy is determined as 400 nm.

Development and Repetitive-Compensated PID Control of a Nanopositioning Stage With Large-Stroke and Decoupling Property

This paper presents a novel flexure-based displacement amplification mechanism to increase the effective actuation stroke of piezoelectric actuator. The proposed mechanism consists of two L-shape lever-type mechanism and one bridge-type mechanism. The flexure hinges in this mechanism are all loaded in tension and bending, which can solve the potential buckling problems. The symmetrical distribution of the L-shape lever mechanisms can avoid the bending moments and lateral forces at the driving end to protect the piezoelectric actuator. An analytical model based on the stiffness matrix method for the calculations of displacement amplification ratio, input stiffness and natural frequency of the mechanism is constructed and optimal design is performed under certain constraints. The finite element analysis results are then given to validate the design model and a prototype of the amplification mechanism is fabricated for performances tests. The results of static and dynamic tests show that the proposed mechanism is capable of travel range of 288.3 μm with motion resolution of 50 nm, and the working resonance frequencies of the mechanism without and with the actuator mounted are 155 Hz and 178 Hz, respectively. The finite element analysis and the experimental results show that good static and dynamic performances are achieved, which verifies the effectiveness of the proposed mechanism.

Design, modeling and testing of a novel flexure-based displacement amplification mechanism

This paper presents a novel two-dimensional vibration-assisted compliant cutting system (2-D VCCS) to be used on conventional machines for generating textured surfaces with uniform and accurate topography. The proposed system is specifically designed to be capable of delivering high-amplitude vibrations with decoupled guidance at the tool tip, while keeping high resistance to cutting forces during the texturing process. The matrix-based compliance modeling method is adopted for compliance and dynamic modeling of the 2-D VCCS. With optimized structural parameters, the model is validated by theoretical and finite element analysis. On-machine performance tests were conducted to identify the vibration amplitudes, stiffness, and frequency responses of the device. Finally, various complex textured surfaces were uniformly and accurately generated by the high-performance 2-D VCCS using a V-shaped diamond tool. The actually textured surfaces were evaluated and shown that they closely match the theoretically predicted surfaces based on the in-process monitored parameters, demonstrating the great potential of the 2-D VCCS to create functional surfaces for industrial products.

Development of a Novel 2-D Vibration-Assisted Compliant Cutting System for Surface Texturing

Modular kinematics and statics modeling for precision positioning stage

This paper presents the design of a novel flexure-based vertical (or Z-axis) nanopositioning stage driven by a piezoelectric actuator (PZT), which is capable of executing large travel range. The proposed stage consists mainly of a hybrid displacement amplification mechanism (DAM), a motion guiding mechanism, and a decoupling mechanism. The hybrid DAM with amplification ratio of 12.1 is developed to transfer the transverse motion of the PZT actuator into the vertical motion. The motion guiding mechanism is introduced to avoid cross coupling at the output end. The decoupling mechanism can significantly reduce the cross coupling at the driving end to protect the PZT. The stiffness and dynamics of the proposed stage are improved by these mechanisms. Analytical modeling and finite element analysis (FEA) are then adopted to optimize dimensions of the stage. Finally, a prototype of the stage is fabricated and tested for verification. The results of static and dynamic tests show that the proposed stage is capable of vertical travel range of 214 μm with resolution of 8 nm, and the first two resonance frequencies are 205 Hz and 1206 Hz, respectively. Cross coupling tests under various lateral loads (0 g-1000 g) show that the maximum variances of the lateral and angular cross couplings are less than 0.78 μm and 95 μrad, respectively, indicating good decoupling capability. In addition, the low-profile structure of the stage is well suited to be used in limited vertical space.

Xiao Xu

Papers

A novel flexure-based vertical nanopositioning stage with large travel range