This paper presents a new method to determine if two task positions used to design a four-bar linkage lie on separate assembly modes (circuits) of a coupler curve, known as an “assembly mode defect.” The proposed approach uses the image space of a kinematic mapping to provide a geometric environment for both the synthesis and analysis of four-bar linkages. The devised algorithm allows assembly mode decisions at an early design stage without resorting to the mechanism dimensions. The numerical effort is low compared to existing solutions.
1.
Waldron
, K. J.
and Stevenson
, E. N.
, Jr., 1979, “Elimination of Branch, Grashof and Order Defects in Path-Angle Generation and Function Generation Synthesis
,” ASME J. Mech. Des.
0161-8458, 101
, pp. 428
–437
.2.
Gupta
, K. C.
, 1980, “Synthesis of Position, Path and Function Generating 4-Bar Mechanisms With Completely Rotatable Driving Links
,” Mech. Mach. Theory
0094-114X, 15
, pp. 93
–101
.3.
Prentis
, J. M.
, 1991, “The Pole Triangle, Burmester Theory and Order and Branching Problems II: The Branching Problem
,” Mech. Mach. Theory
0094-114X, 26
(1
), pp. 31
–39
.4.
Schaefer
, R. S.
, and Kramer
, S. N.
, 1979, “Selective Precision Synthesis of Planar Mechanisms Satisfying Position and Velocity Constraints
,” Mech. Mach. Theory
0094-114X, 14
(3
), pp. 161
–170
.5.
DaLio
, M.
, Cossalter
, V.
, and Lot
, R.
, 2000, “On the Use of Natural Coordinates in Optimal Synthesis of Mechanisms
,” Mech. Mach. Theory
0094-114X, 35
, pp. 1367
–1389
.6.
Blaschke
, W.
, 1911, “Euklidische Kinematik und nichteuklidische Geometrie
,” Zeitschr. Math. Phys.
, 60
, pp. 61
–91
, 203–204.7.
Grünwald
, J.
, 1911, “Ein Abbildungsprinzip, welches die ebene Geometrie und Kinematik mit der räumlichen Geometrie Verknüpft
,” Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Kl., Abt. 2A
0376-2629, 120
, pp. 667
–741
.8.
Bottema
, O.
, and Roth
, B.
, 1990, Theoretical Kinematics
, Dover
New York, NY
.9.
Ravani
, B.
, and Roth
, B.
, 1983, “Motion Synthesis Using Kinematic Mapping
,” ASME J. Mech., Transm., Autom. Des.
0738-0666, 105
(3
), pp. 460
–467
.10.
Hayes
, M. J. D.
, and Zsombor-Murray
, P. J.
, 2002, “Solving the Burmester Problem Using Kinematic Mapping
,” Proceedings of ASME DECT’02
, Montreal
, Canada
, Sept. 29–Oct. 2.11.
Perez
, A.
, and McCarthy
, J. M.
, 2005, “Clifford Algebra Exponentials and Planar Linkage Synthesis Equations
,” ASME J. Mech. Des.
1050-0472, 127
(5
), pp. 931
–940
.12.
Brunnthaler
, K.
, Pfurner
, M.
, and Husty
, M.
, 2005, “Synthesis of Planar Four-Bar Mechanisms
,” Proceedings of MUSME 2005, the International Symposium on Multibody Systems and Mechatronics
, Uberlândia
, Brazil
, 6–9 March.13.
Mirth
, J. A.
and Chase
, T. R.
, 1993, “Circuits and Branches of Single-Degree-Of Freedom Planar Linkages
,” ASME J. Mech. Des.
1050-0472, 115
, pp. 223
–230
.14.
Waldron
, K. J.
, 1976, “Elimination of the Branch Problem in Graphical Burmester Mechanism Synthesis for Four Finitely Separated Positions
,” ASME J. Eng. Ind.
0022-0817, 98
(1
), pp. 176
–182
.15.
Waldron
, K. J.
, and Strong
, R. T.
, 1978, “Improved Solutions of the Branch and Order Problems of Burmester Linkage Systems
,” Mech. Mach. Theory
0094-114X, 13
, pp. 199
–207
.16.
Tu
, C.
, Wang
, W.
, and Wang
, J.
, 2002, “Classifying the Morphology of the Nonsingular Intersection Curve of Two Quadric Surfaces
,” Proceedings of Geometric Modeling and Processing, Theory and Applications
, H.
Suzuki
and R.
Martin
, eds., IEEE Computer Society
, Tokyo, pp. 23
–32
.17.
Tu
, C.
, Wang
, W.
, Mourrain
, B.
, and Wang
, J.
, 2005, “Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
,” University of Hong Kong, Hong Kong, HKU CS Tech Report No. TR-2005-09.18.
Sommerville
, D. M. Y.
, 1934, Analytical Geometry of Three Dimensions
, Cambridge University Press
, London
.19.
Schröcker
, H.-P.
, Husty
, M.
, and McCarthy
, J. M.
, 2005, “Kinematic Mapping Based Evaluation of Assembly Modes for Planar Four-Bar Synthesis
,” Proceedings of ASME 2005 29th Mechanisms and Robotics Conference
, Long Beach, CA
, Sept. 24–28.20.
Erdman
, A. G.
, Sandor
, G. N.
, and Kota
, S.
, 2001, Mechanism Design: Analysis and Synthesis
, 4th Ed., Vol. 1
, Prentice Hall
, Englewood Cliffs, NJ
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.