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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
- 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
Baker, J.E.: An analysis of the Bricard linkages. Mech. Mach. Theory 15(4), 267–286 (1980)
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)
Dietmaier, P.: Einfach übergeschlossene Mechanismen mit Drehgelenken. Habilitation thesis, Graz University of Technology (1995)
Goldberg, M.: New five-bar and six-bar linkages in three dimensions. Trans. ASME 65, 649–656 (1943)
Hegedüs, G., Li, Z., Schicho, J., Schröcker, H.P.: The theory of bonds ii: Closed 6R linkages with maximal genus. ArXiv e-prints (2013)
Hegedüs, G., Schicho, J., Schröcker, H.P.: Factorization of rational curves in the study quadric. Mech. Mach. Theory 69, 142–152 (2013)
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)
Li, Z., Schicho, J.: Classification of angle-symmetric 6R linkages. Mech. Mach. Theory 70, 372–379 (2013)
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)
Li, Z., Schicho, J.: A new technique for analyzing 6R linkages: Quad Polynomials. Tech. rep. (2014)
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)
Waldron, K.J.: Overconstrained linkages. Environ. Plann. B-plann. Des. 6, 393–402 (1979)
Wohlhart, K.: Merging two general Goldberg 5R linkages to obtain a new 6R space mechanism. Mech. Mach. Theory 26, 659–668 (1991)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-06698-1_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06697-4
Online ISBN: 978-3-319-06698-1
eBook Packages: EngineeringEngineering (R0)