This paper examines the problem of finding the assembly configurations (ACs), also called circuits, of spatial single-loop single-DOF mechanisms. All six lower pairs are considered: revolute (R), cylindric (C), prismatic (P), helical (H), spheric (S), and planar (E). The RSSR, CSS, RRSC, CCS, and RRSRR mechanisms are covered, along with all variations in which an R joint is replaced with a P or H joint, or an S joint is replaced with an E joint. The RRCRC, RRRCC, and RRRRCR mechanisms are covered, along with all appropriate variations in which an R joint is replaced by a P or H joint. A numerical method is given to find the ACs, and is illustrated with several examples.
Issue Section:
Research Papers
1.
Foster
, D. E.
, 1999, “Assembly Configurations of Planar Multi-Loop Mechanisms With Kinematic Limitations and Spatial Single-Loop Mechanisms
,” Ph.D. thesis, Purdue University, West Lafayette, IN.2.
Foster
, D. E.
, and Cipra
, R. J.
, 2002, “An Automatic Method for Finding the Assembly Configurations of Planar Non-Single-Input-Dyadic Mechanisms
,” ASME J. Mech. Des.
0161-8458, 124
(1
), pp. 58
–67
.3.
Hunt
, K. H.
, 1978, Kinematic Geometry of Mechanisms
, Oxford University Press
, Oxford
.4.
Foster
, D. E.
, and Cipra
, R. J.
, 1998, “Assembly Configurations of Spatial Single-Loop Mechanisms With Revolute, Cylindrical, and Prismatic Joints
,” Proceedings of the 1998 ASME Design Engineering Technical Conferences
, Atlanta, GA, Sept. 13–16, Paper No. MECH-5897.5.
Freudenstein
, F.
, and Kiss
, I. S.
, 1969, “Type Determination of Skew Four-Bar Mechanisms
,” ASME J. Eng. Ind.
0022-0817, 91
(1
), pp. 220
–224
.6.
Bottema
, O.
, 1971, “The Motion of the Skew Four-Bar
,” J. Mech.
0022-2569, 6
(1
), pp. 69
–79
.7.
Freudenstein
, F.
, and Primrose
, E. J. F.
, 1976, “On the Criteria for the Rotatability of the Cranks of a Skew Four-Bar Linkage
,” ASME J. Eng. Ind.
0022-0817, 98
(4
), pp. 1285
–1288
.8.
Lee
, K. -W.
, Seo
, Y. -J.
, and Yoon
, Y. -S.
, 1992, “Practical Mobility Conditions for RSSR Mechanism
,” Proceedings of the ASME Design Technical Conferences
, Vol. 47
, pp. 199
–206
.9.
Ting
, K. -L.
, and Dou
, X.
, 1994, “Branch, Mobility Criteria, and Classification of RSSR and Other Bimodal Linkages
,” Proceedings of the ASME Design Technical Conferences
, Vol. 70
, pp. 303
–310
.10.
Gupta
, V. K.
, and Radcliffe
, C. W.
, 1971, “Mobility Analysis of Plane and Spatial Mechanisms
,” ASME J. Eng. Ind.
0022-0817, 93
(1
), pp. 125
–130
.11.
Williams
, R. L.
, II, and Reinholtz
, C. F.
, 1987, “Mechanism Link Rotatability and Limit Position Analysis Using Polynomial Discriminants
,” ASME J. Mech., Transm., Autom. Des.
0738-0666, 109
(2
), pp. 178
–182
.12.
Lee
, D.
, Youm
, Y.
, and Chung
, W.
, 1996, “Mobility Analysis of Spatial 4- and 5-Link Mechanisms of the RS Class
,” Mech. Mach. Theory
0094-114X, 31
(5
), pp. 673
–690
.13.
Sandor
, G. N.
, and Zhaung
, X.
, 1984, “On the Elimination of the Branching Problems in the Synthesis of Spatial Motion Generators With Spheric Joints. Part 1: Theory
,” ASME J. Mech., Transm., Autom. Des.
0738-0666, 106
(3
), pp. 312
–318
.14.
Sandor
, G. N.
, Xu
, Y.
, and Weng
, T. -C.
, 1986, “Synthesis of 7-R Spatial Motion Generators With Prescribed Crank Rotations and Elimination of Branching
,” Int. J. Robot. Res.
0278-3649, 5
(2
), pp. 143
–156
.15.
Sandor
, G. N.
, Weng
, T. -C.
, and Xu
, Y.
, 1988, “The Synthesis of Spatial Motion Generators With Prismatic, Revolute and Cylindric Pairs Without Branching Defect
,” Mech. Mach. Theory
0094-114X, 23
(4
), pp. 269
–274
.16.
Rastegar
, J.
, 1989, “On the Derivation of Grashof-Type Movability Conditions With Transmission Angle Limitations for Spatial Mechanisms
,” ASME J. Mech., Transm., Autom. Des.
0738-0666, 111
(4
), pp. 519
–523
.17.
Cheng
, J. -C.
, and Kohli
, D.
, 1992, “Synthesis of Mechanisms Including Circuit Defects, Branch Defects and Input-Crank Rotatability
,” Proceedings of ASME Design Technical Conferences
, Vol. 46
, pp. 111
–119
.18.
Kohli
, D.
, Cheng
, J. -C.
, and Tsai
, K. Y.
, 1994, “Assemblability, Circuits, Branches, Locking Positions, and Rotatability of Input Links of Mechanisms With Four Closures
,” ASME J. Mech. Des.
0161-8458, 116
(1
), pp. 92
–98
.19.
Pamidi
, P. R.
, and Freudenstein
, F.
, 1975, “On the Motion of a Class of Five-Link, R-C-R-C-R, Spatial Mechanisms
,” ASME J. Eng. Ind.
0022-0817, 97
(1
), pp. 334
–339
.20.
Dou
, X.
, and Ting
, K. -L.
, 1996, “Classification, Rotatability and Branch Identification of Simple RCRCR Mechanisms
,” Proceedings of the 1996 ASME Design Engineering Technical Conferences
, Irvine, CA, Aug. 19–22, Paper No. FAS-1363.21.
Duffy
, J.
, 1980, Analysis of Mechanisms and Robot Manipulators
, Wiley
, New York
.22.
Wampler
, C. W.
, Morgan
, A. P.
, and Sommese
, A. J.
, 1990, “Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics
,” ASME J. Mech. Des.
0161-8458, 112
(1
), pp. 59
–68
.23.
Savage
, M.
, and Hall
, A. S.
, 1970, “Unique Descriptions of All Spherical Four-Bar Linkages
,” ASME J. Eng. Ind.
0022-0817, 91
, pp. 559
–563
.24.
Kohli
, D.
, and Khonji
, A.
, 1994, “Grashof-Type Rotatability Criteria of Spherical Five-Bar Linkages
,” ASME J. Mech. Des.
0161-8458, 116
(1
), pp. 99
–104
.25.
Kohli
, D.
, 1992, “Rotatability Laws for Spherical N-Bar Chains
,” Proceedings of the ASME Design Technical Conferences
, Vol. 47
, pp. 629
–637
.26.
Liu
, Y. -W.
, and Ting
, K. -L.
, 1994, “On the Rotatability of Spherical N-Bar Chains
,” ASME J. Mech. Des.
0161-8458, 116
(3
), pp. 920
–923
.27.
Reinholtz
, C. F.
, Sandor
, G. N.
, and Duffy
, J.
, 1986, “Branching Analysis of Spherical RRRR and Spatial RCCC Mechanisms
,” ASME J. Mech., Transm., Autom. Des.
0738-0666, 108
(4
), pp. 481
–486
.28.
Chase
, T. R.
, and Mirth
, J. A.
, 1993, “Circuits and Branches of Single-Degree-of-Freedom Planar Linkages
,” ASME J. Mech. Des.
0161-8458, 115
(2
), pp. 223
–230
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.