Abstract
A compliant toggle-linkage mechanism with the dual functions of displacement amplification and reduction is proposed. A series of compliant amplification mechanisms are examined by combining multi-group flexure toggle linkages, showcasing a flexible design with modular flexure toggle-linkage building blocks. A compliant toggle-lever mechanism is then investigated in detail as a displacement amplifier and a reducer for piezoelectric actuators by exchanging the input and output ports. Its kinetostatic and dynamic performances are captured using an improved dynamic stiffness matrix modeling procedure with high prediction accuracy and robustness, which shifts the end nodes of all adjacent flexure hinge/beam members to be coincident in order to deal with the irregular connection of building blocks. It is interestingly observed that the output displacements with forward and reverse motion directions can be simultaneously achieved with such a compliant toggle-lever mechanism by changing the structural parameters. Finally, the relationship of displacement amplification and reduction ratios between the input and output ports is clarified and discussed by comparing the results among the dynamic stiffness matrix model, finite element simulation, and experimental testing.
References
1.
Howell
, L. L.
, 2013
, “Compliant Mechanisms
,” 21st Century Kinematics: The 2012 NSF Workshop
, Springer London
, London
.2.
Turkkan
, O. A.
, and Su
, H. J.
, 2017
, “A General and Efficient Multiple Segment Method for Kinetostatic Analysis of Planar Compliant Mechanisms
,” Mech. Mach. Theory
, 112
, pp. 205
–217
. 3.
Platl
, V.
, and Zentner
, L.
, 2023
, “An Analytical Approach for Calculating the First Natural Frequency of Flexure Hinges With Variable Cross-Sections for Compliant Mechanisms
,” IFToMM World Congress on Mechanism and Machine Science
, Tokyo, Japan
, Nov. 5–9
, Springer Nature Switzerland
, Cham
, pp. 491
–501
.4.
Wang
, R.
, Li
, X.
, and Huang
, H.
, 2023
, “Design of Thick Panels Origami-Inspired Flexible Grasper With Anti-Interference Ability
,” Mech. Mach. Theory
, 189
, p. 105431
. 5.
Villalba
, D.
, Gonçalves
, M.
, Dias-de-Oliveira
, J.
, Andrade-Campos
, A.
, and Valente
, R.
, 2023
, “IGA-Based Topology Optimization in the Design of Stress-Constrained Compliant Mechanisms
,” Struct. Multidiscip. Optim.
, 66
(12
), p. 244
. 6.
Hao
, G. B.
, 2015
, “Extended Nonlinear Analytical Models of Compliant Parallelogram Mechanisms: Third-Order Models
,” Trans. Can. Soc. Mech. Eng.
, 39
(1
), pp. 71
–83
. 7.
Serafino
, S.
, Fanghella
, P.
, and Verotti
, M.
, 2023
, “Design and Testing of High-Accuracy Curved Cross-Axis Flexural Pivots With Cable-Driven Actuation
,” Mech. Mach. Theory
, 189
, p. 105418
. 8.
Li
, Y.
, Cao
, P.
, Zhang
, P.
, Yang
, H.
, Zhu
, X.
, and Guo
, R.
, 2023
, “Design and Development of a Hair-Like Sensor With Bridge-Type Flexible Amplification Mechanisms
,” Sensors
, 23
(17
), p. 7354
. 9.
Lin
, J.
, Qi
, C.
, Gao
, F.
, Yue
, Y.
, Hu
, Y.
, and Wei
, B.
, 2023
, “Modeling and Verification for a Three-Degree-of-Freedom Flexure-Based Planar Parallel Micro Manipulator
,” ASME J. Mech. Rob.
, 15
(4
), p. 041006
. 10.
Zhang
, Y.
, Song
, Y.
, Lu
, F.
, Zhang
, D.
, Yang
, L.
, Cui
, T.
, He
, X.
, and Zhang
, K.
, 2023
, “Design and Experiment of Greenhouse Self-Balancing Mobile Robot Based on PR Joint Sensor
,” Agriculture
, 13
(10
), p. 2040
. 11.
Ding
, B. X.
, Li
, X.
, Li
, C. L.
, Li
, Y. M.
, and Chen
, S. C.
, 2023
, “A Survey on the Mechanical Design for Piezo-Actuated Compliant Micro-Positioning Stages
,” Rev. Sci. Instrum.
, 94
(10
), p. 101502
. 12.
Iqbal
, S.
, and Malik
, A.
, 2019
, “A Review on MEMS Based Micro Displacement Amplification Mechanisms
,” Sens. Actuators, A
, 300
, p. 111666
. 13.
Kanchan
, M.
, Santhya
, M.
, Bhat
, R.
, and Naik
, N.
, 2023
, “Application of Modeling and Control Approaches of Piezoelectric Actuators: A Review
,” Technologies
, 11
(6
), p. 155
. 14.
Teoh
, C. Y.
, Wong
, J. K.
, Ko
, Y. H.
, Hamid
, M. N. A.
, Ooi
, L. E.
, and Tan
, W. H.
, 2023
, “Design of Two-Stage Force Amplification Frame for Piezoelectric Energy Harvester
,” J. Mech. Eng.
, 20
(3
), pp. 1823
–5514
. 15.
Wang
, K.
, Huang
, P.
, Liu
, Q.
, Zhu
, L.
, and Zhu
, Z.
, 2023
, “Generalized Element-Node Complete Model and Its Implementation for the Optimal Design of a Piezo-Actuated Compliant Amplifier
,” Rev. Sci. Instrum.
, 94
(8
), p. 085004
. 16.
Yoshikawa
, K.
, and Murata
, Y.
, 2023
, “Improvement of Self-Shape Measurement Accuracy in a Self-Sensing Flexible Array Probe
,” IEEE Trans. Electron. Inform. Syst.
, 143
(9
), pp. 854
–861
. 17.
HaLevy
, O.
, Melech
, N.
, Lulinsky
, S.
, and Krylov
, S.
, 2023
, “Compliant Parallel Motion Linkage Amplification Mechanism for Resonant Force/Acceleration Sensing
,” IEEE Sens. J.
, 23
(16
), pp. 18000
–18012
. 18.
Kandharkar
, S. R.
, Pardeshi
, S. S.
, Soman
, R.
, Patange
, A. D.
, and Ostachowicz
, W.
, 2023
, “Development of Distributed Compliant Mechanism for Two Distinct Applications: Displacement Amplifying and Object Holding Mechanism
,” Eng. Res. Express
, 5
(2
), p. 025050
. 19.
Xie
, W. L.
, and Gan
, J. Q.
, 2023
, “Design of a 2-DOF XZ Precision Positioning Platform Using Novel Z-Shaped Flexure Hinges
,” International Conference on Manipulation Automation and Robotics at Small Scales (MARSS)
, IEEE
, pp. 1
–7
.20.
Cui
, F. N.
, Li
, Y. M.
, and Qian
, J. N.
, 2021
, “Development of a 3-DOF Flexible Micro-Motion Platform Based on a New Compound Lever Amplification Mechanism
,” Micromachines
, 12
(6
), p. 686
. 21.
Trimzi
, M. A.
, Ham
, Y. B.
, An
, B. C.
, Choi
, Y. M.
, Park
, J. H.
, and Yun
, S. N.
, 2020
, “Development of a Piezo-Driven Liquid Jet Dispenser With Hinge-Lever Amplification Mechanism
,” Micromachines
, 11
(2
), p. 117
. 22.
Fujimura
, Y.
, Tsukamoto
, T.
, and Tanaka
, S.
, 2018
, “Piezoelectric Moonie-Type Resonant Microactuator
,” Electron. Commun. Jpn.
, 101
(3
), pp. 3
–10
. 23.
Uyen
, T. M. T.
, Minh
, P. S.
, Nguyen
, V. T.
, Do
, T. T.
, Nguyen Le Dang
, H.
, and Nguyen
, V. T. T.
, 2023
, “Amplification Ratio of a Recycled Plastics-Compliant Mechanism Flexure Hinge
,” Appl. Sci.
, 13
(23
), p. 12825
. 24.
Choi
, V. K. B.
, Lee
, J. J.
, Kim
, G. H.
, Lim
, H. J.
, and Kwon
, S. G.
, 2018
, “Amplification Ratio Analysis of a Bridge-Type Mechanical Amplification Mechanism Based on a Fully Compliant Model
,” Mech. Mach. Theory
, 121
, pp. 355
–372
. 25.
Wang
, J.
, Jing
, Z. J.
, Xie
, Z. L.
, Ning
, Z. Q.
, and Qi
, B.
, 2023
, “Analysis and Optimization of Dynamic and Static Characteristics of the Compliant-Amplifying Mechanisms
,” Micromachines
, 14
(8
), p. 1502
. 26.
Li
, P. X.
, Zhu
, H. L.
, and Lai
, L. J.
, 2022
, “An Improved Dynamic Model and Matrix Displacement Model for Distributed-Compliance Bridge-Type Amplification Mechanism
,” Actuators
, 11
(12
), p. 368
. 27.
Ling
, M. X.
, Zhang
, X. M.
, and Cao
, J. Y.
, 2022
, “Extended Dynamic Stiffness Model for Analyzing Flexure-Hinge Mechanisms With Lumped Compliance
,” ASME J. Mech. Des.
, 144
(1
), p. 013304
. 28.
Wang
, F. G.
, Huo
, Z. C.
, Liang
, C. M.
, Shi
, B. C.
, Tian
, Y. L.
, Zhao
, X. Y.
, and Zhang
, D. W.
, 2018
, “A Novel Actuator-Internal Micro/Nano Positioning Stage With an Arch-Shape Bridge-Type Amplifier
,” IEEE Trans. Ind. Electron.
, 66
(12
), pp. 9161
–9172
. 29.
Zhu
, J. X.
, Hao
, G. B.
, Liu
, T. H.
, and Li
, H. Y.
, 2023
, “Design of an Over-Constraint Based Nearly-Constant Amplification Ratio Compliant Mechanism
,” Mech. Mach. Theory
, 186
, p. 105347
. 30.
Zhang
, X. Y.
, Li
, W. P.
, Li
, S.
, and Zheng
, Y.
, 2023
, “Design, Modeling, and Analysis of a Novel XY Micro-Displacement Scanning Stage With an Elliptical Compliant Restraint Mechanism
,” Phys. Scr.
, 98
(11
), p. 115505
. 31.
Huynh
, N. T.
, Nguyen
, M. H.
, and Dinh
, L. C. K
., 2023
, “Design Optimization of a Novel Symmetrical Differential Lever Displacement Magnification Compliant Mechanism
.”32.
Zhang
, T.
, Xiong
, L. G.
, Pan
, Z. Q.
, Zhang
, C. H.
, Qu
, W.
, Wang
, Y. H.
, and Yang
, C. M.
, 2023
, “Design and Analysis of XY Large Travel Micro Stage Based on Secondary Symmetric Lever Amplification
,” Micromachines
, 14
(9
), p. 1805
. 33.
Dong
, G.
, Sun
, S. W.
, Kong
, X. Y.
, Chen
, X. Y.
, Yin
, T. H.
, Wu
, N. S.
, Huang
, P. N.
, and Wang
, Z. X.
, 2024
, “Design and Analysis of a New Micro-Positioning Platform for Ceramic Material Testing
,” Microsyst. Technol.
, 30
(1
), pp. 55
–64
. 34.
Lavanya
, S. B.
, Jayanth
, G. R.
, and Mohanty
, A. K.
, 2023
, “Optimal Design of Bridge Amplifiers for Large-Range Linear Characteristics
,” IFToMM World Congress on Mechanism and Machine Science
, Tokyo, Japan
, Nov. 5–9
, pp. 721
–730
.35.
Zhang
, X.
, Kang
, X.
, and Li
, B.
, 2023
, “Development and Evaluation of a Light-Weight Flexure-Based Lockable Joint for Morphing Wings
,” Aerosp. Sci. Technol.
, 143
, p. 108720
. 36.
Kiziroglou
, M. E.
, Temelkuran
, B.
, Yeatman
, E. M.
, and Yang
, G. Z.
, 2020
, “Micro Motion Amplification–A Review
,” IEEE Access.
, 8
, pp. 64037
–64055
. 37.
Wang
, M. Z.
, Zhang
, C.
, Liu
, S. T.
, and Wang
, X. L.
, 2023
, “Modeling and Analysis of a Conical Bridge-Type Displacement Amplification Mechanism Using the Non-Uniform Rational B-Spline Curve
,” Materials
, 16
(18
), p. 6162
. 38.
Xu
, D. M.
, Yang
, F.
, Yu
, S. M.
, Xu
, C.
, Liu
, X. L.
, Zhao
, Z. W.
, Zhang
, X. H.
, Li
, S. T.
, Yang
, H. X.
, and Lu
, Q.
, 2023
, “A Three-Stage Amplification Piezoelectric-Actuated Micro-Gripper With Adjustable Output Displacement: Design, Modeling, and Experimental Evaluation
,” Smart Mater. Struct.
, 32
(9
), p. 095033
. 39.
Sebald
, G.
, Tung
, N. T.
, Taxil
, G.
, Ducharne
, B.
, Chavez
, J.
, Ono
, T.
, Kuwano
, H.
, Lefeuvre
, E.
, and Lallart
, M.
, 2023
, “Piezoelectric Small Scale Generator: Towards Near-Joule Output Energy Generation
,” Smart Mater. Struct.
, 32
(8
), p. 085009
. 40.
Yu
, S. M.
, Liang
, J. Y.
, Yang
, F.
, Wang
, H. T.
, Liu
, X. L.
, Xu
, C.
, Wang
, Z.
, and Xu
, D. M.
, 2023
, “A Novel Inchworm Piezoelectric Actuator Using Two-Stage Amplification Mechanism With High Speed: Design, Modeling, and Experimental Evaluation
,” Smart Mater. Struct.
, 32
(5
), p. 055020
. 41.
Yuan
, X. Q.
, Liu
, Y. X.
, Zou
, H.
, Ji
, J. J.
, Zhou
, T.
, and Wang
, W. D.
, 2022
, “Design and Analysis of a 2-D Piezoelectric Platform Based on Three-Stage Amplification and L-Shaped Guiding
,” IEEE Trans. Instrum. Meas.
, 71
, pp. 1
–12
. 42.
Zhou
, K. Y.
, Liu
, P. B.
, Lu
, S. S.
, and Yan
, P.
, 2022
, “Design and Modeling of a Piezo-Driven Three-Dimensional Bridge-Type Amplification Mechanism With Input/Output Guiding Constraint
,” Rev. Sci. Instrum.
, 93
(2
), p. 025005
. 43.
Chang
, W. T.
, Lee
, W. I.
, and Hsu
, K. L.
, 2021
, “Analysis and Experimental Verification of Mechanical Errors in Nine-Link Type Double-Toggle Mold/Die Clamping Mechanisms
,” Appl. Sci.
, 11
(2
), p. 832
. 44.
Park
, S.
, Bae
, J.
, Jeon
, Y.
, Chu
, K.
, Bak
, J.
, Seo
, T.
, and Kim
, J.
, 2018
, “Optimal Design of Toggle-Linkage Mechanism for Clamping Applications
,” Mech. Mach. Theory
, 120
, pp. 203
–212
. 45.
Huang
, M. S.
, Lin
, T. Y.
, and Fung
, R. F.
, 2011
, “Key Design Parameters and Optimal Design of a Five-Point Double-Toggle Clamping Mechanism
,” Appl. Math. Model.
, 35
(9
), pp. 4304
–4320
. 46.
Lin
, W. Y.
, and Hsiao
, K. M.
, 2003
, “Investigation of the Friction Effect at Pin Joints for the Five-Point Double-Toggle Clamping Mechanisms of Injection Molding Machines
,” Int. J. Mech. Sci.
, 45
(11
), pp. 1913
–1927
. 47.
Gao
, J. Z.
, Zhao
, S. D.
, Li
, J. X.
, Jiang
, F.
, Du
, W.
, Zheng
, Z. H.
, and Feng
, Z. Y.
, 2022
, “A Novel Main Drive System for the Servo Press: Combination of Integrated Motor and Symmetrically Toggle Booster Mechanism
,” CIRP J. Manuf. Sci. Technol.
, 37
, pp. 596
–612
. 48.
Jencks
, C. L.
, and Murphy
, F. H.
, 1964
, “Electric Circuit Breaker Including Stop Means for Limiting Movement of a Toggle Linkage
,” U.S. Patent No. 3158717.49.
Nagai
, S.
, Yumiba
, H.
, and Saitoh
, A.
, 2002
, “Electric Clamp Apparatus
,” U.S. Patent No. 6354580.50.
Bakermans
, J. C. W.
, 1977
, “Hand Tool Having Double Toggle Linkage
,” U.S. Patent No. 4005516.51.
Ling
, M. X.
, Cao
, J. Y.
, and Pehrson
, N.
, 2019
, “Kinetostatic and Dynamic Analyses of Planar Compliant Mechanisms Via a Two-Port Dynamic Stiffness Model
,” Precis. Eng.
, 57
, pp. 149
–161
. 52.
Abdalla
, M.
, Frecker
, M.
, Gürdal
, Z.
, Johnson
, T.
, and Lindner
, D. K.
, 2005
, “Design of a Piezoelectric Actuator and Compliant Mechanism Combination for Maximum Energy Efficiency
,” Smart Mater. Struct.
, 14
(6
), pp. 1421
–1430
. 53.
Tantanawat
, T.
, and Kota
, S.
, 2007
, “Design of Compliant Mechanisms for Minimizing Input Power in Dynamic Applications
,” ASME J. Mech. Des.
, 129
(10
), pp. 1064
–1075
. 54.
Chen
, F. X.
, Du
, Z. J.
, Yang
, M.
, Gao
, F. T.
, Dong
, W.
, and Zhang
, D.
, 2017
, “Design and Analysis of a Three-Dimensional Bridge-Type Mechanism Based on the Stiffness Distribution
,” Precis. Eng.
, 51
, pp. 48
–58
. 55.
Ling
, M. X.
, Zhou
, H.
, and Chen
, L. G.
, 2023
, “Dynamic Stiffness Matrix With Timoshenko Beam Theory and Linear Frequency Solution for Use in Compliant Mechanisms
,” ASME J. Mech. Rob.
, 15
(6
), p. 061002
. 56.
Ling
, M. X.
, Wu
, S. L.
, Luo
, Z. H.
, Chen
, L. G.
, and Huang
, T.
, 2023
, “An Electromechanical Dynamic Stiffness Matrix of Piezoelectric Stacks for Systematic Design of Micro/Nano Motion Actuators
,” Smart Mater. Struct.
, 32
(11
), p. 115012
. Copyright © 2025 by ASME
You do not currently have access to this content.
