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Sharp Linkages

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Abstract

In this chapter, we consider a special kind of overconstrained \(6\)R closed linkages which we call sharp linkages. These are linkages with the property that their bond diagram looks like a \(\sharp \) sign. We give a construction of this linkage using the bond theory and motion polynomial factorization methods. These two methods are introduced recently in [6, 7]. Another type of 6R linkages is also introduced. To my knowledge, both types of linkages are new.

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Notes

  1. 1.

    http://people.ricam.oeaw.ac.at/z.li/softwares/sharplinkages.html

  2. 2.

    http://people.ricam.oeaw.ac.at/z.li/softwares/quadpolynomials.html

  3. 3.

    One can check that \(L_c\) does not fulfill the necessary conditions of Waldrons double Bennett hybrid, Dietmaier 6R linkages or Bricard plane symmetric 6R linkages as an exercise.

References

  1. Baker, J.E.: An analysis of the Bricard linkages. Mech. Mach. Theory 15(4), 267–286 (1980)

    Article  Google Scholar 

  2. Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanisms based on matrices. Transactions of the ASME. J. Appl. Mech. 22, 215–221 (1955)

    MATH  MathSciNet  Google Scholar 

  3. Dietmaier, P.: Einfach übergeschlossene Mechanismen mit Drehgelenken. Habilitation thesis, Graz University of Technology (1995)

    Google Scholar 

  4. Goldberg, M.: New five-bar and six-bar linkages in three dimensions. Trans. ASME 65, 649–656 (1943)

    Google Scholar 

  5. Hegedüs, G., Li, Z., Schicho, J., Schröcker, H.P.: The theory of bonds ii: Closed 6R linkages with maximal genus. ArXiv e-prints (2013)

    Google Scholar 

  6. Hegedüs, G., Schicho, J., Schröcker, H.P.: Factorization of rational curves in the study quadric. Mech. Mach. Theory 69, 142–152 (2013)

    Article  Google Scholar 

  7. Hegedüs, G., Schicho, J., Schröcker, H.P.: The theory of bonds: a new method for the analysis of linkages. Mech. Mach. Theory 70, 407–424 (2013)

    Article  Google Scholar 

  8. Li, Z., Schicho, J.: Classification of angle-symmetric 6R linkages. Mech. Mach. Theory 70, 372–379 (2013)

    Article  Google Scholar 

  9. Li, Z., Schicho, J.: Three types of parallel 6R linkages. In: Thomas, F., Perez Gracia, A. (eds.) Computational Kinematics, Mechanisms and Machine Science, vol. 15, pp. 111–119. Springer, Netherlands (2014)

    Google Scholar 

  10. Li, Z., Schicho, J.: A new technique for analyzing 6R linkages: Quad Polynomials. Tech. rep. (2014)

    Google Scholar 

  11. Sarrus, P.: Note sur la transformation des mouvements rectilignes alternatifs, en mouvements circulaires: et rèciproquement. Comptes Rendus des Séances de l’Académie des Sciences de Paris 36, 1036–1038 (1853)

    Google Scholar 

  12. Waldron, K.J.: Overconstrained linkages. Environ. Plann. B-plann. Des. 6, 393–402 (1979)

    Article  Google Scholar 

  13. Wohlhart, K.: Merging two general Goldberg 5R linkages to obtain a new 6R space mechanism. Mech. Mach. Theory 26, 659–668 (1991)

    Article  Google Scholar 

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Acknowledgments

We would like to thank Gábor Hegedüs, Hans-Peter Schröcker and Josef Schicho for discussion and helpful remarks. The research was supported by the Austrian Science Fund (FWF): W1214-N15, project DK9.

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Correspondence to Zijia Li .

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Li, Z. (2014). Sharp Linkages. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_15

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  • DOI: https://doi.org/10.1007/978-3-319-06698-1_15

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  • Publisher Name: Springer, Cham

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