This paper presents a synthesis method for the open path generation of a four-bar mechanism using the Haar wavelet. The synthesis method utilizes the wavelet transform and normalization to extract the wavelet output feature parameters (WOFP) of the open path. Analysis of the WOFP reveals a particular characteristic: for the same four-bar mechanism, not only do variations of the mechanism origin and angles and the proportional scaling of the linkage lengths have no influence on the details of the WOFP but the same holds true for the position of the point that generates the coupler curve. Based on this finding, a numerical atlas database comprises 192,596 groups of basic dimensional types was established and a method of matching recognition was proposed as well. According to the internal relationship of the wavelet characteristic dimension parameters (WCDP), the actual mechanism parameter values and position parameters of an objective four-bar mechanism can be calculated. Four examples are presented to verify the accuracy and practicality of the proposed theory.
Issue Section:
Mechanisms and Robotics
References
1.
Norton
, R. L.
, 1992
, Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines
. McGraw-Hill
, New York
.2.
Suh
, C. H.
, and Radcliffe
, C. W.
, 1967
, “Synthesis of Plane Linkage With Use of the Displacement Matrix
,” ASME J. Eng. Ind.
, 89
(2
), pp. 206
–214
.10.1115/1.36100293.
Tong
, S. H.
, and Chiang
, C. H.
, 1992
, “Syntheses of Planar and Spherical Four-Bar Path Generators by the Pole Method
,” Mech. Mach. Theory
, 27
(2
), pp. 143
–155
.10.1016/0094-114X(92)90004-24.
Ma
, O.
, and Angeles
, J.
, 1988
, “Performance Evaluation of Path-Generating Planar, Spherical and Spatial Four-Bar Linkages
,” Mech. Mach. Theory
, 23
(7
), pp. 257
–268
.10.1016/0094-114X(88)90017-15.
Cabrera
, J. A.
, Simon
, A.
, and Prado
, M.
, 2002
, “Optimal Synthesis of Mechanisms With Genetic Algorithms
,” Mech. Mach. Theory
, 37
(10
), pp. 1165
–1177
.10.1016/S0094-114X(02)00051-46.
Sanchez Marin
, F. T.
, and Gonzalez
, A. P.
, 2004
, “Open-Path Synthesis of Linkages Through Geometrical Adaptation
,” Mech. Mach. Theory
, 33
(9
), pp. 943
–955
.10.1016/j.mechmachtheory.2004.04.0027.
Smaili
, A.
, and Diab
, N.
, 2007
, “A New Approach to Shape Optimization for Closed Path Synthesis of Planar Mechanisms
,” ASME J. Mech. Des.
, 129
(9
), pp. 941
–948
.10.1115/1.27531648.
Hrones
, J. A.
, and Nelson
, G. L.
, 1951
, Analysis of the Four-Bar Linkage
, MIT Press and Wiley
, New York
.9.
Hoeltzel
, D. A.
, and Chieng
, W. H.
, 1990
, “Pattern Matching Synthesis as an Automated Approach to Mechanism Design
,” ASME J. Mech. Des.
, 112
(6
), pp. 190
–199
.10.1115/1.291259210.
Buskiewicz
, J.
, Starosta
, R.
, and Walczak
, T.
, 2009
, “On the Application of the Curve Curvature in Path Synthesis
,” Mech. Mach. Theory
, 44
(6
), pp. 1223
–1239
.10.1016/j.mechmachtheory.2008.08.00111.
Buskiewicz
, J.
, 2010
, “Use of Shape Invariants in Optimal Synthesis of Geared Five-Bar Linkage
,” Mech. Mach. Theory
, 45
(2
), pp. 273
–290
.10.1016/j.mechmachtheory.2009.09.00412.
Watanabe
, K.
, 1992
, “Application of Natural Equations to Synthesis of Curve Generating Mechanisms
,” Mech. Mach. Theory
, 27
(3
), pp. 261
–273
.10.1016/0094-114X(92)90016-B13.
Zhang
, C.
, Norton
, P. E. R. L.
, and Hammonds
, T.
, 1984
, “Optimization of Parameters for Specified Path Generation Using an Atlas of Coupler Curves of Geared Five-Bar Linkages
,” Mech. Mach. Theory
, 19
(6
), pp. 459
–466
.10.1016/0094-114X(84)90052-114.
Freudenstein
, F.
, 1959
, “Harmonic Analysis of Crank-and-Rocker Mechanisms With Application
,” ASME J. Mech. Des.
, 26
(1
), pp. 673
–675
.15.
Fanhang
, K.
, Midha
, A.
, and Bajaj
, A.
, 1988
, “Synthesis of Harmonic Motion Generating Linkages—Part II: Path and Motion Generation
,” ASME J. Mech. Des.
, 110
(1
), pp. 22
–27
.10.1115/1.325889916.
McGarva
, J.
, 1994
, “Rapid Search and Selection of Path Generating Mechanisms From a Library
,” Mech. Mach. Theory
, 29
(2
), pp. 223
–235
.10.1016/0094-114X(94)90032-917.
Ullah
, I.
, and Kota
, S.
, 1997
, “Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Method
,” ASME J. Mech. Des.
, 119
(4
), pp. 504
–510
.10.1115/1.282639618.
Yu
, H. Y.
, Tang
, D. W.
, and Wang
, Z. X.
, 2007
, “Study on a New Computer Path Synthesis Method of a Four-Bar Linkage
,” Mech. Mach. Theory
, 42
(4
), pp. 383
–392
.10.1016/j.mechmachtheory.2006.05.00319.
Mullineux
, G.
, 2011
, “Atlas of Spherical Four-Bar Mechanisms
,” Mech. Mach. Theory
, 46
(11
), pp. 1811
–1823
.10.1016/j.mechmachtheory.2011.06.00120.
Chu
, J. K.
, and Sun
, J. W.
, 2010
, “Numerical Atlas Method for Path Generation of Spherical Four-Bar Mechanism
,” Mech. Mach. Theory
, 45
(6
), pp. 867
–879
.10.1016/j.mechmachtheory.2009.12.00521.
Wu
, J.
, Ge
, Q. J.
, Gao
, F.
, and Guo
, W. Z.
, 2010
, “On the Extension of a Fourier Descriptor Based Method for Four-Bar Linkage Synthesis for Generation of Open and Closed Paths
,” ASME
Paper No. DETC2010-29028. 10.1115/DETC2010-2902822.
Wu
, J.
, Ge
, Q. J.
, and Gao
, F.
, 2009
, “An Efficient Method for Synthesizing Crank–Rocker Mechanisms for Generating Low Harmonic Curves
,” ASME
Paper No. DETC2009-87140. 10.1115/DETC2009-8714023.
Yue
, C.
, Su
, H. J.
, and Ge
, Q. J.
, 2012
, “A Hybrid Computer-Aided Linkage Design System for Tracing Open and Closed Planar Curves
,” Comput.-Aided Des.
, 44
(11
), pp. 1141
–1150
.10.1016/j.cad.2012.06.00424.
Wu
, X.
, Chu
, J. K.
, and Cao
, W. Q.
, 1998
, “Analysis of Output Function of 4-Bar Linkages Using Wavelet Transform
,” Mech. Sci. Technol.
, 17
(2
), pp. 180
–186
.25.
Wang
, C. Z.
, and Ji
, Y. B.
, 2004
, “Research on Applying Wavelet Analysis to Path Synthesis for Coupler Curves of Planar Four-Bar Linkages
,” Chin. J. Mech. Eng.
, 40
(8
), pp. 34
–39
.10.3901/JME.2004.08.03426.
Galán-Marín
, G.
, Alonso
, F. J.
, and Del Castillo
, J. M.
, 2009
, “Shape Optimization for Path Synthesis of Crank–Rocker Mechanisms Using a Wavelet-Based Neural Network
,” Mech. Mach. Theory
, 44
(6
), pp. 1132
–1143
.10.1016/j.mechmachtheory.2008.09.00627.
Daubechies
, L.
, 2001
, Ten Lectures on Wavelet
, Society for Industrial and Applied Mathematics
, Philadelphia, PA
.28.
Li
, X. Y.
, Zhao
, P.
, and Ge
, Q. J.
, 2012
, “A Fourier Descriptor Based Approach to Design Space Decomposition for Planar Motion Approximation
,” ASME
Paper No. DETC2012-71264. 10.1115/DETC2012-7126429.
Wu
, J.
, Wang
, J. S.
, Wang
, L. P.
, and Li
, T. M.
, 2009
, “Dynamics and Control of a Planar 3-DOF Parallel Manipulator With Actuation Redundancy
,” Mech. Mach. Theory
, 44
(4
), pp. 835
–849
.10.1016/j.mechmachtheory.2008.04.00230.
Wu
, J.
, Chen
, X. M.
, Li
, T. M.
, and Wang
, L. P.
, 2013
, “Optimal Design of a 2-DOF Parallel Manipulator With Actuation Redundancy Considering Kinematics and Natural Frequency
,” Rob. Comput. Integr. Manuf.
, 29
(1
), pp. 80
–85
.10.1016/j.rcim.2012.07.00531.
Wu
, J.
, Li
, T. M.
, Wang
, J. S.
, and Wang
, L. P.
, 2013
, “Performance Analysis and Comparison of Planar 3-DOF Parallel Manipulators With One and Two Additional Branches
,” J. Intell. Rob. Syst.
, 72
(1
), pp. 73
–82
.10.1007/s10846-013-9824-8Copyright © 2015 by ASME
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