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Machines
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Optimization and Design of Compliant Mechanisms
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Optimization and Design of Compliant Mechanisms

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Robotics, Mechatronics and Intelligent Machines".

Deadline for manuscript submissions: 15 May 2025 | Viewed by 8380

Special Issue Editors

Dr. Bingxiao Ding

E-Mail Website
Guest Editor
Department of Mechanical Design, Manufacturing and Automation, Jishou University, Xiangxi 416000, China
Interests: robotics; micro-positioning; smart actuators; nonlinear system control
Prof. Dr. Jinqing Zhan

E-Mail Website
Guest Editor
School of Mechatronics and Vehicle Engineering, East China Jiaotong University, Nanchang 33013, China
Interests: compliant mechanisms; micromanipulators; precision positioning; topology optimization; finite element analysis
Dr. Nguyen Vu Linh

E-Mail Website
Guest Editor
College of Engineering and Computer Science, VinUniversity, Hanoi, Vietnam
Interests: mechanism and machine design; robotic machining; robot design; kinematics and statics analysis; multibody dynamic systems; physical human-robot interaction; reliability-based design optimization

Special Issue Information

Dear Colleagues,

Compliant mechanisms are rationally designed structures of precision geometrical shape, leading to ultra-precision motion and special force displacement chracteristics. Unlike conventional rigid-link mechanisms, the motion of compliant mechanisms is realized via using flexible elements whereby deformation requires no lubrication while achieving high movement accuracy without friction. As compliant mechanisms differ significantly from traditional rigid mechanisms, the recent research focus has been on investigating various technologies and approaches to address challenges in their design and synthesis, optimization, analysis, materials, fabrication methods, and actuation. Applications of these structures include micro manipulation, precision manufacturing, vibration isolation, medical robots, and so on. The focus of this Special Issue is the design, optimization, control, and applications of compliant mechanisms.

Dr. Bingxiao Ding
Prof. Dr. Jinqing Zhan
Dr. Nguyen Vu Linh
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Machines is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • compliant mechanism
  • constant force mechanism
  • optimization
  • micro-positioner
  • robotics

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Published Papers (7 papers)

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Research

19 pages, 1424 KiB  
Article
Development and Testing of a Dual-Driven Piezoelectric Microgripper with High Amplification Ratio for Cell Micromanipulation
by Boyan Lu, Shengzheng Kang, Luyang Zhou, Dewen Hua, Chengdu Yang and Zimeng Zhu
Machines 2024, 12(10), 722; https://doi.org/10.3390/machines12100722 - 12 Oct 2024
Viewed by 524
Abstract
Cell micromanipulation is an important technique in the field of biomedical engineering. Microgrippers play a crucial role in connecting macroscopic and microscopic objects in micromanipulation systems. However, since the operated biological cells are deformable, vulnerable, and typically distributed in sizes ranging from micrometers [...] Read more.
Cell micromanipulation is an important technique in the field of biomedical engineering. Microgrippers play a crucial role in connecting macroscopic and microscopic objects in micromanipulation systems. However, since the operated biological cells are deformable, vulnerable, and typically distributed in sizes ranging from micrometers to millimeters, it poses a huge challenge to microgripper performance. To solve this problem, this paper develops a dual-driven piezoelectric microgripper with a high displacement amplification ratio, large stroke, and parallel gripping. By adopting modular configuration, three kinds of flexure-based mechanisms, including the lever mechanism, Scott–Russell mechanism, and parallelogram mechanism are connected in series to realize three-stage amplification, which effectively makes up for the shortage of small output displacement of the piezoelectric actuator. At the same time, the use of the parallelogram mechanism also isolates the parasitic rotation movement, and realizes the parallel movement of the gripping jaws. In addition, the kinematics, statics, and dynamics models of the microgripper are established by using the pseudo-rigid body and Lagrange methods, and the key geometric parameters are also optimized. Finite element simulation and experimental tests verify the effectiveness of the developed microgripper. The results show that the developed microgripper allows an amplification ratio of 46.4, a clamping stroke of 2180 μm, and a natural frequency of 203.1 Hz. Based on the developed microgripper, the nondestructive micromanipulation of zebrafish embryos is successfully realized. Full article
(This article belongs to the Special Issue Optimization and Design of Compliant Mechanisms)
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20 pages, 10148 KiB  
Article
Modelling and Design Optimization of a Novel Compliant XY Positioner for Vibration-Assisted CNC Milling
by Minh Phung Dang, Chi Thien Tran, Hieu Giang Le, Vo Quoc Anh Tran and Hong Van Tran
Machines 2024, 12(8), 534; https://doi.org/10.3390/machines12080534 - 6 Aug 2024
Viewed by 811
Abstract
Vibration-assisted machining, known as hybrid processing technology, offers several benefits over conventional machining methods. However, developing mechanical structure designs to generate a non-resonant frequency source remains challenging. The objective of this study is to propose a novel design for an XY flexure positioner [...] Read more.
Vibration-assisted machining, known as hybrid processing technology, offers several benefits over conventional machining methods. However, developing mechanical structure designs to generate a non-resonant frequency source remains challenging. The objective of this study is to propose a novel design for an XY flexure positioner by combining the pseudo-rigid-body model with the Lagrange technique, finite element analysis and Crayfish optimization algorithm. Firstly, the mechanism was designed by combining a hybrid amplifier and parallel driving mechanism integrated with right circular hinges to increase the natural frequency and precision for potential application to VAM CNC milling. Then, the analytical model was established by the pseudo-rigid-body and Lagrange method. Next, the theoretical result was verified by finite element analysis. The first natural frequency results of theory and FEM methods were found at 990.74 Hz and 1058.5 Hz, respectively. The error between the two methods was 6.4%, demonstrating a reliable modeling approach. Based on the analytical equations, the Crayfish optimization algorithm was utilized for optimizing the main design variables of the mechanism. Next, the prototype was fabricated. The results showed that the experimental and simulated frequencies were 1127.62 Hz and 1216.6 Hz, with an error between the two methods of 7.31%. Finally, the workpiece was installed on the prototype and a real vibration-assisted CNC milling process was carried out in the frequency range [700 Hz, 1000 Hz]. The best surface roughness of the specimen was achieved at a frequency of 900 Hz with a Ra of 0.287 µm. This demonstrates that the proposed XY mechanism is an effective structure for generating a non-resonant frequency source for vibration-assisted machining. Full article
(This article belongs to the Special Issue Optimization and Design of Compliant Mechanisms)
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30 pages, 12505 KiB  
Article
Analysis and Optimization of a Novel Compact Compliant 2-DOF Positioner for Positioning to Assess Bio-Specimen Characteristics
by Minh Phung Dang, Hieu Giang Le, Chi Thien Tran, Vo Duc Trieu Nguyen and Ngoc Le Chau
Machines 2024, 12(6), 421; https://doi.org/10.3390/machines12060421 - 19 Jun 2024
Cited by 2 | Viewed by 715
Abstract
A novel compact 2-DOF compliant positioner is developed for the purpose of achieving good characteristics such as high natural frequency, high displacement amplification ratio, good linear motion, and compact structure based on its symmetrical structure. To be specific, the developed stage is proposed [...] Read more.
A novel compact 2-DOF compliant positioner is developed for the purpose of achieving good characteristics such as high natural frequency, high displacement amplification ratio, good linear motion, and compact structure based on its symmetrical structure. To be specific, the developed stage is proposed according to an advanced six-lever displacement amplifier arranged at an inclination angle of the rigid bar utilizing right circular hinges and a parallel guiding mechanism with integrated flexure leaf hinges to attain the above-mentioned characteristics and reduce the decoupling mobility error. First, to quickly assess the initial quality response, an integration method of kinetostatic analysis, the Lagrange method, and finite element analysis was applied to evaluate and verify the quality characteristic of the stage. The experimental result showed that the error between the analytical method and the FEA method was 1.3%, which was relatively small and reliable for quickly assessing the primary quality response of the proposed positioner. Next, to boost the important output characteristics of the developed positioner, the integration approach of the response surface method and NSGA-II algorithm was utilized to find the optimal design variables. Finally, a prototype was manufactured based on the CNC milling method to validate the experimental and FEA analysis results. The attained results show that the optimal results of safety factor and output displacement were 2.4025 and 248.9 µm. Moreover, the FEA verification results were 2.4989 and 242.16 µm, with errors for safety factor and output displacement between the optimal result and the FEA result of 3.86% and 2.78%, respectively. In addition, the simulation and experimental results of the first natural frequency were 371.83 Hz and 329.59 Hz, respectively, and the error between the FEA result and experimental result for the first natural frequency was 11.36%. Furthermore, the achieved results show that the relationship between input displacement and output displacement of the experimental result and the FEA result of the developed structure achieved a good linear connection. These results suggest that the proposed positioner will be a potential structure employed in precise positioning systems and nanoindentation testing positioning systems for checking bio-specimens’ behaviors. Full article
(This article belongs to the Special Issue Optimization and Design of Compliant Mechanisms)
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13 pages, 5419 KiB  
Article
Design and Test of a 2-DOF Compliant Positioning Stage with Antagonistic Piezoelectric Actuation
by Haitao Wu, Hui Tang and Yanding Qin
Machines 2024, 12(6), 420; https://doi.org/10.3390/machines12060420 - 19 Jun 2024
Cited by 3 | Viewed by 867
Abstract
This paper designs a two-degrees-of-freedom (DOF) compliant positioning stage with antagonistic piezoelectric actuation. Two pairs of PEAs are arranged in an antagonistic configuration to generate reciprocating motions. Flexure mechanisms are intentionally adopted to construct the fixtures for PEAs, whose elastic deformations can help [...] Read more.
This paper designs a two-degrees-of-freedom (DOF) compliant positioning stage with antagonistic piezoelectric actuation. Two pairs of PEAs are arranged in an antagonistic configuration to generate reciprocating motions. Flexure mechanisms are intentionally adopted to construct the fixtures for PEAs, whose elastic deformations can help to reduce the stress concentration on the PEA caused by the extension of the PEA in the other direction. Subsequently, the parameter and performance of the 2-DOF compliant positioning stage is optimized and verified by finite element analysis. Finally, a prototype is fabricated and tested. The experimental results show that the developed positioning stage achieves a working stroke of 28.27 μm × 27.62 μm. Motion resolutions of both axes are 8 nm and natural frequencies in the working directions are up to 2018 Hz, which is promising for high-precision positioning control. Full article
(This article belongs to the Special Issue Optimization and Design of Compliant Mechanisms)
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16 pages, 6124 KiB  
Article
Structural Optimization of Scarfing Machine with Acceleration Profile and Multi-Objective Genetic Algorithm Approach
by Sangbin Lee, Yoonjae Lee, Byeonghui Park and Changwoo Lee
Machines 2024, 12(6), 398; https://doi.org/10.3390/machines12060398 - 12 Jun 2024
Viewed by 936
Abstract
Scarfing is a type of flame treatment used to improve the quality of metal generated during steelmaking. It employs the principles of gas cutting to remove impurities and defects. Due to the high-temperature conditions and the need for uniform metal treatment, mechanical scarfing [...] Read more.
Scarfing is a type of flame treatment used to improve the quality of metal generated during steelmaking. It employs the principles of gas cutting to remove impurities and defects. Due to the high-temperature conditions and the need for uniform metal treatment, mechanical scarfing performed via a frame is preferred over manual hand scarfing. To achieve stable mechanical scarfing, a properly designed frame is essential. Generally, while using more material can create stable equipment, it also increases costs. Therefore, this study proposed a design method that selects an acceleration profile to minimize the shock on the frame during scarfing equipment operation while using a multi-objective genetic algorithm to minimize weight and maximize rigidity. Because modifying existing scarfing equipment based on the optimization results would incur additional costs and time, pre-optimizing through simulation before equipment fabrication is crucial. Optimization was achieved via the dimensional optimization of the existing frame equipment. As a result, the weight of each part and the deformation decreased by an average of 17.05 kg and 3.93%, respectively. Full article
(This article belongs to the Special Issue Optimization and Design of Compliant Mechanisms)
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11 pages, 42274 KiB  
Article
Ultra-Compact Orthoplanar Spring via Euler-Spiral Flexures
by Jacob Sutton, Collin Ynchausti, Kyle Dahl, Spencer P. Magleby, Larry L. Howell and Brian D. Jensen
Machines 2024, 12(4), 273; https://doi.org/10.3390/machines12040273 - 18 Apr 2024
Cited by 1 | Viewed by 1818
Abstract
Orthoplanar springs are single-component compliant mechanisms that can be fabricated from sheet material and undergo deflection orthogonal to the plane of the mechanism. They are useful in applications where spatial constraints are significant. An Euler spiral is a curve whose curvature is linearly [...] Read more.
Orthoplanar springs are single-component compliant mechanisms that can be fabricated from sheet material and undergo deflection orthogonal to the plane of the mechanism. They are useful in applications where spatial constraints are significant. An Euler spiral is a curve whose curvature is linearly proportional to the arc length allowing for the curve to assume a flat position under a load. In this work, orthoplanar spring and Euler-spiral concepts are synthesized to create a single-component spring mechanism that lies flat under a load. Where traditional planar springs under a load will take on an out-of-plane contour, the Euler-spiral orthoplanar spring lies completely flat under a load. The relationship between the load needed to flatten the orthoplanar Euler-spiral spring and its physical geometry is examined. A use case where the Euler-spiral orthoplanar spring is utilized as a deployment mechanism for a mid-flight emerging antenna on the surface of a flight body is presented. Full article
(This article belongs to the Special Issue Optimization and Design of Compliant Mechanisms)
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21 pages, 2921 KiB  
Article
Topology Optimization of Geometrically Nonlinear Structures Based on a Self-Adaptive Material Interpolation Scheme
by Junwen Liang, Xianmin Zhang, Benliang Zhu, Rixin Wang, Chaoyu Cui and Hongchuan Zhang
Machines 2023, 11(12), 1047; https://doi.org/10.3390/machines11121047 - 24 Nov 2023
Cited by 2 | Viewed by 1467
Abstract
In this paper, a simple and effective self-adaptive material interpolation scheme is proposed to solve the numerical instability problem, which may occur in topology optimization considering geometrical nonlinearity when using density-based method. The primary concept of the proposed method revolves around enhancing the [...] Read more.
In this paper, a simple and effective self-adaptive material interpolation scheme is proposed to solve the numerical instability problem, which may occur in topology optimization considering geometrical nonlinearity when using density-based method. The primary concept of the proposed method revolves around enhancing the deformation resistance of minimum-density or intermediatedensity elements, thus avoiding numerical instability due to excessive distortion of these elements. The proposed self-adaptive material interpolation scheme is based on the power law method, and the stiffness of minimum-density or intermediate-density elements can be adjusted by a single parameter, α. During the optimization process, the parameter α will be changed according to an adaptive adjustment strategy to ensure that elements within the design domain are not excessively distorted, while the mechanical behavior of the structure can be approximated with acceptable accuracy. Numerical examples of minimizing compliance and maximizing displacement of structure are given to prove the validity of the proposed self-adaptive material interpolation scheme. Full article
(This article belongs to the Special Issue Optimization and Design of Compliant Mechanisms)
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