Abstract
The paper gives a construction of a new series of overconstrained spatial mechanisms with six systems connected via nine spherical 2R-joints. The mechanisms are designed by means of plane equiform motions. This new type of overconstrained mechanisms will be called Möbius mechanisms. By removing one of its joints, the so-called reduced Möbius mechanisms will be set up, still being overconstrained. A special example is being studied in detail: It admits interesting self-motions of different degrees of freedom. This is why it represents a new example of kinematotropic mechanisms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bottema, O., Roth, B. (1979), Theoretical Kinematics. North-Holland, Amsterdam - New York - Oxford.
Krause, M., (1910), Zur Theorie der ebenen ähnlich veränderlichen Systeme. Jahresber. d. Deutschen Mathematiker-Vereinigung, 19, pp. 327–329.
Röschel, O., (1985), Rationale Zwangläufe vierter Ordnung. Sber. d. Österr. Akad. Wiss., 194, pp. 185–202.
Röschel, O., (1995), Zwangläufig bewegliche Polyedermodelle I. Math. Pann., 61, pp. 267–284.
Röschel, O., (1996), Zwangläufig bewegliche Polyedermodelle II. Studia Sci. Math. Hung., 32, pp. 383–393.
Röschel, O., (1996), Linked Darboux motions. Math. Pannonica 7/2, pp. 291–301.
Stachel, H., (1991), The HEUREKA-Polyhedron. Proceedings of Coll. Math. Soc. J. Bolyai, pp. 447–459.
Stachel, H., (1992), Zwei bemerkenswerte bewegliche Strukturen. Journ. of Geom., 43, pp. 14–21.
Stachel, H., (1999), On the tetrahedra in a dodekahedron. Preprint (to appear).
Verheyen, H.F., (1989), The complete set of Jitterbug transformers and the analysis of their motion. Computers Math. Applic., 17, pp. 203–250.
Wohlhart, K., (1993), Dynamics of the “Turning Tower”. Proc. d. IV. Ogolnopolska Konf. Maszyn Wlokienniczych i Dzwigowych, pp. 325–332.
Wohlhart, K., (1993), Heureka Octahedron and Brussels folding cube as special cases of the turning tower. Proc. 6th IFToMM Symp. Bucuresti, pp. 303–312.
Wohlhart, K., (1995), Das dreifach plansymmetrische Oktoid und seine Punktbahnen. Math. Pann., 6/2, pp. 243–265.
Wohlhart, K., (1995), New Overconstrained Spheroidal Linkages. Proc. 9th World Congr. on the Theory of the Machines and Mechanisms, Milano, pp. 149–155.
Wohlhart, K., (1996), Kinematotropic Linkages. pp. 357–368. In: Recent Advances in Robot Kinematics (J. Lenarcic - V. Parenti - Castelli, eds.), Kluwer Acad. Pbl., Netherlands.
Wohlhart, K., (1998), The kinematics of Röschel polyhedra. pp. 277–286. In: Advances in Robot Kinematics (J. Lenarcic - M. Husty, eds.), Kluwer Acad. Pbl., Netherlands.
Wunderlich, W., (1973), Ebene Kinematik. Bibliograph. Inst. Mannheim, Vol. 447/447a.
Yaglom, I.M., (1968), Geometric transformations II. Random House, Washington.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Röschel, O. (2000). Möbius Mechanisms. In: Lenarčič, J., Stanišić, M.M. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4120-8_39
Download citation
DOI: https://doi.org/10.1007/978-94-011-4120-8_39
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5803-2
Online ISBN: 978-94-011-4120-8
eBook Packages: Springer Book Archive