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On the Synthesis of Periodic Linkages with a Specific Constant Poisson’s Ratio

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

Abstract

Poisson’s ratio is one of the most studied material proper- ties that can be designed in mechanical metamaterials. However, in most studies so far, Poisson’s ratio is not constant for larger compressions. Only for structures in which ν = 1, structures with a constant Poisson’s ratio have been demonstrated. This paper studies the design of planar mechanical metamaterials with a constant Poisson’s ratio based on the pantograph, inversor, straight-line and parabolograph mechanisms. Using these classical mechanisms as building blocks, periodic mechanisms with \( v = - 1,\frac{ - 1}{2} \), 0 and 1 are proposed.

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References

  1. A.A. Zadpoor, Mater. Horizons 3(5), 371 (2016).

    Google Scholar 

  2. K. Bertoldi, V. Vitelli, J. Christensen, M. Van Hecke, Nat. Rev. Mater. 2 (2017).

    Google Scholar 

  3. K.E. Evans, Endeavour 15(4), 170 (1991).

    Article  Google Scholar 

  4. H.A. Kolken, A.A. Zadpoor, RSC Adv. 7(9), 5111 (2017).

    Article  Google Scholar 

  5. X. Ren, R. Das, P. Tran, T.D. Ngo, Y.M. Xie, Smart Mater. Struct. 27(2), 023001 (2018).

    Article  Google Scholar 

  6. J.N. Grima, V. Zammit, R. Gatt, A. Alderson, K.E. Evans, in Phys. Status Solidi Basic Res., vol. 244 (2007), vol. 244, pp. 866–882.

    Google Scholar 

  7. R. Hutchinson, N. Fleck, J. Mech. Phys. Solids 54(4), 756 (2006).

    Google Scholar 

  8. C.S. Borcea, I. Streinu, in Proc. 4th IEEE/IFToMM Int. Conf. Reconfigurable Mech. Robot. (Delft, the Netherlands, 2018), June, pp. 20–22

    Google Scholar 

  9. J.N. Grima, K.E. Evans, J. Mater. Sci. Lett. 19(17), 1563 (2000).

    Google Scholar 

  10. J.N. Grima, R. Gatt, A. Alderson, K.E. Evans, Mol. Simul. 31(13), 925 (2005).

    Google Scholar 

  11. D. Attard, J.N. Grima, Phys. status solidi 245(11), 2395 (2008).

    Google Scholar 

  12. D. Attard, J.N. Grima, Phys. status solidi 249(7), 1330 (2012).

    Google Scholar 

  13. J.N. Grima, K.E. Evans, J. Mater. Sci. 41(10), 3193 (2006).

    Google Scholar 

  14. C.S. Borcea, I. Streinu, Proc. R. Soc. a-Mathematical Phys. Eng. Sci. 466(2121), 2633 (2010).

    Article  MathSciNet  Google Scholar 

  15. E. Ross, B. Schulze, W. Whiteley, Int. J. Solids Struct. 48(11), 1711 (2011).

    Google Scholar 

  16. C. Kittel, in Introd. to solid state Phys. (Wiley, Hoboken, NJ :, 2005), chap. 1. Crystal, p. 680.

    Google Scholar 

  17. E. Dijksman, Motion geometry of mechanisms. (Cambridge University Press, Cambridge, UK, 1976)

    Google Scholar 

  18. I.I. Artobolevskii, Mechanisms for the generation of plane curves (Pergamon Press, 1964)

    Google Scholar 

  19. A.B. Kempe, Proc. London Math. Soc. s1-7(1), 213 (1875).

    Google Scholar 

  20. T. Mullin, S. Deschanel, K. Bertoldi, M.C. Boyce, Phys. Rev. Lett. 99(8) (2007).

    Google Scholar 

  21. K. Bertoldi, M. Boyce, S. Deschanel, S. Prange, T. Mullin, J. Mech. Phys. Solids 56(8), 2642 (2008).

    Google Scholar 

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Correspondence to F. G. J. Broeren .

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Broeren, F.G.J., Herder, J.L., van der Wijk, V. (2019). On the Synthesis of Periodic Linkages with a Specific Constant Poisson’s Ratio. 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_25

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