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Parametric Euler-Savary Equations For Spherical Instantaneous Kinematics

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Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 73))

Abstract

The paper presents a parametric form of Euler-Savary equations for spherical instantaneous kinematics. The formulation procedures are explained for Ball and Ball-Burmester points. The parametric forms of the equations are used to determine the coordinates of fixed joints of various four bar mechanisms for validation.

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References

  1. Sandor, G., et al., New complex-number forms of the Euler-Savary equation in a computer-oriented treatment of planar path-curvature theory for higher-pair rolling contact. Journal of Mechanical Design, 1982. 104(1): p. 227-232.

    Google Scholar 

  2. Sandor, G.N., A.G. Erdman, and E. Raghavacharyulu, Double-valued solutions of the Euler-Savary Equation and its counterpart in bobillier’s construction. Mechanism and machine theory, 1985. 20(2): p. 145-148.

    Google Scholar 

  3. Sandor, G.N., Y. Xu, and T.-C. Weng, A graphical method for solving the Euler- Savary equation. Mechanism and Machine Theory, 1990. 25(2): p. 141-147.

    Google Scholar 

  4. Ting, K.-L. and S. Wang, Fourth and fifth order double Burmester points and the highest attainable order of straight lines. Journal of Mechanical Design, 1991. 113(3): p. 213-219.

    Google Scholar 

  5. Wang, D., J. Liu, and D. Xiao, A unified curvature theory in kinematic geometry of mechanism. Science in China Series E: Technological Sciences, 1998. 41(2): p. 196-202.

    Google Scholar 

  6. Dooner, D.B. and M.W. Griffis, On spatial Euler–Savary equations for envelopes. Journal of Mechanical Design, 2007. 129(8): p. 865-875.

    Google Scholar 

  7. Masal, M., M. Tosun, and A.Z. Pirdal, Euler savary formula for the one parameter motions in the complex plane C. International Journal of Physical Sciences, 2010. 5(1): p. 6-10.

    Google Scholar 

  8. Pereira, N.T.S. and S. Ersoy, Elliptical harmonic motion and Euler–Savary formula. Advances in Applied Clifford Algebras, 2016. 26(2): p. 731-755.

    Google Scholar 

  9. Gürses, N., M. Akbiyik, and S. Yüce, One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane $${\mathbb {C} _ {J}} $$ C J. Advances in Applied Clifford Algebras, 2016. 26(1): p. 115-136.

    Google Scholar 

  10. Akbıyık, M. and S. Yüce, Euler Savary’s Formula On Complex Plane C. Applied Mathematics E-Notes, 2016. 16: p. 65-71.

    Google Scholar 

  11. Fu, T.-T. and C.-H. Chiang, Simulating a given spherical motion by the polode method. Mechanism and machine theory, 1994. 29(2): p. 237-249.

    Google Scholar 

  12. Kamphuis, H., Application of spherical instantaneous kinematics to the spherical slider-crank mechanism. Journal of Mechanisms, 1969. 4(1): p. 43-56.

    Google Scholar 

  13. CH, C., Kinematics of spherical mechanisms. . Krieger Publishing, Melbourne, 2000

    Google Scholar 

  14. Özçelik, Z. and Z. Şaka, Ball and Burmester points in spherical kinematics and their special cases. Forschung im Ingenieurwesen, 2010. 74(2): p. 111-122.

    Google Scholar 

  15. Özçelik, Z. and Z. Şaka, On the Derivation of the Coordinates of Coupler Points in Spherical Mechanisms.

    Google Scholar 

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Correspondence to Osman Acar .

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Acar, O., Şaka, Z., Özçelik, Z. (2019). Parametric Euler-Savary Equations For Spherical Instantaneous Kinematics. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_35

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