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.
Issue Section:
Technical Papers
Keywords:
manipulator kinematics
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
.Copyright © 2003
by ASME
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