Analysis and design of spatial compliant mechanisms using a 3-D dynamic stiffness model

Ling, Mingxiang; Song, Dezhi; Zhang, Xianmin; He, Xiaoping; Li, Hai; Wu, Mengxiang; Cao, Lei; Shen, Lu

doi:10.1016/j.mechmachtheory.2021.104581

Cited by 15 publications

(7 citation statements)

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“…Any number of piezoelectric stacks connected to compliant mechanisms in serial-parallel configurations can be considered without a loss of generality. Compliant mechanisms with distributed and lumped compliance including rigid bodies and lumped mass can also be involved [53,54]. The following performances are concerned: (a) the intrinsically static and dynamic characteristics, such as the displacement amplification ratio, cross-axis/parasitic motion errors, input and output stiffness and natural frequencies; (b) the responses of mechanical displacement and electrical impedance on the frequency domain; and (c) the time-domain response including piezoelectric hysteresis and dynamic bandwidth of the power amplifier.…”

Section: Systematic Modeling Frameworkmentioning

confidence: 99%

“…If piezoelectric stacks are not considered, the above modeling process will degenerate into a similar dynamic stiffness matrix modeling procedure for compliant mechanisms in [52][53][54]. By solving the linear equation sets in equation (22) with the dynamic frequency ω = 0 and without the consideration of piezoelectric stacks, the kinetostatic performances of the solely compliant mechanism, such as the displacement amplification ratio, parasitic/cross-axis motion errors as well as input and output stiffness can be easily calculated.…”

Section: Systematic Modeling Frameworkmentioning

confidence: 99%

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An electromechanical dynamic stiffness matrix of piezoelectric stacks for systematic design of micro/nano motion actuators

Ling

Luo

et al. 2023

Smart Mater. Struct.

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Piezoelectric stacks have proved to be effective for micro/nano motion actuators with large blocking forces. A critical problem is to build their electro-mechanical model for systematic design of statics and dynamics including piezoelectric hysteresis and elasto-kinematics of compliant mechanisms. To ease this issue, this paper proposes a new electro-mechanical dynamic stiffness matrix of piezoelectric stacks to enable a systematic analysis. Positive and inverse piezoelectric effects are included into the dynamic stiffness matrix of Timoshenko beams in the form of Taylor’s series with a clear definition of physical parameters. Consequently, the Jacobian matrix, input/output stiffness, natural frequencies, frequency-domain spectrums of mechanical displacement and electrical impedance as well as the time-domain response of piezoelectric hysteresis can be fully obtained with a single modeling process. Particularly, the time-domain response in the presence of piezoelectric rate-dependent hysteresis and dynamic resonance behaviors of compliant mechanisms is captured in a parameter-insightful way but not the manner in Hammerstein hysteresis model with a black-box transfer function. Experiments on a proof-of-concept prototype of precision positioning stage verify the easy operation and satisfying prediction accuracy of the presented approach.

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Section: Systematic Modeling Frameworkmentioning

confidence: 99%

Section: Systematic Modeling Frameworkmentioning

confidence: 99%

An electromechanical dynamic stiffness matrix of piezoelectric stacks for systematic design of micro/nano motion actuators

Ling

Luo

et al. 2023

Smart Mater. Struct.

Self Cite

View full text Add to dashboard Cite

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“…There are many modeling methods for analyzing compliant mechanisms as reviewed in the literature of [ 34 , 35 , 36 ], including Castigliano’s second theorem, elastic beam theory, compliance matrix modeling (CMM) method, finite element method, pseudo-rigid-body (PRB) method, the chained beam constraint model and the 3-D dynamic stiffness model. Both merits and shortcomings were comprehensively reported.…”

Section: Modeling and Analysismentioning

confidence: 99%

Design and Modeling of a Novel Tripteron-Inspired Triaxial Parallel Compliant Manipulator with Compact Structure

Xie

Cheung

2022

Micromachines

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Compliant mechanisms are popular to the applications of micro/nanoscale manipulations. This paper proposes a novel triaxial parallel-kinematic compliant manipulator inspired by the Tripteron mechanism. Compared to most conventional triaxial compliant mechanisms, the proposed manipulator has the merits of structure compactness and being free of assembly error due to its unique configuration and the utilize of 3D printing technology. The compliance matrix modeling method is employed to determine the input stiffness of the compliant manipulator, and it is verified by finite-element analysis (FEA). Results show that the deviations between simulation works and the derived analytical models are in an acceptable range. The simulation results also reveal that the compliant manipulator can achieve a 16 μm × 16 μm × 16 μm cubic workspace. In this motion range, the observed maximum stress is much lower than the yield strength of the material. Moreover, the dynamic characteristics of the manipulator are investigated via the simulations as well.

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“…Limited discretenode function values in the workspace are adopted to evaluate the objective performance (global performance index, GPI) due to the difficulty in obtaining its analytical expressions in the workspace. It significantly increases the performance index evaluation's computational cost (Lian et al, 2017). Therefore, effective multi-objective optimization design is challenging.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective optimization design of parallel manipulators using a neural network and principal component analysis

Yang,

Li,

Wang

et al. 2023

Mech. Sci.

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Abstract. In this work, a multi-objective optimization design method is proposed based on principal component analysis (PCA) and a neural network to obtain a mechanism's optimal comprehensive performance. First, multi-objective optimization mathematical modeling, including design parameters, objective functions, and constraint functions, is established. Second, the sample data are obtained through the design of the experiment (DOE) and are then standardized to eliminate the adverse effects of a non-uniform dimension of objective functions. Third, the first k principal components are established for p performance indices (k<p) using the variance-based PCA method, and then the factor analysis method is employed to define its physical meaning. Fourth, the overall comprehensive performance evaluation index is established by objectively determining weight factors. Finally, the computational cost of the modeling is improved by combining the neural network and a particle swarm optimization (PSO) algorithm. Dimensional synthesis of a Sprint (3RPS) parallel manipulator (PM) is taken as a case study to implement the proposed method, and the optimization results are verified by a comprehensive performance comparison of robots before and after optimization.

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Analysis and design of spatial compliant mechanisms using a 3-D dynamic stiffness model

Cited by 15 publications

References 50 publications

An electromechanical dynamic stiffness matrix of piezoelectric stacks for systematic design of micro/nano motion actuators

An electromechanical dynamic stiffness matrix of piezoelectric stacks for systematic design of micro/nano motion actuators

Design and Modeling of a Novel Tripteron-Inspired Triaxial Parallel Compliant Manipulator with Compact Structure

Multi-objective optimization design of parallel manipulators using a neural network and principal component analysis

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