0
TECHNICAL PAPERS

On Mobility Analysis of Linkages Using Group Theory

[+] Author and Article Information
José Marı́a Rico Martı́nez

Instituto Tecnológico de Celaya, Dept. de Ingenierı́a Mecánica Celaya, Gto. 38000, Méxicoe-mail: mrico@itc.mx

Bahram Ravani

Dept. of Mechanical and Aeronautical Engineering, University of California, Davis, Davis, CA 95616e-mail: bravani@ucdavis.edu

J. Mech. Des 125(1), 70-80 (Mar 21, 2003) (11 pages) doi:10.1115/1.1541628 History: Received November 01, 2001; Revised August 01, 2002; Online March 21, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kuznetsov, E. N., 1991, Underconstrained Structural Systems, New York: Springer Verlag.
Chebyshev, P. L., 1869, “On Parallelograms,” Collected Works, in Russian, Moscow, 1955, pp. 664–669.
Sylvester, J. J., 1870–73, “On Recent Discoveries in the Mechanical Conversion of Motion,” Collected Mathematical Papers, Vol. 3, pp. 7–25.
Grübler,  M., 1883, “Allgemeine Eigenschaften der zwangläufigen ebenen kinematische kette: I,” Civilingenieur, 29, pp. 167–200.
Grübler,  M., 1885, “Allgemeine Eigenschaften der zwangläufigen ebenen kinematische kette: II,” Verein zur Beforderung des Gewerbefleisses. Verhandlungen, 64, pp. 179–223.
Somov,  P. O., 1887, “On the Degree of Freedom of the Motion of Kinematic Chains,” J. Phys. Chem. Soc. of Russia 19, 9 , pp. 7–25.
Kutzbach,  K., 1933, “Einzelfragen aus dem Gebiet der Maschinenteile,” Zeitschrift der Verein Deutscher Ingenieur, 77 , pp. 1168.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms., Oxford University Press, Oxford.
Hervé,  J. M., 1978, “Analyse Structurelle des Mécanismes par Groupe des Déplacements,” Mech. Mach. Theory, 13, pp. 437–450.
Bottema,  O., 1950, “On Gruebler’s Formulae for Mechanisms,” Appl. Sci. Res., Sect. A, A2, pp. 162–164.
Freudenstein, F., and Alizade, R., 1975, “On the Degree of Freedom of Mechanisms with Variable General Constraint,” Proceedings of the Fourth World Congress on the Theory of Machines and Mechanisms, London, The Institution of Mechanical Engineers, pp. 51–55.
Bagci, C., 1988, “Determining General and Overclosing Constraints in Mechanism Mobility Using Structural Finite Element Joint Freedoms,” Proceedings of the ASME 20th Mechanisms Conference, Vol. 15-1, Trends and Developments in Mechanisms, Machines and Robotics, New York, American Society of Mechanical Engineers, pp. 27–36.
Sarrus,  P., 1853, “Note sur Transformation des Mouvements Rectilignes Alternatifs, en Mouvements Circularies; et Reciproquement,” Comptes Rendus, Acad, Sci, Paris, 36, pp. 1036–1038.
Bennett,  G. T., 1903, “A New Mechanism,” Engineering, 76, pp. 777–778.
Bricard, R., 1927, Lecons de Cinématique, Vol. II., Gauthier-Villars, Paris.
Myard,  F. E., 1931, “Sur les Chaı⁁nes Fermées à Quatre Couples Rotoides non Concourants, Déformables au Premier Degré de Liberté. Isogramme Torique,” Comptes Rendus, Acad. Sci. Paris, 192, pp. 1194–1196.
Goldberg,  M., 1943, “New Five-bars and Six-bars Linkages in Three Dimensions,” Trans. ASME, 65, pp. 649–661.
Dimentberg, F. M., and Yoslovich, I. V., 1966, “A Spatial Four-link Mechanism Having Two Prismatic Pairs,” Journal of Mechanisms 1 , pp. 291–300. (English translation by C. W. McLarnan).
Hunt, K. H., 1967, “Prismatic Pairs in Spatial Linkages,” Journal of Mechanisms 2 , pp. 213–230.
Waldron,  K. J., 1973, “A Study of Overconstrained Linkage Geometry by Solution of Closure Equations-Part I. Method of Study,” Mech. Mach. Theory, 8, pp. 95–104.
Waldron,  K. J., 1973, “A Study of Overconstrained Linkage Geometry by Solution of Closure Equations-Part II. Four-bar Linkages with Lower Pair Joints other than Screw Joints,” Mech. Mach. Theory, 8, pp. 233–247.
Baker,  J. E., 1979, “A Compendium of Line-Symmetric Four-Bars,” ASME J. Mech. Des., 101, pp. 509–514.
Baker,  J. E., 1979, “The E-H-H-H-Linkage,” Mech. Mach. Theory, 14, pp. 361–372.
Baker,  J. E., 1981, “The S-H-H-H-Linkage,” Mech. Mach. Theory, 16, pp. 599–609.
Baker,  J. E., 1982, “On Completing the Determination of Existence Criteria for Overconstrained 4-Bars with Helical Joints,” Mech. Mach. Theory, 17, pp. 133–142.
Baker,  J. E., 1989, “Overconstrained Five-Bars with Prismatic Joints and Parallel Adjacent Joint Axes,” Mech. Mach. Theory, 24, pp. 267–273.
Baker,  J. E., 1995, “On Testing for Gross Mobility of New Kinematic Loops with Screw System Algebra,” Mech. Mach. Theory, 30, pp. 679–693.
Baker,  J. E., 1996, “On 5-Revolute Kinematic Loops with Intersecting Adjacent Joint Axes,” Mech. Mach. Theory, 31, pp. 1167–1183.
Wohlhart,  K., 1991, “Merging 2 General Goldberg’s 5R-Linkages to obtain a New 6R-Space Mechanism,” Mech. Mach. Theory, 26, pp. 659–668.
Wohlhart,  K., 1993, “The 2 Types of the Orthogonal Bricard Linkage,” Mech. Mach. Theory, 28, pp. 809–817.
Hervé, J. M., 1997, “Conjugacy and Invariance in the Displacement Group as a Tool for Mechanism Design,” Technical Report, Mechanical Research Team. Ecole Centrale Paris, France.
Fanghella,  P., 1988, “Kinematics of Spatial Linkages by Group Algebra: A Structure-Based Approach,” Mech. Mach. Theory, 23, pp. 171–183.
Fanghella,  P., and Galletti,  C., 1994, “Mobility Analysis of Single-Loop Kinematic Chains: An Algorithmic Approach Based on Displacement Groups,” Mech. Mach. Theory, 29, pp. 1187–1204.
Fanghella,  P., and Galletti,  C., 1995, “Metric Relations and Displacement Groups in Mechanism and Robot Kinematics,” ASME J. Mech. Des., 117, pp. 470–478.
Rico, J. M., and Ravani, B., 2002, “On Mobility Analysis of Linkages Using Group Theory,” ASME Paper DETC02/MECH-34249, CD-Rom, Proceedings of the Design Engineering Technical Conference 2002, Montreal, Canada.
Angeles, J., 1982, Spatial Kinematic Chains, Springer Verlag, New York.
Baker,  J. E., and Waldron,  K. J., 1974, “The C-H-C-H Linkage,” Mech. Mach. Theory, 9, pp. 285–297.

Figures

Grahic Jump Location
The two possible paths between rigid bodies i and j
Grahic Jump Location
Intersection of Hc(i,j) and Hcc(i,j) in Case 1
Grahic Jump Location
The two possibilities of intersection of Hc(i,j) and Hcc(i,j) in Case 2
Grahic Jump Location
Intersection of Hc(i,j) and Hcc(i,j) in Case 3
Grahic Jump Location
Spatial Chain 4P-4R with Partitioned Mobility.
Grahic Jump Location
A movable exceptional chain obtained from the intersection of a pair of planar subgroups
Grahic Jump Location
A movable exceptional chain obtained from the intersection of a planar subgroup with a Schönflies subgroup
Grahic Jump Location
A spatial chain formed by a couple of parallel dyads
Grahic Jump Location
A movable chain obtained from a unique Schönflies subgroup
Grahic Jump Location
A four revolute spatial chain
Grahic Jump Location
Single loop kinematic chain
Grahic Jump Location
The three basic types of kinematic pairs

Tables

Errata

Discussions

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