This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way based on D'alembert's principle. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo-static model. The superiority of the proposed method is that when it is used for the dynamic modeling of compliant mechanisms, the traditional dynamic modeling procedures, such as calculation of the elastic and kinetic energies as well as using Lagrange's equation, are avoided and the dynamic modeling is converted to a statics-similar problem. Comparison of the proposed method with an elastic-beam-based model in previous literature and finite element analysis for an exemplary XY precision positioning stage reveals its high accuracy and easy operation.
Issue Section:
Research Papers
Keywords:
Compliant mechanisms
References
1.
Howell
, L. L.
, 2001
, Compliant Mechanisms
, Wiley
, New York.2.
Howell
, L. L.
, and Midha
, A.
, 1994
, “A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots
,” ASME J. Mech. Des.
, 116
(1
), pp. 280
–290
.3.
Su
, H. J.
, 2009
, “A Pseudo-Rigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads
,” ASME J. Mech. Rob.
, 1
(2
), p. 021008
.4.
Midha
, A.
, Bapat
, S. G.
, Mavanthoor
, A.
, and Chinta
, V.
, 2015
, “Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model Concept
,” ASME J. Mech. Rob.
, 7
(3
), p. 031007
.5.
Calogero
, J.
, Frecker
, M.
, Hasnain
, Z.
, and Hubbard
, J. E.
, 2018
, “Tuning of a Rigid-Body Dynamics Model of a Flapping Wing Structure With Compliant Joints
,” ASME J. Mech. Rob.
, 10
(1
), p. 011007
.6.
Awtar
, S.
, and Sen
, S.
, 2010
, “A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation
,” ASME J. Mech. Des.
, 132
(8
), p. 081008
.7.
Chen
, G.
, and Bai
, R.
, 2016
, “Modeling Large Spatial Deflections of Slender Bisymmetric Beams in Compliant Mechanisms Using Chained Spatial-Beam Constraint Model
,” ASME J. Mech. Rob.
, 8
(4
), p. 041011
.8.
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
.9.
Kurita
, Y.
, Sugihara
, F.
, Ueda
, J.
, and Ogasawara
, T.
, 2012
, “Piezoelectric Tweezer-Type End Effector With Force-and Displacement-Sensing Capability
,” IEEE/ASME Trans. Mechatronics
, 17
(6
), pp. 1039
–1048
.10.
Ling
, M.
, Cao
, J.
, Zeng
, M.
, Lin
, J.
, and Inman
, D. J.
, 2016
, “Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms
,” Smart Mater. Struct.
, 25
(7
), pp. 75022
–75032
.11.
Lobontiu
, N.
, and Garcia
, E.
, 2003
, “Analytical Model of Displacement Amplification and Stiffness Optimization for a Class of Flexure-Based Compliant Mechanisms
,” Comput. Struct.
, 81
(32
), pp. 2797
–2810
.12.
Yong
, Y. K.
, and Leang
, K. K.
, 2016
, “Mechanical Design of High-Speed Nanopositioning Systems
,” Nanopositioning Technologies
, Springer International Publishing
, New York, pp. 61
–121
.13.
Li
, Y.
, and Xu
, Q.
, 2010
, “Development and Assessment of a Novel Decoupled XY Parallel Micropositioning Platform
,” IEEE/ASME Trans. Mechatronics
, 15
(1
), pp. 125
–135
.14.
Koseki
, Y.
, Tanikawa
, T.
, Koyachi
, N.
, and Arai
, T.
, 2002
, “Kinematic Analysis of a Translational 3-DOF Micro-Parallel Mechanism Using the Matrix Method
,” Adv. Rob.
, 16
(3
), pp. 251
–264
.15.
Choi
, 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
.16.
Lobontiu
, N.
, 2014
, “Compliance-Based Matrix Method for Modeling the Quasi-Static Response of Planar Serial Flexure-Hinge Mechanisms
,” Precis. Eng.
, 38
(3
), pp. 639
–650
.17.
Jiang
, Y.
, Li
, T. M.
, and Wang
, L. P.
, 2015
, “Stiffness Modeling of Compliant Parallel Mechanisms and Applications in the Performance Analysis of a Decoupled Parallel Compliant Stage
,” Rev. Sci. Instrum.
, 86
(9
), p. 095109
.18.
Yu
, Y. Q.
, Howell
, L. L.
, Lusk
, C.
, Yue
, Y.
, and He
, M. G.
, 2005
, “Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model
,” ASME J. Mech. Des.
, 127
(4
), pp. 760
–765
.19.
Guo
, Z.
, Tian
, Y.
, Liu
, C.
, Wang
, F.
, Liu
, X.
, Shirinzadeh
, B.
, and Zhang
, D.
, 2015
, “Design and Control Methodology of a 3-DOF Flexure-Based Mechanism for Micro/Nano-Positioning
,” Rob. Comput. Integr. Manuf.
, 32
, pp. 93
–105
.20.
Chen
, W.
, Qu
, J.
, Chen
, W.
, and Zhang
, J.
, 2017
, “A Compliant Dual-Axis Gripper With Integrated Position and Force Sensing
,” Mechatronics
, 47
, pp. 105
–115
.21.
Xu
, Q.
, 2013
, “Design, Testing and Precision Control of a Novel Long-Stroke Flexure Micropositioning System
,” Mech. Mach. Theory
, 70
, pp. 209
–224
.22.
Wang
, F.
, Liang
, C.
, Tian
, Y.
, Zhao
, X.
, and Zhang
, D.
, 2015
, “Design of a Piezoelectric-Actuated Microgripper With a Three-Stage Flexure-Based Amplification
,” IEEE/ASME Trans. Mechatronics
, 20
(5
), pp. 2205
–2213
.23.
Li
, Y.
, and Wu
, Z.
, 2016
, “Design, Analysis and Simulation of a Novel 3-DOF Translational Micromanipulator Based on the PRB Model
,” Mech. Mach. Theory
, 100
, pp. 235
–258
.24.
Tang
, H.
, and Li
, Y.
, 2014
, “Development and Active Disturbance Rejection Control of a Compliant Micro-/Nanopositioning Piezostage With Dual Mode
,” IEEE Trans. Ind. Electron.
, 61
(3
), pp. 1475
–1492
.25.
Zhu
, X.
, Xu
, X.
, Wen
, Z.
, Ren
, J.
, and Liu
, P.
, 2015
, “A Novel Flexure-Based Vertical Nanopositioning Stage With Large Travel Range
,” Rev. Sci. Instrum.
, 86
(10
), p. 105112
.26.
Zhu
, W. L.
, Zhu
, Z.
, Guo
, P.
, and Ju
, B. F.
, 2018
, “A Novel Hybrid Actuation Mechanism Based XY Nanopositioning Stage With Totally Decoupled Kinematics
,” Mech. Syst. Signal Process.
, 99
, pp. 747
–759
.27.
Polit
, S.
, and Dong
, J.
, 2011
, “Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing
,” IEEE/ASME Trans. Mechatronics
, 16
(4
), pp. 724
–733
.28.
Liu
, P.
, Yan
, P.
, and Zhang
, Z.
, 2015
, “Design and Analysis of an X–Y Parallel Nanopositioner Supporting Large-Stroke Servomechanism
,” Proc. Inst. Mech. Eng., Part C
, 229
(2
), pp. 364
–376
.29.
Ryu
, J. W.
, Lee
, S. Q.
, Gweon
, D. G.
, and Moon
, K. S.
, 1999
, “Inverse Kinematic Modeling of a Coupled Flexure Hinge Mechanism
,” Mechatronics
, 9
(6
), pp. 657
–674
.30.
Choi
, S. B.
, Han
, S. S.
, Han
, Y. M.
, and Thompson
, B. S.
, 2007
, “A Magnification Device for Precision Mechanisms Featuring Piezoactuators and Flexure Hinges: Design and Experimental Validation
,” Mech. Mach. Theory
, 42
(9
), pp. 1184
–1198
.31.
Kim
, H.
, and Gweon
, D. G.
, 2012
, “Development of a Compact and Long Range XYθz Nano-Positioning Stage
,” Rev. Sci. Instrum.
, 83
(8
), p. 085102
.32.
Lai
, L. J.
, and Zhu
, Z. N.
, 2017
, “Design, Modeling and Testing of a Novel Flexure-Based Displacement Amplification Mechanism
,” Sens. Actuators A
, 266
, pp. 122
–129
.33.
Lee
, H. J.
, Kim
, H. C.
, Kim
, H. Y.
, and Gweon
, D. G.
, 2013
, “Optimal Design and Experiment of a Three-Axis out-of-Plane Nano Positioning Stage Using a New Compact Bridge-Type Displacement Amplifier
,” Rev. Sci. Instrum.
, 84
(11
), p. 115103
.34.
Ling
, M.
, Cao
, J.
, Jiang
, Z.
, and Lin
, J.
, 2017
, “A Semi-Analytical Modeling Method for the Static and Dynamic Analysis of Complex Compliant Mechanism
,” Precis. Eng.
, 52
, pp. 64–72.35.
Rösner
, M.
, Lammering
, R.
, and Friedrich
, R.
, 2015
, “Dynamic Modeling and Model Order Reduction of Compliant Mechanisms
,” Precis. Eng.
, 42
, pp. 85
–92
.36.
Shen
, Y.
, Chen
, X.
, Jiang
, W.
, and Luo
, X.
, 2014
, “Spatial Force-Based Non-Prismatic Beam Element for Static and Dynamic Analyses of Circular Flexure Hinges in Compliant Mechanisms
,” Precis. Eng.
, 38
(2
), pp. 311
–320
.37.
Pereira
, E.
, Aphale
, S. S.
, Feliu
, V.
, and Moheimani
, S. R.
, 2011
, “Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator
,” IEEE/ASME Trans. Mechatronics
, 16
(2
), pp. 232
–240
.38.
Lobontiu
, N.
, Paine
, J. S.
, Garcia
, E.
, and Goldfarb
, M.
, 2001
, “Corner-Filleted Flexure Finges
,” ASME J. Mech. Des.
, 123
(3
), pp. 346
–352
.39.
Yong
, Y. K.
, Lu
, T. F.
, and Handley
, D. C.
, 2008
, “Review of Circular Flexure Hinge Design Equations and Derivation of Empirical Formulations
,” Precis. Eng.
, 32
(2
), pp. 63
–70
.40.
Wang
, H.
, and Zhang
, X.
, 2008
, “Input Coupling Analysis and Optimal Design of a 3-DOF Compliant Micro-Positioning Stage
,” Mech. Mach. Theory
, 43
(4
), pp. 400
–410
.41.
Cao
, L.
, Dolovich
, A. T.
, and Zhang
, W. C.
, 2015
, “Hybrid Compliant Mechanism Design Using a Mixed Mesh of Flexure Hinge Elements and Beam Elements Through Topology Optimization
,” ASME J. Mech. Des.
, 137
(9
), p. 092303
.42.
Banerjee
, J. R.
, and Williams
, F. W.
, 1985
, “Exact Bernoulli–Euler Dynamic Stiffness Matrix for a Range of Tapered Beams
,” Int. J. Numer. Methods Eng.
, 21
(12
), pp. 2289
–2302
.43.
Ling
, M.
, Cao
, J.
, Howell
, L. L.
, and Zeng, M., 2018
, “Kinetostatic Modeling of Complex Compliant Mechanisms With Serial-Parallel Substructures: A Semi-Analytical Matrix Displacement Method
,” Mech. Mach. Theory
, 125
, pp. 169–184.44.
Ling
, M.
, Cao
, J.
, Jiang
, Z.
, and Lin
, J.
, 2017
, “Modular Kinematics and Statics Modeling for Precision Positioning Stage
,” Mech. Mach. Theory
, 107
, pp. 274
–282
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