Despite the tidiness with which the Bennett linkage can be related geometrically to its associated quadric surfaces, the corresponding algebraic determinations have generally turned out to be cumbersome, and so practically noninvertible. In particular, although earlier work has delineated the linkage in terms of parameters peculiar to its quadric surfaces, the inverse dependences could not be given. We here use the loop strictly as a basis for derivation of the surfaces and employ cartesian co-ordinates throughout, thereby effectively completing the conversion process.
Issue Section:
Technical Papers
1.
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.
2.
Baker
, J. E.
, 2001
, “The Axodes of the Bennett Linkage
,” Mech. Mach. Theory
, 36
(1
), pp. 105
–116
.3.
Bennett
, G. T.
, 1903
, “A New Mechanism
,” Engineering
, 76
, pp. 777
–778
.4.
Bricard
, R.
, 1906
, “Sur une Proprie´te´ de l’Hyperboloi¨de Orthogonal et sur un Syste`me Articule´
,” Nouvelles Annales de Mathe´matiques, 4s.
, VI
, pp. 69
–80
.5.
Bennett
, G. T.
, 1914
, “The Skew Isogram Mechanism
,” Proc. London Math. Soc.
, 2s., 13
, pp. 151
–173
.6.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press, Oxford, U.K.
7.
Phillips, J., 1984, 1990, Freedom in Machinery, Cambridge University Press, Cambridge, U.K.
8.
Borel
, E.
, 1908
, “Me´moire sur les De´placements a` Trajectoires Sphe´riques
,” Me´moires pre´sente´s par divers savants a` l’Acade´mie des Sciences de l’Institut National de France
, XXXIII
(1
), pp. 1
–128
.9.
Yu
, H.-C.
, 1981
, “The Bennett Linkage, its Associated Tetrahedron and the Hyperboloid of its Axes
,” Mech. Mach. Theory
, 16
(2
), pp. 105
–114
.10.
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.
11.
Baker
, J. E.
, 1988
, “The Bennett Linkage and its Associated Quadric Surfaces
,” Mech. Mach. Theory
, 23
(2
), pp. 147
–156
.Copyright © 2004
by ASME
You do not currently have access to this content.