0
Research Papers: Design of Mechanisms and Robotic Systems

Overconstrained Mechanisms Derived From RPRP Loops

[+] Author and Article Information
Kuan-Lun Hsu

Mechanical Engineering Department,
Tennessee Technological University,
Cookeville, TN 38505
e-mail: kuanlunhsu@outlook.com

Kwun-Lon Ting

Professor
Mechanical Engineering Department,
Tennessee Technological University,
Cookeville, TN 38505

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 4, 2017; final manuscript received February 15, 2018; published online March 23, 2018. Assoc. Editor: David Myszka.

J. Mech. Des 140(6), 062301 (Mar 23, 2018) (9 pages) Paper No: MD-17-1539; doi: 10.1115/1.4039449 History: Received August 04, 2017; Revised February 15, 2018

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Grubler, M. , 1917, Getriebelehre: Eine Theorie Des Zwanglaufes Und Der Ebenen Mechanismen, Springer, Berlin.
Kutzbach, K. , 1929, “Mechanische Leitungsverzweigung, Ihre Gesetze Und Anwendungen,” Maschinenbau-Betr., 8(21), pp. 710–716.
Sarrus, P. T. , 1853, “Note Sur La Transformation Des Mouvements Rectilignes Alternatifs, Enmouvements Circulaires, Et Reciproquement,” Acad. Des. Sci., 36, pp. 1036–1038.
Bennett, G. T. , 1903, “A New Mechanism,” Engineering, 76, pp. 777–778.
Bennett, G. T. , 1905, “The Parallel Motion of Sarrus and Some Allied Mechanisms,” Philos. Mag., 9, pp. 803–810. [CrossRef]
Delassus, E. , 1922, “Les Chaînes Articulées Fermées Et Déformables à Quatre Membres,” Bull. Sci. Math., 46, pp. 283–304.
Bricard, R. , 1927, Leçons De Cinématique, Vol. 2, Gauthier-Villars, Villars, Paris, pp. 7–12.
Myard, F. E. , 1931, “Contribution à La Géométrie Des Systèmes Articulés,” Bull. Soc. Math. France, 59, pp. 183–210. [CrossRef]
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.
Goldberg, M. , 1943, “New Five-Bar and Six-Bar Linkages in Three Dimensions,” Trans. ASME, 65(1), pp. 649–656.
Franke, R. , 1951, Vom Aufbau Der Getriebe, Deutscher Ingenieur, Düsseldorf, Germany, pp. 97–106.
Altmann, P. G. , Grodzinski, P. , and M'Ewen, E. , 1954, “Link Mechanisms in Modern Kinematics,” Proc. Inst. Mech. Eng., 168(37), pp. 889–896.
Harrisberger, L. , and Soni, A. H. , 1966, “A Survey of Three Dimensional Mechanisms With One General Constraint,” ASME Paper No. 66-MECH-44.
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. [CrossRef]
Waldron, K. J. , 1969, “The Mobility of Linkages,” Doctoral dissertation, Stanford University, Stanford, CA.
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. [CrossRef]
Waldron, K. J. , 1968, “Hybrid Over-Constrained Linkages,” J. Mech., 3(2), pp. 73–78. [CrossRef]
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.
Wohlhart, K. , 1991, “Merging Two General Goldberg 5R Linkages to Obtain a New 6R Space Mechanism,” Mech. Mach. Theory, 26(2), pp. 659–668. [CrossRef]
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.
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. [CrossRef]
Mavroidis, C. , and Roth, B. , 1995, “New and Revised Over-Constrained Mechanisms,” Trans. ASME, 117(1), pp. 75–82. [CrossRef]
Mavroidis, C. , and Roth, B. , 1995, “Analysis of Over-Constrained Mechanisms,” ASME J. Mech. Des., 117(1), pp. 69–74. [CrossRef]
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.
Schatz, P. , 1998, Rhythmusforschung Und Technik, Verlag Freies Geistesleben, Stuttgart, Germany.
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.
Li, Z. , and Schicho, J. , 2013, “Classification of Angle-Symmetric 6R Linkages,” Mech. Mach. Theory, 70, pp. 372–379.
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. [CrossRef]
Baker, J. E. , 1978, “Over-Constrained Five-Bars With Parallel Adjacent Joint Axes—II the Linkages,” Mech. Mach. Theory, 13(2), pp. 219–233. [CrossRef]
Baker, J. E. , 1978, “An Over-Constrained Five-Bar With a Plane of Quasi-Symmetry,” Mech. Mach. Theory, 13(4), pp. 467–473. [CrossRef]
Baker, J. E. , 1981, “The S-H-H-H- Linkage,” Mech. Mach. Theory, 16(6), pp. 599–609. [CrossRef]
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. [CrossRef]
Baker, J. E. , 1989, “Over-Constrained Five-Bars With Prismatic Joints and Parallel Adjacent Joint Axes,” Mech. Mach. Theory, 24(4), pp. 267–273. [CrossRef]
Baker, J. E. , 1996, “On 5-Revolute Linkages With Intersecting Adjacent Joint Axes,” Mech. Mach. Theory, 31(8), pp. 1167–1183. [CrossRef]
Baker, J. E. , 1996, “Overconstrained Six-Bars With Parallel Adjacent Joint-Axes,” Mech. Mach. Theory, 38(11), pp. 1323–1323. [CrossRef]
Baker, J. E. , 2004, “Curious New Family of Overconstrained Six-Bars,” ASME J. Mech. Des., 127(4), pp. 602–606. [CrossRef]
Mueller, A. , 2007, “Generic Mobility of Rigid Body Mechanisms: On the Existence of Overconstrained Mechanisms,” ASME Paper No. DETC2007-34621.
Pfurner, M. , 2008, “A New Family of Overconstrained 6R-Mechanisms,” Second European Conference on Mechanism Science, Cassino, Italy, Sept. 17–20, pp. 117–124.
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. [CrossRef]
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. [CrossRef]
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.
Li, Z. , Schicho, J. , and Schröcker, H. P. , 2016, “A Survey on the Theory of Bonds,” IMA J. Math. Control Inf., epub.
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.
Baker, J. E. , 1979, “The Bennett, Goldberg and Myard Linkages—In Perspective,” Mech. Mach. Theory, 14(4), pp. 239–253. [CrossRef]
Baker, J. E. , 1980, “An Analysis of the Bricard Linkages,” Mech. Mach. Theory, 15(4), pp. 267–286. [CrossRef]
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. [CrossRef]
Baker, J. E. , 1993, “A Comparative Survey of the Bennett-Based, 6-Revolute Kinematic Loops,” Mech. Mach. Theory, 28(1), pp. 83–96. [CrossRef]
Baker, J. E. , 1993, “A Geometrico-Algebraic Exploration of Altmann's Linkage,” Mech. Mach. Theory, 28(2), pp. 249–260. [CrossRef]
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. [CrossRef]
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.
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.
Chen, Y. , You, Z. , and Tarnai, T. , 2005, “Threefold-Symmetric Bricard Linkages for Deployable Structures,” Int. J. Solids Struct., 42(8), pp. 2287–2301. [CrossRef]
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. [CrossRef]
Chen, Y. , and You, Z. , 2008, “On Mobile Assemblies of Bennett Linkages,” Proc. R. Soc. A, 464(2093), pp. 1275–1293. [CrossRef]
Chen, Y. , and You, Z. , 2009, “An Extended Myard Linkage and Its Derived 6R Linkage,” ASME J. Mech. Des., 130(5), p. 052301. [CrossRef]
Liu, S. Y. , and Chen, Y. , 2009, “Myard Linkage and Its Mobile Assemblies,” Mech. Mach. Theory, 44(10), pp. 1950–1963. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Baker, J. E. , 1978, “On Coaxial Screws in Spatial Linkages,” Mech. Mach. Theory, 13(3), pp. 345–349. [CrossRef]
Lee, C. C. , 1995, “Kinematic Analysis and Dimensional Synthesis of Bennett 4R Mechanism,” JSME Int. J., Ser. C, 38(1), pp. 199–207.
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.
Lee, C. C. , 1996, “Kinematic Analysis and Dimensional Synthesis of General-Type Sarrus Mechanism,” JSME Int. J., Ser. C, 39(4), pp. 790–799.
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. [CrossRef]
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. [CrossRef]
Kong, X. , 2015, “Kinematic Analysis of a 6R Single-Loop Overconstrained Spatial Mechanism for Circular Translation,” Mech. Mach. Theory, 93, pp. 163–174. [CrossRef]
Zhang, K. , and Dai, J. S. , 2014, “Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms,” ASME J. Mech. Des., 136(5), p. 051003. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

A folded RPRP loop

Grahic Jump Location
Fig. 2

An unfolded RPRP loop

Grahic Jump Location
Fig. 3

Assembly configuration of two folded RPRP loops

Grahic Jump Location
Fig. 4

A 2R-3P mechanism by combining two folded RPRP loops

Grahic Jump Location
Fig. 5

A 3R-2P mechanism by combining two folded RPRP loops

Grahic Jump Location
Fig. 6

Assembly configuration of three folded RPRP loops

Grahic Jump Location
Fig. 7

A 3R-3P mechanism by combining three folded RPRP loops

Grahic Jump Location
Fig. 8

Assembly configuration of a folded and an unfolded RPRP loop

Grahic Jump Location
Fig. 9

A 2R-3P mechanism by combining a folded and an RPRP loop

Grahic Jump Location
Fig. 10

Assembly configuration of two unfolded RPRP loops

Grahic Jump Location
Fig. 11

A 3R-2P mechanism by combining two unfolded RPRP loops

Grahic Jump Location
Fig. 12

A 2R-3P mechanism by combining two unfolded RPRP loops

Grahic Jump Location
Fig. 13

Assembly configuration of three unfolded RPRP loops

Grahic Jump Location
Fig. 14

A 3R-3P mechanism by combining three unfolded RPRP loops

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In