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Exact Synthesis of a 1-dof Planar Linkage for Visiting 10 Poses

  • Shaoping BaiEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

It is well known that a four-bar linkage is able to visit exactly 5 poses. An interesting problem of synthesis is to obtain 1-dof linkages for visiting more than five poses. In this paper, an approach of 1-dof linkage synthesis is proposed by constraining planar parallel mechanism. A solution of 13-revolute-joint linkage is thus obtained, which is able to visit exactly maximum 10 poses. The problem formulation is provided, with a synthesis example included.

Keywords

exact motion synthesis 10-pose synthesis problem polynomial equations coupler curve 

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References

  1. 1.
    R.S. Hartenberg and J. Denavit. Kinematic Synthesis of Linkages. McGraw-Hill, New York, 1964.Google Scholar
  2. 2.
    K. H. Hunt. Kinematic Geometry of Mechanisms. Oxford University Press, New York, 1978.Google Scholar
  3. 3.
    O. Bottema and B. Roth. Theoretical Kinematics. North-Holland Pub. Co., New York, 1979.Google Scholar
  4. 4.
    J. M. McCarthy and G. S. Soh. Geometric Design of Linkages. Springer, New York, 2011.Google Scholar
  5. 5.
    K. Al-Widyan, J. Angeles, and J. J. Cervantes-Sánchez. A numerical robust algorithm to solve the five-pose Burmester problem. In Proc. ASME DETC2002, Montreal, #MECH-34270, 2002.Google Scholar
  6. 6.
    G. N. Sandor and A. G. Erdman. Advanced Mechanism Design: Analysis and Synthesis, volume 2. Prentice-Hall, Inc., New Jersey, 1984.Google Scholar
  7. 7.
    B. Ravani and B. Roth. Motion synthesis using kinematic mappings. ASME Journal of Mechanism, Transmissions, and Automation in Design, 105:460–467, 1983.CrossRefGoogle Scholar
  8. 8.
    S. Bai, D. Wang, and H. Dong. A unified formulation for dimensional synthesis of Stephenson linkages. ASME Journal of Mechanisms and Robotics, 8(4):041009, 2016.CrossRefGoogle Scholar
  9. 9.
    C. W. McLarnan. Synthesis of six-link plane mechanisms by numerical analysis. ASME Journal of Engineering for Industry, 85(1):5–10, 1963.CrossRefGoogle Scholar
  10. 10.
    H.S. Kim, S Hamid, and A.H. Soni. Synthesis of six-link mechanisms for point path generation. Journal of Mechanisms, 6(4):447–461, 1972.CrossRefGoogle Scholar
  11. 11.
    G. S. Soh and J. M. McCarthy. The synthesis of six-bar linkages as constrained planar 3R chains. Mechanism and Machine Theory, 43(2):160 – 170, 2008.CrossRefGoogle Scholar
  12. 12.
    Y. Liu and J. McPhee. Automated kinematic synthesis of planar mechanisms with revolute joints. Mechanics Based Design of Structures and Machines, 35(4):405– 445, 2007.CrossRefGoogle Scholar
  13. 13.
    S. Bai. Dimensional synthesis of six-bar linkages with incomplete data set. In Proc. 5th European Conference on Mechanism Science, September 16-20th, 2014, Guimarães, Portugal, pages 1–8, 2014.Google Scholar
  14. 14.
    P.W. Jensen. Synthesis of four-bar linkages with a coupler point passing through 12 points. Mechanism and Machine Theory, 19:149–156, 12 1984.CrossRefGoogle Scholar
  15. 15.
    G. Soh and F. Ying. Dimensional synthesis of planar eight-bar linkages based on a parallel robot with a prismatic base joint. In Proc. of ASME. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pages DETC2013–12799, 2013.Google Scholar
  16. 16.
    C. Chen and J. Angeles. A novel family of linkages for advanced motion synthesis. Mechanism and Machine Theory, 43(7):882–890, 2008.CrossRefGoogle Scholar
  17. 17.
    Chung, W.-Y. Synthesis of two four-bar in series for body guidance. MATEC Web Conf., 95:04006, 2017. Exact synthesis of 1-dof Linkage.CrossRefGoogle Scholar
  18. 18.
    H. A. Suárez-Velásquez, J. J. Cervantes-Sánchez, and J. M. Rico-Martínez. Synthesis of a novel planar linkage to visit up to eight poses. Mechanics Based Design of Structures and Machines, 46(6):781–799, 2018.CrossRefGoogle Scholar
  19. 19.
    C. W. Wampler, A. P. Morgan, and A. J. Sommese. Numerical continuation methods for solving polynomial systems arising in kinematics. ASME Journal of Mechanical Design, 112(1):59–68, 1990.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Materials and ProductionAalborg UniversityAalborgDenmark

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