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Appropriate Synthesis of a Crank Rocker Linkage

  • Joshua K. PickardEmail author
  • Juan Antonio Carretero
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

The appropriate design methodology is used to model uncertainties and variations in the design of a crank-rocker four-bar linkage. Each design parameter is modelled as a closed interval, such that the appropriate design of a linkage describes a family of linkages. Interval analysis routines are developed and applied to reliably determine the range of performance of the family of linkages. Appropriate synthesis concerns the determination of the complete set of appropriate design solutions which satisfy a given task. Here, a task is modelled with multiple precision points with allowable errors (i.e., boxes). An appropriate design solution must generate a coupler curve which passes within all precision points. Any linkage design contained within the set of appropriate design solutions is guaranteed to satisfy the task requirements.

Keywords

Interval analysis mechanism design appropriate design crank-rocker 

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References

  1. 1.
    S. Bai and J. Angeles, Coupler-curve synthesis of four-bar linkages via a novel formulation, Mechanism and Machine Theory 94 (2015), 177–187.CrossRefGoogle Scholar
  2. 2.
    R. R. Bulatović and S. R. Dordević, On the optimum synthesis of a four-bar link-age using differential evolution and method of variable controlled deviations, Mechanism and Machine Theory 44 (2009), no. 1, 235–246.CrossRefGoogle Scholar
  3. 3.
    J.A. Cabrera, A. Simon, and M. Prado, Optimal synthesis of mechanisms with genetic algorithms, Mechanism and Machine Theory 37 (2002), no. 10, 1165–1177.CrossRefGoogle Scholar
  4. 4.
    T. R. Chase and J. A. Mirth, Circuits and branches of single-degree-of-freedom planar linkages, Journal of Mechanical Design–Transactions of the ASME 115 (1993), no. 2, 223–230.CrossRefGoogle Scholar
  5. 5.
    G. B. Chatterjee and A. K. Mallik, Mechanical error of a four-bar linkage coupler curve, Mechanism and Machine Theory 22 (1987), no. 1, 85–88.CrossRefGoogle Scholar
  6. 6.
    V. Goulet, W. Li, H. Cheong, F. Iorio, and C.-G. Quimper, Four-bar linkage synthesis using non-convex optimization, pp. 618–635, Springer International Publishing, 2016.Google Scholar
  7. 7.
    K. H. Hunt, Kinematic geometry of mechanisms, Oxford engineering science series, Clarendon Press, 1978.Google Scholar
  8. 8.
    L. V. Kantorovich and G. E. Forsythe, Functional analysis and applied mathematics, NBS report, National Bureau of Standards, 1952.Google Scholar
  9. 9.
    R. Krawczyk, Newton-algorithmen zur bestimmung von nullstellen mit fehler-schranken, Computing 4 (1969), no. 3, 187–201.MathSciNetCrossRefGoogle Scholar
  10. 10.
    J. McCarthy and G. Song Soh, Geometric design of linkages, Interdisciplinary Applied Mathematics, Springer, 2010.Google Scholar
  11. 11.
    J.-P. Merlet and D. Daney, Smart devices and machines for advanced manufacturing, ch. Appropriate Design of Parallel Manipulators, pp. 1–25, Springer London, London, 2008.Google Scholar
  12. 12.
    S. Roberts, On three-bar motion in plane space, Proceedings of the London Mathematical Society s1-7 (1875), no. 1, 14–23.MathSciNetCrossRefGoogle Scholar
  13. 13.
    H. Schröcker, M. L. Husty, and J. McCarthy, Kinematic mapping based assembly mode evaluation of planar four-bar mechanisms, Journal of Mechanical Design 129 (2006), no. 9, 924–929.Google Scholar
  14. 14.
    C. W. Wampler, A. P. Morgan, and A. J. Sommese, Complete solution of the nine-point path synthesis problem for four-bar linkages, Journal of Mechanical Design–Transactions of the ASME 114 (1992), no. 1, 153–159.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Inria Bordeaux Sud-OuestTalence cedexFrance
  2. 2.University of New BrunswickFrederictonCanada

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