Three position synthesis of a spatial RR chain yields two solutions that can be assembled to form a Bennett linkage. In this paper, we show that the cylindroid associated with Bennett’s linkage can be generated directly from the three specified positions, and used to simplify the design equations. Analysis of these equations shows that there are always two solutions and that their symmetry yields a Bennett linkage. An example design is presented.

1.
Veldkamp
,
G. R.
,
1967
, “
Canonical Systems and Instantaneous Invariants in Spatial Kinematics
,”
J. Mec.
,
3
, pp.
329
388
.
2.
Suh
,
C. H.
,
1969
, “
On the Duality in the Existence of R-R Links for Three Positions
,”
ASME J. Ind.
,
91
(
B
), pp.
129
134
.
3.
Tsai
,
L. W.
, and
Roth
,
B.
,
1973
, “
A Note on the Design of Revolute-Revolute Cranks
,”
Mech. Mach. Theory
,
8
, pp.
23
31
.
4.
Huang, C., 1996, “The Cylindroid Associated with Finite Motions of the Bennett Mechanism,” Proceedings of the ASME Design Engineering Technical Conferences, Irvine, CA.
5.
Bennett
,
G. T.
,
1903
, “
A New Mechanism
,”
Engineering
,
76
, pp.
777
778
.
6.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland (reprinted by Dover Publications, 1990).
7.
McCarthy, J. M., 1990, Introduction to Theoretical Kinematics, The MIT Press.
8.
Huang
,
C.
,
1994
, “
On the Finite Screw System of the Third Order Associated with a Revolute-Revolute Chain
,”
ASME J. Mech. Des.
,
116
, pp.
875
883
.
9.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press.
10.
Parkin
,
I. A.
,
1992
, “
A Third Conformation with the Screw Systems: Finite Twist Displacements of a Directed Line and Point
,”
Mech. Mach. Theory
,
27
,
177
188
.
11.
Parkin, I. A., 1997, “Finding the Principal Axes of Screw Systems,” Proceedings of the ASME Design Engineering Technical Conferences, Sacramento, CA.
12.
Suh, C. H., and Radcliffe, C. W., 1978, Kinematics and Mechanisms Design, John Wiley & Sons.
13.
McCarthy, J. M., 2000, Geometric Design of Linkages, Springer-Verlag.
14.
Tsai, L. W., 1972, “Design of Open-Loop Chains for Rigid Body Guidance,” Stanford University Ph.D. dissertation.
15.
Yu
,
H. C.
,
1981
, “
The Bennett Linkage, its Associated Tetrahedron and the Hyperboloid of Its Axes
,”
Mech. Mach. Theory
,
16
, pp.
105
114
.
16.
Baker, J. E., 1998, “On the Motion Geometry of the Bennett Linkage,” Proc. 8th Internat. Conf. on Engineering Computer Graphics and Descriptive Geometry, Austin, Texas, Vol. 2, pp. 433–437.
17.
Huang
,
C.
, and
Sun
,
C.
,
2000
, “
An Investigation of Screw Systems in the Finite Displacements of Bennett-Based 6R Linkages
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
426
430
.
18.
Perez
,
A.
, and
McCarthy
,
J. M.
,
2002
, “
Bennett’s Linkage and the Cylindroid
,”
Mech. Mach. Theory
,
37
(
11
), pp.
1245
1260
.
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