This paper investigates, via numerical simulations, the finite displacements of all the known Bennett-based 6R overconstrained linkages: Goldberg’s 6R, variant Goldberg 6R, Waldron’s hybrid 6R, and Wohlhart’s hybrid 6R linkages. An investigation of the finite displacements of nine distinct linkages reveals that every Bennett-based 6R linkage, except for the isomerization of Wohlhart’s hybrid linkage, inherits the linear properties of the Bennett mechanism. The relative finite displacement screws of some non-adjacent links of these linkages form screw systems of the second order. Thirty-one screw systems are reported in this paper. [S1050-0472(00)02204-2]

1.
Brat
,
V.
,
1969
, “
A Six-Link Spatial Mechanism
,”
J. Mec.
,
4
, pp.
325
336
.
2.
Currey, N. S., 1988, “Aircraft Landing Gear Design: Principles and Practices,” AIAA Education Series, Washington D.C.
3.
Phillips, J., 1990, Freedom in Machinery, Volume 2, Cambridge University Press.
4.
Bennett
,
G. T.
,
1903
, “
A New Mechanism
,”
Engineering
,
76
, pp.
777
778
.
5.
Goldberg
,
M.
,
1943
, “
New Five-Bar and Six-Bar Linkages in Three Dimensions
,”
Trans. ASME
,
65
, pp.
649
661
.
6.
Yu
,
H.-C.
, and
Baker
,
J. E.
,
1981
, “
On the Generation of New Linkages from Bennett Loops
,”
Mech. Mach. Theory
,
16
, No.
5
, pp.
473
485
.
7.
Baker
,
J. E.
,
1993
, “
A Comparative Survey of the Bennett-Based, 6-Revolute Kinematic Loops
,”
Mech. Mach. Theory
,
28
, No.
1
, pp.
83
96
.
8.
Huang, C., 1996, “The Cylindroid Associated with Finite Motions of the Bennett Mechanism,” Proc. of the 1996 ASME Design Engineering Technical Conference, Aug. 18–22, 1996, Irvine, California.
9.
Huang, C., and Liu, T-E., 1997, “On the Linear Finite Motions of the Goldberg Overconstrained Linkages,” Proceedings of the Fifth Applied Mechanisms and Robotics Conference, Cincinnati, Ohio, October 12–15.
10.
Waldron
,
K. J.
,
1968
, “
Hybrid Overconstrained Linkages
,”
J. Mec.
,
3
, pp.
73
78
.
11.
Wohlhart
,
K.
,
1991
, “
Merging Two General Goldberg 5R Linkages to Obtain a New 6R Space Mechanism
,”
Mech. Mach. Theory
,
7
, pp.
659
668
.
12.
Parkin
,
I. A.
,
1992
, “
A Third Conformation with the Screw Systems: Finite Twist Displacements of a Directed Line and Point
,”
Mech. Mach. Theory
,
27
, pp.
177
188
.
13.
Ball, R. S., 1900, A Treatise of the Theory of Screws, Cambridge University Press.
14.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon, Oxford.
15.
Roth, B., 1984, “Screws, Motors, and Wrenches that Cannot Be Bought in a Hardware Store,” Robotics Research, the First International Symposium, M. Brady and R. Paul, eds., MIT Press, pp. 679–694.
16.
Huang
,
C.
, and
Roth
,
B.
,
1994
, “
Analytic Expressions for the Finite Screw Systems
,”
Mech. Mach. Theory
,
29
, No.
2
, pp.
207
222
.
17.
Hunt
,
K. H.
, and
Parkin
,
I. A.
,
1995
, “
Finite Displacements of Pints, Planes, and Lines via Screw Theory
,”
Mech. Mach. Theory
,
30
, No.
2
, pp.
177
192
.
18.
Huang
,
C.
,
1994
, “
On the Finite Screw System of the Third Order Associated with a Revolute-Revolute Chain
,”
ASME Mech. Des.
,
116
, pp.
875
883
.
19.
Huang
,
C.
, and
Chen
,
C. M.
,
1995
, “
The Linear Representation of the Screw Triangle—A Unification of Finite and Infinitesimal Kinematics
,”
ASME Mech. Des.
,
117
, pp.
554
560
.
You do not currently have access to this content.