Research Papers: Mechanisms and Robotics

Dimensional Synthesis of Open Path Generator of Four-Bar Mechanisms Using the Haar Wavelet

[+] Author and Article Information
Jianwei Sun

School of Mechatronic Engineering,
Changchun University of Technology,
No. 2055, Yanan Road,
Changchun, Jilin 130012, China
e-mail: avensun@tom.com

Wenrui Liu

School of Mechatronic Engineering,
Changchun University of Technology,
No. 2055, Yanan Road,
Changchun, Jilin 130012, China
e-mail: wenruilv@126.com

Jinkui Chu

School of Mechanical Engineering,
Dalian University of Technology,
No. 2, Linggong Road, Ganjingzi District,
Dalian, Liaoning 116023, China
e-mail: chujk@dlut.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 15, 2015; final manuscript received May 4, 2015; published online June 16, 2015. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 137(8), 082303 (Aug 01, 2015) (8 pages) Paper No: MD-15-1027; doi: 10.1115/1.4030651 History: Received January 15, 2015; Revised May 04, 2015; Online June 16, 2015

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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Norton, R. L., 1992, Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines. McGraw-Hill, New York.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Cabrera, J. A., Simon, A., and Prado, M., 2002, “Optimal Synthesis of Mechanisms With Genetic Algorithms,” Mech. Mach. Theory, 37(10), pp. 1165–1177. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Hrones, J. A., and Nelson, G. L., 1951, Analysis of the Four-Bar Linkage, MIT Press and Wiley, New York.
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. [CrossRef]
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. [CrossRef]
Buskiewicz, J., 2010, “Use of Shape Invariants in Optimal Synthesis of Geared Five-Bar Linkage,” Mech. Mach. Theory, 45(2), pp. 273–290. [CrossRef]
Watanabe, K., 1992, “Application of Natural Equations to Synthesis of Curve Generating Mechanisms,” Mech. Mach. Theory, 27(3), pp. 261–273. [CrossRef]
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. [CrossRef]
Freudenstein, F., 1959, “Harmonic Analysis of Crank-and-Rocker Mechanisms With Application,” ASME J. Mech. Des., 26(1), pp. 673–675.
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. [CrossRef]
McGarva, J., 1994, “Rapid Search and Selection of Path Generating Mechanisms From a Library,” Mech. Mach. Theory, 29(2), pp. 223–235. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Mullineux, G., 2011, “Atlas of Spherical Four-Bar Mechanisms,” Mech. Mach. Theory, 46(11), pp. 1811–1823. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
Daubechies, L., 2001, Ten Lectures on Wavelet, Society for Industrial and Applied Mathematics, Philadelphia, PA.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]


Grahic Jump Location
Fig. 1

A four-bar mechanism within a coordinate system

Grahic Jump Location
Fig. 2

Solution of the path generation problem

Grahic Jump Location
Fig. 4

Example 3: (a) the prescribed curve and (b) a comparison graph

Grahic Jump Location
Fig. 3

Example 2: (a) a comparison graph and (b) error graph

Grahic Jump Location
Fig. 5

A three-dimensional illustration of the drilling machine: (a) drilling mechanism and (b) feed mechanism

Grahic Jump Location
Fig. 6

The prescribed curve for example 4

Grahic Jump Location
Fig. 7

Comparison and error graphs for example 4




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In