Modular kinematics and statics modeling for precision positioning stage

In this paper, we explore the applicability of the positioning stage based on flexible hinges for noncontact processing. According to the actual application of the positioning stage, Hooke’s law, the Euler–Bernoulli beam theory, and the geometric relationship of the structure are applied to analyze the coupled displacement in the movement of the positioning stage and the changes in the performance of the positioning stage caused by external loads. The coupled-displacement matrix and the external-load matrix obtained from the analysis are substituted into the ideal-displacement expression of the positioning stage to obtain the displacement expression of the platform in noncontact machining. The platform trajectory obtained by the referenced curve is analyzed. In addition, the coupled displacement in the X- and Y-directions and the coupled displacement caused by the external load in the Z-direction are nanoscales and about one-thousandth of the output displacement, which meets the requirement of tracking accuracy for micron-level machining. Finally, we use finite element analysis (FEA) and experiments to prove the correctness of the theoretical analysis.

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“…According to the research in the literature [9], the expression of the moving displacement X stg of the platform is as follows:…”

Section: The Kinematic Analysis Of Positioning Stagementioning

confidence: 99%

Motion and Load Analysis of the Flexible Platform Based on Noncontact Processing

Lin

Jiang

Xu³

et al. 2022

Micromachines

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“…Advances. Elastic beam theory was widely used for bridge-type compliant mechanisms [179][180][181][182]. Ma et al [77] derived the analytical formula of the displacement amplification ratio for bridge-type compliant mechanisms based on elastic beam theory.…”

Section: Keymentioning

confidence: 99%

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

Ling

Howell

Cao

et al. 2020

Applied Mechanics Reviews

Self Cite

165

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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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“…If the condition of F out = 0 is assumed, the amplification ratio and input stiffness of the bridge-type amplification mechanism can be expressed as [50]:Ramp=2xout2xin=C21C11, Kin=Finxin=2C11.…”

Section: Mathematical Model Of the Positioning Stagementioning

confidence: 99%

Design, Modeling, and Testing of a Novel XY Piezo-Actuated Compliant Micro-Positioning Stage

et al. 2019

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A novel decoupled XY compliant micro-positioning stage, based on a bridge-type amplification mechanism and parallelogram mechanisms, is designed in this paper. Analytical models of the bridge-type amplification mechanism and parallelogram mechanisms are developed by Castigliano’s second theorem and a Beam constrained model. The amplification ratio, input stiffness, and output stiffness of the stage are further derived, based on the proposed model. In order to verify the theoretical analysis, the finite element method (FEM) is used for simulation and modal analysis, and the simulation results indicate that the errors of the amplification ratio, input stiffness, and output stiffness of the stage between the proposed model and the FEM results are 2.34%, 3.87%, and 2.66%, respectively. Modal analysis results show that the fundamental natural frequency is 44 Hz, and the maximum error between the theoretical model and the FEM is less than 4%, which further validates the proposed modeling method. Finally, the prototype is fabricated to test the amplification ratio, cross-coupling error, and workspace. The experimental results demonstrate that the stage has a relatively large workspace, of 346.1 μm × 357.2 μm, with corresponding amplification ratios of 5.39 in the X-axis and 5.51 in the Y-axis, while the cross-coupling error is less than 1.5%.

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Modular kinematics and statics modeling for precision positioning stage

Cited by 54 publications

References 25 publications

Motion and Load Analysis of the Flexible Platform Based on Noncontact Processing

Motion and Load Analysis of the Flexible Platform Based on Noncontact Processing

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

Design, Modeling, and Testing of a Novel XY Piezo-Actuated Compliant Micro-Positioning Stage

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