This paper addresses the assembly strategy capable of deriving a family of overconstrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of overconstrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of overconstrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer-aided design (CAD) software and their mobility were validated with input–output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of overconstrained mechanisms.
Issue Section:
Design of Mechanisms and Robotic Systems
References
1.
Grubler
, M.
, 1917
, Getriebelehre: Eine Theorie Des Zwanglaufes Und Der Ebenen Mechanismen
, Springer
, Berlin
.2.
Kutzbach
, K.
, 1929
, “Mechanische Leitungsverzweigung, Ihre Gesetze Und Anwendungen
,” Maschinenbau-Betr.
, 8
(21), pp. 710
–716
.3.
Sarrus
, P. T.
, 1853
, “Note Sur La Transformation Des Mouvements Rectilignes Alternatifs, Enmouvements Circulaires, Et Reciproquement
,” Acad. Des. Sci.
, 36
, pp. 1036
–1038
.4.
Bennett
, G. T.
, 1903
, “A New Mechanism,” Engineering
, 76
, pp. 777
–778
.5.
Bennett
, G. T.
, 1905
, “The Parallel Motion of Sarrus and Some Allied Mechanisms
,” Philos. Mag.
, 9
, pp. 803
–810
.6.
Delassus
, E.
, 1922
, “Les Chaînes Articulées Fermées Et Déformables à Quatre Membres
,” Bull. Sci. Math.
, 46
, pp. 283
–304
.7.
Bricard
, R.
, 1927
, Leçons De Cinématique
, Vol. 2
, Gauthier-Villars
, Villars, Paris, pp. 7
–12
.8.
Myard
, F. E.
, 1931
, “Contribution à La Géométrie Des Systèmes Articulés
,” Bull. Soc. Math. France
, 59
, pp. 183
–210
.9.
Myard
, F. E.
, 1931
, “Sur Les Chaines Fermees a Quatre Couples Rotoides Nonconcourants, Deformables Au Permier Degre De Liberte. Isogramme Torique
,” Comptes Rendus Hebdomadaires Des Stances De I'Acadimie De Science
, Vol. 192
, Paris, pp. 1194
–1196
.10.
Goldberg
, M.
, 1943
, “New Five-Bar and Six-Bar Linkages in Three Dimensions
,” Trans. ASME
, 65
(1), pp. 649
–656
.11.
Franke
, R.
, 1951
, Vom Aufbau Der Getriebe
, Deutscher Ingenieur
, Düsseldorf, Germany
, pp. 97
–106
.12.
Altmann
, P. G.
, Grodzinski
, P.
, and M'Ewen
, E.
, 1954
, “Link Mechanisms in Modern Kinematics
,” Proc. Inst. Mech. Eng.
, 168
(37
), pp. 889
–896
.13.
Harrisberger
, L.
, and Soni
, A. H.
, 1966
, “A Survey of Three Dimensional Mechanisms With One General Constraint,” ASME Paper No. 66-MECH-44.14.
Dimentberg
, F. M.
, and Yoslovich
, I. V.
, 1966
, “A Spatial Four-Link Mechanism Having Two Prismatic Pairs
,” J. Mech.
, 1
(3–4
), pp. 291
–300
.15.
Waldron
, K. J.
, 1969
, “The Mobility of Linkages,” Doctoral dissertation, Stanford University, Stanford, CA.16.
Pamidi
, P. R.
, Soni
, A. H.
, and Dukkipati
, R. V.
, 1973
, “Necessary and Sufficient Existence Criteria of Over-Constrained Five-Link Spatial Mechanisms With Helical, Cylinder, Revolute, and Prism Pairs
,” J. Eng. Ind.
, 95
(3
), pp. 737
–743
.17.
Waldron
, K. J.
, 1968
, “Hybrid Over-Constrained Linkages
,” J. Mech.
, 3
(2
), pp. 73
–78
.18.
Wohlhart
, K.
, 1987
, “A New 6R Space Mechanism
,” Seventh World Congress on the Theory of Machines and Mechanisms
, Sevilla, Spain, Sept. 17–22, pp. 193
–198
.19.
Wohlhart
, K.
, 1991
, “Merging Two General Goldberg 5R Linkages to Obtain a New 6R Space Mechanism
,” Mech. Mach. Theory
, 26
(2
), pp. 659
–668
.20.
Lee
, C. C.
, and Yan
, H. S.
, 1990
, “Movable Spatial 6R Mechanisms With Three Adjacent Concurrent Axes
,” Trans. Can. Soc. Mech. Eng.
, 14
(3
), pp. 85
–90
.21.
Lee
, C. C.
, and Yan
, H. S.
, 1993
, “Movable Spatial 6R Mechanisms With Three Adjacent Parallel Axes
,” ASME J. Mech. Des.
, 115
(3
), pp. 522
–529
.22.
Mavroidis
, C.
, and Roth
, B.
, 1995
, “New and Revised Over-Constrained Mechanisms
,” Trans. ASME
, 117
(1
), pp. 75
–82
.23.
Mavroidis
, C.
, and Roth
, B.
, 1995
, “Analysis of Over-Constrained Mechanisms
,” ASME J. Mech. Des.
, 117
(1
), pp. 69
–74
.24.
Dietmeier
, P.
, 1995
, “A New 6R Space Mechanism
,” Ninth World Congress on the Theory of Machines and Mechanisms
, Milano, Italy, Aug. 29–Sept. 2, pp. 52
–56
.25.
Schatz
, P.
, 1998
, Rhythmusforschung Und Technik
, Verlag Freies Geistesleben
, Stuttgart, Germany
.26.
Alizade
, R. I.
, Selvi, O., and Gezgin, E., 2010
, “Structural Design of Parallel Manipulators With General Constraint One
,” Mech. Mach. Theory
, 45
(1), pp. 1–14.27.
Li
, Z.
, and Schicho
, J.
, 2013
, “Classification of Angle-Symmetric 6R Linkages
,” Mech. Mach. Theory
, 70
, pp. 372
–379
.28.
Baker
, J. E.
, 1978
, “Over-Constrained Five-Bars With Parallel Adjacent Joint Axes—I: Method of Analysis
,” Mech. Mach. Theory
, 13
(2
), pp. 213
–218
.29.
Baker
, J. E.
, 1978
, “Over-Constrained Five-Bars With Parallel Adjacent Joint Axes—II the Linkages
,” Mech. Mach. Theory
, 13
(2
), pp. 219
–233
.30.
Baker
, J. E.
, 1978
, “An Over-Constrained Five-Bar With a Plane of Quasi-Symmetry
,” Mech. Mach. Theory
, 13
(4
), pp. 467
–473
.31.
Baker
, J. E.
, 1981
, “The S-H-H-H- Linkage
,” Mech. Mach. Theory
, 16
(6
), pp. 599
–609
.32.
Baker
, J. E.
, 1982
, “On Completing the Determination of Existence Criteria for Over-Constrained 4-Bars With Helical Joints
,” Mech. Mach. Theory
, 17
(2
), pp. 133
–142
.33.
Baker
, J. E.
, 1989
, “Over-Constrained Five-Bars With Prismatic Joints and Parallel Adjacent Joint Axes
,” Mech. Mach. Theory
, 24
(4
), pp. 267
–273
.34.
Baker
, J. E.
, 1996
, “On 5-Revolute Linkages With Intersecting Adjacent Joint Axes
,” Mech. Mach. Theory
, 31
(8
), pp. 1167
–1183
.35.
Baker
, J. E.
, 1996
, “Overconstrained Six-Bars With Parallel Adjacent Joint-Axes
,” Mech. Mach. Theory
, 38
(11
), pp. 1323
–1323
.36.
Baker
, J. E.
, 2004
, “Curious New Family of Overconstrained Six-Bars
,” ASME J. Mech. Des.
, 127
(4
), pp. 602
–606
.37.
Mueller
, A.
, 2007
, “Generic Mobility of Rigid Body Mechanisms: On the Existence of Overconstrained Mechanisms,” ASME
Paper No. DETC2007-34621.38.
Pfurner
, M.
, 2008
, “A New Family of Overconstrained 6R-Mechanisms
,” Second European Conference on Mechanism Science
, Cassino, Italy, Sept. 17–20, pp. 117
–124
.39.
Fang
, Y. F.
, and Tsai
, L. W.
, 2004
, “Enumeration of a Class of Over-Constrained Mechanisms Using the Theory of Reciprocal Screws
,” Mech. Mach. Theory
, 39
(11
), pp. 1175
–1187
.40.
Liu
, J.
, Li
, Y.
, and Huang
, Z.
, 2011
, “Mobility Analysis of Altmann Over-Constrained Linkages by Modified Grubler-Kutzbach Criterion
,” Chin. J. Mech. Eng.
, 24
(4
), pp. 638
–646
.41.
Hegedüs
, G.
, Schicho
, J.
, and Schröcker
, H. P.
, 2013
, “The Theory of Bonds: A New Method for the Analysis of Linkages,” Mech. Mach. Theory
, 70, pp. 407
–424
.42.
Li
, Z.
, Schicho
, J.
, and Schröcker
, H. P.
, 2016
, “A Survey on the Theory of Bonds
,” IMA J. Math. Control Inf.
, epub.43.
Gallet
, M.
, Koutschan
, C.
, Li
, Z.
, Regensburger
, G.
, Schicho
, J.
, and Villamizar
, N.
, 2017
, “Planar Linkages Following a Prescribed Motion,” Math. Comput.
, 86(303), pp. 473
–506
.44.
Baker
, J. E.
, 1979
, “The Bennett, Goldberg and Myard Linkages—In Perspective
,” Mech. Mach. Theory
, 14
(4
), pp. 239
–253
.45.
Baker
, J. E.
, 1980
, “An Analysis of the Bricard Linkages
,” Mech. Mach. Theory
, 15
(4
), pp. 267
–286
.46.
Yu
, H. C.
, and Baker
, J. E.
, 1981
, “On the Generation of New Linkages From Bennett Loops
,” Mech. Mach. Theory
, 16
(5
), pp. 473
–485
.47.
Baker
, J. E.
, 1993
, “A Comparative Survey of the Bennett-Based, 6-Revolute Kinematic Loops
,” Mech. Mach. Theory
, 28
(1
), pp. 83
–96
.48.
Baker
, J. E.
, 1993
, “A Geometrico-Algebraic Exploration of Altmann's Linkage
,” Mech. Mach. Theory
, 28
(2
), pp. 249
–260
.49.
Baker
, J. E.
, 1995
, “On Bricard's Doubly Collapsible Octahedron and Its Planar, Spherical and Skew Counterparts
,” J. Franklin Inst.
, 332
(6
), pp. 657
–679
.50.
Lee
, C. C.
, 1996
, “On the Simple Stationary Configurations of Single-Loop Spatial N-Revolute Over-Constrained Linkages
,” Trans.-Can. Soc. Mech. Eng.
, 20
(1
), pp. 17
–39
.51.
Chen
, Y.
, and Baker
, J. E.
, 2005
, “Using a Bennett Linkage as a Connector Between Other Bennett Loops
,” Proc. Inst. Mech. Eng., J. Multi-Body Dyn.
, 219
(2
), pp. 177
–185
.52.
Chen
, Y.
, You
, Z.
, and Tarnai
, T.
, 2005
, “Threefold-Symmetric Bricard Linkages for Deployable Structures
,” Int. J. Solids Struct.
, 42
(8
), pp. 2287
–2301
.53.
Chen
, Y.
, and You
, Z.
, 2007
, “Spatial 6R Linkages Based on the Combination of Two Goldberg 5R Linkages
,” Mech. Mach. Theory
, 42
(11
), pp. 1484
–1498
.54.
Chen
, Y.
, and You
, Z.
, 2008
, “On Mobile Assemblies of Bennett Linkages
,” Proc. R. Soc. A
, 464
(2093
), pp. 1275
–1293
.55.
Chen
, Y.
, and You
, Z.
, 2009
, “An Extended Myard Linkage and Its Derived 6R Linkage
,” ASME J. Mech. Des.
, 130
(5
), p. 052301
.56.
Liu
, S. Y.
, and Chen
, Y.
, 2009
, “Myard Linkage and Its Mobile Assemblies
,” Mech. Mach. Theory
, 44
(10
), pp. 1950
–1963
.57.
Chai
, W. H.
, and Chen
, Y.
, 2010
, “The Line-Symmetric Octahedral Bricard Linkage and Its Structural Closure
,” Mech. Mach. Theory
, 45
(5
), pp. 772
–779
.58.
Chen
, Y.
, and Chai
, W. H.
, 2011
, “Bifurcation of a Special Line and Plane Symmetric Bricard Linkage
,” Mech. Mach. Theory
, 46
(4
), pp. 515
–533
.59.
Song
, C. Y.
, and Chen
, Y.
, 2011
, “A Family of Mixed Double-Goldberg 6R Linkages
,” Proc. R. Soc. A: Math., Phys. Eng. Sci.
, 468
(2139
), pp. 871
–890
.60.
Song
, C. Y.
, and Chen
, Y.
, 2011
, “A Spatial 6R Linkage Derived From Subtractive Goldberg 5R Linkages
,” Mech. Mach. Theory
, 46
(8
), pp. 1097
–1106
.61.
Song
, C. Y.
, and Chen
, Y.
, 2012
, “Multiple Linkage Forms and Bifurcation Behaviours of the Double-Subtractive-Goldberg 6R Linkage
,” Mech. Mach. Theory
, 57
, pp. 95
–110
.62.
Song
, C. Y.
, Chen
, Y.
, and Chen
, I. M.
, 2013
, “A 6R Linkage Reconfigurable Between the Line-Symmetric Bricard Linkage and the Bennett Linkage
,” Mech. Mach Theory
, 70
, pp. 278
–292
.63.
Song
, C. Y.
, Feng
, H. J.
, Chen
, Y.
, Chen
, I.-M.
, and Kanga
, R.
, 2015
, “Reconfigurable Mechanism Generated From the Framework of Bennett Linkages
,” Mech. Mach. Theory
, 88
, pp. 49
–62
.64.
Baker
, J. E.
, 1978
, “On Coaxial Screws in Spatial Linkages
,” Mech. Mach. Theory
, 13
(3
), pp. 345
–349
.65.
Lee
, C. C.
, 1995
, “Kinematic Analysis and Dimensional Synthesis of Bennett 4R Mechanism
,” JSME Int. J., Ser. C
, 38
(1
), pp. 199
–207
.66.
Lee
, C. C.
, 1995
, “On the Synthesis of Movable Spatial 6R Linkages From Movable 4R Chains
,” J. Appl. Mech. Rob.
, 2
(2
), pp. 42
–49
.67.
Lee
, C. C.
, 1996
, “Kinematic Analysis and Dimensional Synthesis of General-Type Sarrus Mechanism
,” JSME Int. J., Ser. C
, 39
(4
), pp. 790
–799
.68.
Huang
, C.
, and Sun
, C. 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
.69.
Pfurner
, M.
, Kong
, X.
, and Huang
, C.
, 2014
, “Complete Kinematic Analysis of Single-Loop Multiple-Mode 7-Link Mechanisms Based on Bennett and Overconstrained RPRP Mechanisms
,” Mech. Mach. Theory
, 73
, pp. 117
–129
.70.
Kong
, X.
, 2015
, “Kinematic Analysis of a 6R Single-Loop Overconstrained Spatial Mechanism for Circular Translation
,” Mech. Mach. Theory
, 93
, pp. 163
–174
.71.
Zhang
, K.
, and Dai
, J. S.
, 2014
, “Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms
,” ASME J. Mech. Des.
, 136
(5
), p. 051003
.72.
Shen
, H.
, Huang
, H.
, and Ji
, T.
, 2015
, “Normalized-Constrained Approach for Joint Clearance Design of Deployable Overconstrained Myard 5R Mechanism
,” J. Adv. Mech. Des., Syst., Manuf.
, 9
(5
), p. JAMDSM0064
.73.
Huang
, C.
, and Tu
, H.-T.
, 2005
, “Linear Property of the Screw Surface of the Spatial RPRP Mechanism
,” ASME J. Mech. Des.
, 128
(3
), pp. 581
–586
.74.
Lu
, Y.
, 2004
, “Using CAD Functionalities for the Kinematics Analysis of Spatial Parallel Manipulators With 3-, 4-, 5-, 6-Linearly Driven Limbs
,” Mech. Mach. Theory
, 39
(1
), pp. 41
–60
.75.
Kinzel
, E. C.
, Schmiedeler
, J. P.
, and Pennock
, G. R.
, 2005
, “Kinematic Synthesis for Finitely Separated Positions Using Geometric Constraint Programming
,” ASME J. Mech. Des.
, 128
(5
), pp. 1070
–1079
.Copyright © 2018 by ASME
You do not currently have access to this content.
