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Some Properties of Jitterbug-Like Polyhedral Linkages

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Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 5))

Abstract

A formal definition for Jitterbug-like polyhedral linkages is presented. It is shown that the supporting polyhedral shapes cannot be arbitrary and some topological properties are derived. Also it is demonstrated that the link lengths of the spatial loops comprising the linkage cannot be arbitrary. The spherical indicatrices of spatial loops are examined and are shown to be immobile.

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References

  1. Bennett, G.T., Deformable octahedra. Proc. Lond. Math. Soc., 2:309–343, 1911.

    Google Scholar 

  2. Bottema, O. and Roth, B., Theoretical Kinematics. North-Holland, pp. 305–307, 1979.

    MATH  Google Scholar 

  3. Bricard, R., Mëmoire sur la thëorie de l’octa`edre articulë. J. Math. Pures Appl., 3:113–150, 1897.

    Google Scholar 

  4. Cromwell, P.R., Polyhedra. Cambridge University Press, p. 77, 1997.

    Google Scholar 

  5. Galiliunas, P. and Sharp, J., Duality of polyhedra. Int. J. Math. Educ. Sci. Tech., 36:617–642, 2005.

    Article  Google Scholar 

  6. Goldberg, M., Polyhedral linkages. Nat. Math. Mag., 16:323–332, 1942.

    Article  MathSciNet  Google Scholar 

  7. Hunt, K.H., Kinematic Geometry of Mechanisms. Clarendon Press, p. 287, 1978.

    MATH  Google Scholar 

  8. Kiper, G., Fulleroid-like linkages. In Proceedings 2nd EUCOMES, Springer, pp. 423–430, 2008.

    Google Scholar 

  9. Koväcs, F., Tarnai, T., Fowler, P.W., and Guest, S.D., A class of expandable polyhedral linkages. Int. J. Solids Struct., 41:1119–1137, 2004.

    Article  Google Scholar 

  10. Röschel, O., Linked Darboux motions. Math. Pannonica, 7:291–301, 1996

    Google Scholar 

  11. Röschel, O., Zwangläufig Bewegliche Polyedermodelle I. Math. Pannonica, 6:267–284, 1995.

    Google Scholar 

  12. Röschel, O., Zwangläufig Bewegliche Polyedermodelle II. Studia Sci. Math. Hung., 32:383–393, 1996.

    Google Scholar 

  13. Röschel, O., Zwangläufig Bewegliche Polyedermodelle III. Math. Pannonica, 12:55–68, 2001.

    Google Scholar 

  14. Stachel, H., The Heureka Polyhedron. In Fejes Töth, G. (Ed.), Intuitive Geometry, Coll. Math. Soc. J. Bolyai, Vol. 63, North-Holland, pp. 447–459, 1994.

    Google Scholar 

  15. Verheyen, H.F., The complete set of Jitterbug transformers and the analysis of their motion. Int. J. Comput. Math. Appl., 17:203–250, 1989.

    MATH  MathSciNet  Google Scholar 

  16. Wohlhart, K., New overconstrained spheroidal linkages. In Proceedings 9th World Congress on Mechanism and Machine Science, Milano, Vol. 1, pp. 149–154, 1995.

    Google Scholar 

  17. Wohlhart, K., Kinematics and dynamics of the fulleroid. Multibody System Dynam., 1:241–258, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  18. Wohlhart, K., The kinematics of Röschel polyhedra. In Lenarcic, J. and Husty, M. (Eds.), Advances in Robot Kinematics, Kluwer Academic Publishers, pp. 277–286, 1998.

    Google Scholar 

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Correspondence to G. Kiper .

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Kiper, G. (2010). Some Properties of Jitterbug-Like Polyhedral Linkages. In: Pisla, D., Ceccarelli, M., Husty, M., Corves, B. (eds) New Trends in Mechanism Science. Mechanisms and Machine Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9689-0_16

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  • DOI: https://doi.org/10.1007/978-90-481-9689-0_16

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9688-3

  • Online ISBN: 978-90-481-9689-0

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