Abstract
Local models are given for the singularities which can appear on the trajectories of general two-dimensional motions of the plane. Versal unfoldings of these model singularities give rise to computer generated pictures describing the family of trajectories arising from small deformations of the tracing point.
Supported by a grant from the Science and Engineering Research Council.
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References
C. G. Gibson and P. E. Newstead, “On the Geometry of the Planar 4-Bar Mechanism”, Acta Applicandae Mathematicae, 7, 113–135 (1986).
P. S. Donelan, “Generic Properties in Euclidean Kinematics”, Acta Applicandae Mathematicae, 12, 265–286 (1988).
C. A. Hobbs, “Kinematic Singularities of Low Dimension”, Ph.D. Thesis, University of Liverpool (1993).
C. G. Gibson and C. A. Hobbs, “Local Models for General One-Parameter Motions of the Plane and Space”, Preprint, University of Liverpool (1992).
C. G. Gibson, “Kinematic Singularities — A New Mathematical Tool”, Third International Workshop on Advances in Robot Kinematics, 209–215, Ferrara, Italy (1992).
C. G. Gibson and C. A. Hobbs, “Local Models for General Two—Parameter Motions of the Plane”, In Preparation (1994).
C. G. Gibson and C. A. Hobbs, “Local Models for General Two—Parameter Motions of Space”, In Preparation (1994).
C. G. Gibson and W. Hawes, “Local Models for General Multi—Parameter Motions of the Plane”, In Preparation (1994).
H. Whitney, “On Singularities of Mappings of Euclidean Space I: Mappings of the Plane to the Plane”, Ann. Math., 62, 374–410 (1955).
T. Gaffney, “The Structure of TA(f), classification and an application to differential geometry”, AMS — Proceedings of Symposia in Pure Mathematics, 40 (Singularities) Part 1, 409–427 (1983).
L. Kergosien, “Topologie Différentielle — La Famille des Projections Orthogonales d’une Surfaces et ses Singularités”, Comptes Rendus des séances de l’Académie des Sciences, 292, 929–932 (1981).
J. Rieger, “Apparent Contours and their Singularities”, Ph.D. Thesis, University of London (1988).
J. Rieger, “Families of Maps from the Plane to the Plane”, London Math. Soc., 2, 351–369 (1987).
O. Bottema and B. Roth, Theoretical Kinematics, Dover Publications, New York (1990).
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© 1994 Springer Science+Business Media Dordrecht
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Gibson, C.G., Hawes, W., Hobbs, C.A. (1994). Local Pictures for General Two-parameter Planar Motions. In: Lenarčič, J., Ravani, B. (eds) Advances in Robot Kinematics and Computational Geometry. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8348-0_5
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DOI: https://doi.org/10.1007/978-94-015-8348-0_5
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