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TECHNICAL PAPERS

The Composition of Bennett’s Hyperboloids From the Loop Itself

[+] Author and Article Information
J. Eddie Baker

Honorary Research Associate, School of Information Technologies, The University of Sydney, NSW 2006, Australiae-mail: jebaker@it.usyd.edu.au

J. Mech. Des 126(5), 875-880 (Oct 28, 2004) (6 pages) doi:10.1115/1.1767183 History: Received October 01, 2003; Revised January 01, 2004; Online October 28, 2004
Copyright © 2004 by ASME
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References

Baker, J. E., 1998, “On the Motion Geometry of the Bennett Linkage,” Proc. Eighth International Conference on Engineering Design Graphics and Descriptive Geometry, Jul. 31–Aug. 3, Austin, Texas, Vol. 2, pp. 433–437.
Baker,  J. E., 2001, “The Axodes of the Bennett Linkage,” Mech. Mach. Theory, 36(1), pp. 105–116.
Bennett,  G. T., 1903, “A New Mechanism,” Engineering,76, pp. 777–778.
Bricard,  R., 1906, “Sur une Propriété de l’Hyperboloïde Orthogonal et sur un Système Articulé,” Nouvelles Annales de Mathématiques, 4s.,VI, pp. 69–80.
Bennett,  G. T., 1914, “The Skew Isogram Mechanism,” Proc. London Math. Soc., 2s., 13, pp. 151–173.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press, Oxford, U.K.
Phillips, J., 1984, 1990, Freedom in Machinery, Cambridge University Press, Cambridge, U.K.
Borel,  E., 1908, “Mémoire sur les Déplacements à Trajectoires Sphériques,” Mémoires présentés par divers savants à l’Académie des Sciences de l’Institut National de France,XXXIII(1), pp. 1–128.
Yu,  H.-C., 1981, “The Bennett Linkage, its Associated Tetrahedron and the Hyperboloid of its Axes,” Mech. Mach. Theory, 16(2), pp. 105–114.
Yu, H.-C., 1987, “Geometry of the Bennett Linkage via its Circumscribed Sphere,” Proc. 7th World Congress on the Theory of Machines and Mechanisms, Sep. 17–22, Sevilla, Spain, Vol. 1, pp. 227–229.
Baker,  J. E., 1988, “The Bennett Linkage and its Associated Quadric Surfaces,” Mech. Mach. Theory, 23(2), pp. 147–156.

Figures

Grahic Jump Location
The frames of reference of the loop’s J-hyperboloid and L-hyperboloid in relation to each other
Grahic Jump Location
The center O of the chain’s J-hyperboloid in relation to adjacent vertices
Grahic Jump Location
The linkage’s line of symmetry in relation to opposing joint axes
Grahic Jump Location
The Bennett linkage in outline with frame defined

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