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Synthesis of Double-Rocker Mechanisms for Motion Generation Using Fourier Descriptor

  • Cheng-Yuan Hsieh
  • Win-Bin Shieh
  • Ching-Kong Chen
  • Jyh-Jone LeeEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

Dimensional synthesis of a double-rocker linkage using the discrete Fourier transform (DFT) is presented. The coupler point curve of a double-rocker linkage is open and cannot be expressed by the Fourier series with periodic coefficients. Hence, in this study, a procedure is first proposed to transform such an open curve into a closed curve such that the DFT can be applied. Subsequently, the relations between the path of a coupler point and the design parameters of linkage are established and the motion generation problem is formulated as two prescribed paths having a constant distance. Finally, a least-square based optimization scheme is used to synthesize the design parameters and two numerical examples are illustrated for the procedure.

Keywords

Fourier Descriptor Discrete Fourier Transform Motion Generation Double-Rocker Mechanisms 

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References

  1. 1.
    Freudenstein, F.: Harmonic analysis of crank-and-rocker mechanisms with application. ASME Journal of Applied Mechanics, 26, 673–675 (1959).Google Scholar
  2. 2.
    Nie, X., Krovi, V.: Fourier methods for kinematic synthesis of coupled serial chain mecha-nisms. ASME Journal of Mechanical Design, 127(2), pp. 232–241 (2005).CrossRefGoogle Scholar
  3. 3.
    Ullah, L., Kota, S.: Optimal synthesis of mechanisms for path generation using Fourier de-scriptor and global search methods. ASME Journal of Mechanical Design, 119(4), pp. 504–510 (1997).CrossRefGoogle Scholar
  4. 4.
    Cortese, J.M., Dyre, B.P.: Perceptual similarity of shapes generated from Fourier descriptors. Journal of Experimental Psychology: Human Perception and Performance, 22(1), pp. 133–143 (1996).Google Scholar
  5. 5.
    Bloom, M., Corriveau, J., Giordano, P., Lecakes, G., Mandayam, S., Sukumaran, B.: Imag-ing system and algorithms for the numerical characterization of three-dimension shapes of granular particles. IEEE Trans. Instrum. Meas., 59(9), pp. 2365–2375 (2010).CrossRefGoogle Scholar
  6. 6.
    Shu, X., Wu, X.-J.: A Novel Contour Descriptor for 2D Shape Matching and Its Application to Image Retrieval. Image Vision Comput., 29(4), pp. 286–294 (2011).CrossRefGoogle Scholar
  7. 7.
    McGarva, J.: Rapid search and selection of path generating mechanisms from a library. Mechanism and Machine Theory, 29(2), pp. 223–235 (1994).CrossRefGoogle Scholar
  8. 8.
    Wu, J., Ge, Q. J., Gao, F., Guo, W. Z.: On the extension of a Fourier descriptor based method for planar four-bar linkage synthesis for generation of open and closed paths. ASME Journal of Mechanisms and Robotics, 3(3), 031002 (2011).CrossRefGoogle Scholar
  9. 9.
    Li, X., Zhong, X., Ge, Q. J.: Parametrization-independent non-uniform Fourier approach to path synthesis of four-bar mechanism. In Proceedings of the 14th IFToMM World Congress, Taipei, Taiwan. pp. 440–448 (2015).Google Scholar
  10. 10.
    Uesaka, Y.: A new Fourier descriptor applicable to open curves. Electron. Commun. Jpn., 67(8), pp. 1–10 (1984).MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ding, J.-J., Chao, W.-L., Huang, J.-D., Kuo, C.-j.: Asymmetric Fourier descriptor of non-closed segments. 17th IEEE International Conference on Image Processing, pp. 1613–616 (2010).Google Scholar
  12. 12.
    Wandling, G. R. Sr.: Synthesis of mechanisms for function, path, and motion generation using invariant characterization, storage and search methods. Retrospective Theses and Dis-sertations. 12383. (2000). https://lib.dr.iastate.edu/rtd/12383
  13. 13.
    Li, X., Wu, J., Ge, Q. J.: A Fourier descriptor-based approach to design space decomposition for planar motion approximation. ASME. J. Mechanisms and Robotics. 8(6):064501-064501-5. doi: https://doi.org/10.1115/1.4033528 (2016).
  14. 14.
    Sharma, S., Purwar, A., Ge, Q. J.: An optimal parametrization scheme for path generation Using Fourier descriptors for four-bar mechanism synthesis. ASME. J. Comput. Inf. Sci. Eng.; 19(1):014501-014501-5. doi: https://doi.org/10.1115/1.4041566 (2018).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Cheng-Yuan Hsieh
    • 1
  • Win-Bin Shieh
    • 2
  • Ching-Kong Chen
    • 3
  • Jyh-Jone Lee
    • 1
    Email author
  1. 1.National Taiwan UniversityTaipeiTaiwan
  2. 2.Ming Chi University of TechnologyNew TaipeiTaiwan
  3. 3.National Taipei University of TechnologyTaipeiTaiwan

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