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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A.A. Zadpoor, Mater. Horizons 3(5), 371 (2016).
K. Bertoldi, V. Vitelli, J. Christensen, M. Van Hecke, Nat. Rev. Mater. 2 (2017).
K.E. Evans, Endeavour 15(4), 170 (1991).
H.A. Kolken, A.A. Zadpoor, RSC Adv. 7(9), 5111 (2017).
X. Ren, R. Das, P. Tran, T.D. Ngo, Y.M. Xie, Smart Mater. Struct. 27(2), 023001 (2018).
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.
R. Hutchinson, N. Fleck, J. Mech. Phys. Solids 54(4), 756 (2006).
C.S. Borcea, I. Streinu, in Proc. 4th IEEE/IFToMM Int. Conf. Reconfigurable Mech. Robot. (Delft, the Netherlands, 2018), June, pp. 20–22
J.N. Grima, K.E. Evans, J. Mater. Sci. Lett. 19(17), 1563 (2000).
J.N. Grima, R. Gatt, A. Alderson, K.E. Evans, Mol. Simul. 31(13), 925 (2005).
D. Attard, J.N. Grima, Phys. status solidi 245(11), 2395 (2008).
D. Attard, J.N. Grima, Phys. status solidi 249(7), 1330 (2012).
J.N. Grima, K.E. Evans, J. Mater. Sci. 41(10), 3193 (2006).
C.S. Borcea, I. Streinu, Proc. R. Soc. a-Mathematical Phys. Eng. Sci. 466(2121), 2633 (2010).
E. Ross, B. Schulze, W. Whiteley, Int. J. Solids Struct. 48(11), 1711 (2011).
C. Kittel, in Introd. to solid state Phys. (Wiley, Hoboken, NJ :, 2005), chap. 1. Crystal, p. 680.
E. Dijksman, Motion geometry of mechanisms. (Cambridge University Press, Cambridge, UK, 1976)
I.I. Artobolevskii, Mechanisms for the generation of plane curves (Pergamon Press, 1964)
A.B. Kempe, Proc. London Math. Soc. s1-7(1), 213 (1875).
T. Mullin, S. Deschanel, K. Bertoldi, M.C. Boyce, Phys. Rev. Lett. 99(8) (2007).
K. Bertoldi, M. Boyce, S. Deschanel, S. Prange, T. Mullin, J. Mech. Phys. Solids 56(8), 2642 (2008).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-20131-9_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20130-2
Online ISBN: 978-3-030-20131-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)