An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

Chen, Guimin; Ma, Fengying; Bai, Ruiyu; Zhu, Weidong; Magleby, Spencer P.; Howell, Larry L.

doi:10.1115/1.4050472

Cited by 19 publications

(6 citation statements)

References 32 publications

(38 reference statements)

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“…In the coordinate system PDQ, the values of P and Q characterize the position of a cross section in beam CD and the deflection, respectively. Considering geometrical nonlinearity, the bending moment of beam CD is expressed as For transverse deflection within 10% of the beam length, the beam curvature can be linearized by assuming the linear slope with a small prediction error [44,45]; thus, the Euler-Bernoulli beam equation is simplified as…”

Section: Nonlinear Modelling Of the Undetermined Beammentioning

confidence: 99%

Nonlinear design, analysis, and testing of a single-stage compliant orthogonal displacement amplifier with a single input force for microgrippers

Chen,

Fan,

et al. 2024

J. Micromech. Microeng.

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To achieve dexterous and stable micro/nanomanipulation, a large grasping stroke, compact design, and parallel grasping are required for microgrippers; thus, a single-stage compliant orthogonal displacement amplifier (CODA) with a single input force would be an ideal transmission mechanism. However, the existing small-deflection-based design schemes cannot adapt to large deflections or shearing effect, thereby affecting the orthogonal movement transformation accuracy. This study proposed, analyzed, and experimentally investigated a nonlinear design scheme for a single-stage CODA with a single input force. First, the nonlinear design principle is described qualitatively. By combining closed-form analytical modelling, finite element analysis, and numerical fitting, the nonlinear extent of a pre-set variable cross-sectional beam in the CODA is formulated. By utilizing the beam constraint model and small-deflection-based modelling, the nonlinear extent of the undetermined uniform straight beam in the CODA is derived. Based on the design principle and nonlinear models, a nonlinear design scheme is proposed quantitatively. Finite element simulations and experimental tests are conducted to verify the proposed scheme, and the limitations of our previous study are revealed.

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Section: Nonlinear Modelling Of the Undetermined Beammentioning

confidence: 99%

Nonlinear design, analysis, and testing of a single-stage compliant orthogonal displacement amplifier with a single input force for microgrippers

Chen,

Fan,

et al. 2024

J. Micromech. Microeng.

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“…In this section, modeling the straight and curved beams is performed using FEM and Castigliano’s second theorem. 39 It should be noted that all the formulations in this research are derived based on linear deflections.…”

Section: Modelingmentioning

confidence: 99%

Topology optimization of the compliant mechanisms considering curved beam elements using metaheuristic algorithms

Mokhtari

Varedi-Koulaei

Zhu

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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Compliant mechanisms use the flexibility of the limbs for movement and can be produced monolithic and joint-less. These flexible mechanisms have wide applications in several fields such as sensors, grippers, parallel mechanisms, micro-electro-mechanical systems, high-precision devices, and biomedical and surgery robots. Topology optimization is regarded as one of the most frequently used approaches for designing compliant mechanisms. The present study aimed to develop the ground structure approach by meshing the design domain using curved beam elements. Moreover, it seeks to implement three different metaheuristic algorithms, including the genetic algorithm, the imperialist competition algorithm, and the equilibrium optimizer for the topology optimization problem. The structural analysis of the compliant mechanism is necessary for determining the values of the objective functions for the optimization process. In the present study, the finite element method was used to analyze the obtained compliant mechanism. Based on the results, an optimum compliant mechanism with both straight and curved beam elements had better performance compared with a compliant mechanism with only straight beams.

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“…VenKiteswaran et al [ 21 ] conducted a study on the pseudo-rigid body model of a compliant beam with three rotations and derived its kinematic and static equations based on this model. Guimin Chen et al [ 22 ], combining Castigliano’s first theorem with the Crotti–Engesser theorem, established an energy-based kinetostatic modeling framework suitable for compliant mechanisms. Ren J and Wu [ 23 ] proposed a three-degree-of-freedom 3-PSS/S flexible parallel micro-turntable and modeled its kinetostatics using both the pseudo-rigid body model approach and the compliance matrix method.…”

Section: Introductionmentioning

confidence: 99%

Compliance Modeling and Kinetostatic Analysis of a Generalized 3-PSS Compliant Parallel Micro-Motion Platform

Ren,

Lan

2024

Micromachines

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In order to expand the range of motion performance of the 3-PSS-compliant parallel micro-motion platform, a variable inclination angle of the mechanism’s guide rails was introduced to construct a category of generalized 3-PSS compliant parallel micro-motion platforms with distinct configurations (exhibiting different motion performances) but identical motion patterns (three translational degrees of freedom). The compliance and kinetostatics of such micro-motion platform are modeled and analyzed. Firstly, the compliance model is established based on the coordinate transformation method. Then, simplifying the micro-motion platform into a spring system, the kinetostatic model in terms of input force–output displacement is established based on the compliance model using the compliance matrix method. For practical application considerations, the kinetostatic model in terms of input displacement–output displacement is further derived based on the input force–output displacement model. Then, the correctness of the established compliance model and kinetostatic model is successively verified through finite element simulation. Finally, using two specified motion trajectories (spatial spiral trajectory and planar circular trajectory) as examples, an analysis is conducted on the influence of guide rail inclination angle variations on the kinetostatic performance of the micro-motion platform. This analysis serves as guidance for the rational design of such micro-motion platforms.

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An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

Cited by 19 publications

References 32 publications

Nonlinear design, analysis, and testing of a single-stage compliant orthogonal displacement amplifier with a single input force for microgrippers

Nonlinear design, analysis, and testing of a single-stage compliant orthogonal displacement amplifier with a single input force for microgrippers

Topology optimization of the compliant mechanisms considering curved beam elements using metaheuristic algorithms

Compliance Modeling and Kinetostatic Analysis of a Generalized 3-PSS Compliant Parallel Micro-Motion Platform

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