Advertisement

Spatial Overconstrained Linkages—The Lost Jade

  • Yan Chen
  • Zhong You
Part of the History of Mechanism and Machine Science book series (HMMS, volume 15)

Abstract

This paper is to review all the discovered three-dimensional overconstrained linkage with only revolute joints. There are 15 types well known and several types recently proposed. Although the kinematics study on this family of linkages is in depth, little industry application has been developed. So it is the lost jade in the treasure box of mechanisms, waiting for being recovered and cherished.

Keywords

Revolute Joint Machine Theory Universal Joint Deployable Structure Prism Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hunt, K.H.: Kinematic geometry of mechanisms. Oxford University Press, Oxford (1978)zbMATHGoogle Scholar
  2. 2.
    Phillips, J.: Freedom in Machinery: Screw theory exemplified, vol. 2. Cambridge University Press, Cambridge (1984)Google Scholar
  3. 3.
    Sarrus, P.T.: Note sur la transformation des mouvements rectilignes alternatifs, en mouvements circulaires, et reciproquement. Academie des Sciences 36, 1036–1038 (1853)Google Scholar
  4. 4.
    Bennett, G.T.: A new mechanism. Engineering 76, 777–778 (1903)Google Scholar
  5. 5.
    Delassus, E.: Les chaînes articulées fermées et déformables à quatre membres. Bulletin des Sciences Mathématiques, 2nd Series 46, 283–304 (1922)Google Scholar
  6. 6.
    Bricard, R.: Mémoire sur la théorie de l’octaèdre articulé. Journal de Mathématiques Pures et Appliquées 3, 113–148 (1897)Google Scholar
  7. 7.
    Bricard, R.: Leçons de cinématique. In: Tome II Cinématique Appliquée, pp. 7–12. Gauthier-Villars, Paris (1927)Google Scholar
  8. 8.
    Myard, F.E.: Contribution à la géométrie des systèmes articulés. Bulletin de la Société Mathématique de France 59, 183–210 (1931)MathSciNetGoogle Scholar
  9. 9.
    Goldberg, M.: New five-bar and six-bar linkages in three dimensions. Trans. ASME 65, 649–663 (1943)Google Scholar
  10. 10.
    Waldron, K.J.: A family of overconstrained linkages. Journal of Mechanisms 2, 201–211 (1967)CrossRefGoogle Scholar
  11. 11.
    Waldron, K.J.: Hybrid overconstrained linkages. Journal of Mechanisms 3, 73–78 (1968)CrossRefGoogle Scholar
  12. 12.
    Waldron, K.J.: Symmetric overconstrained linkages. Transactions of the ASME. Journal of Engineering for Industry 91, 158–164 (1969)CrossRefGoogle Scholar
  13. 13.
    Wohlhart, K.: A new 6R space mechanism. In: Congress on the Theory of Machines and Mechanisms, Seville, Spain, pp. 193–198 (1987)Google Scholar
  14. 14.
    Wohlhart, K.: Merging two general Goldberg 5R linkages to obtain a new 6R space mechanism. Mechanism and Machine Theory 26, 659–668 (1991)CrossRefGoogle Scholar
  15. 15.
    Wohlhart, K.: The two types of the orthogonal Bricard linkage. Mechanism and Machine Theory 28, 809–817 (1991)CrossRefGoogle Scholar
  16. 16.
    Dietmaier, P.: A new 6R space mechanism. In: Proceeding 9th World Congress IFToMM, Milano, pp. 52–56 (1995)Google Scholar
  17. 17.
    Pamidi, P.R., Soni, A.H., Dukkipati, R.V.: Necessary and sufficient existence criteria of overconstrained five-link spatial mechanisms with helical, cylinder, revolute and prism pairs. Transactions of the ASME. Journal of Engineering for Industry 95, 737–743 (1973)CrossRefGoogle Scholar
  18. 18.
    Baker, J.E.: A comparative survey of the Bennett-based, 6-revolute kinematic loops. Mechanism and Machine Theory 28, 83–96 (1993)CrossRefGoogle Scholar
  19. 19.
    Baker, J.E.: Displacement-closure equations of the unspecialised double-Hooke’s-joint linkage. Mechanism and Machine Theory 37, 1127–1144 (2002)CrossRefGoogle Scholar
  20. 20.
    Schmelz, F., Aucktor, E.: Universal Joints and Driveshafts: Analysis, Design, Applications. Speinger, Heidelberg (2006)Google Scholar
  21. 21.
    Lu, Z., Yang, G., Wang, Q., Nan, R.: Research on mechanism of actuated active reflectors for FAST. Journal of Beijing University of Aeronautics and Astronautics 32, 233–238 (2006)Google Scholar
  22. 22.
    Zhao, J.S., Chu, F., Feng, Z.J.: Synthesis of Rectilinear Motion Generating Spatial Mechanism With Application to Automotive Suspension. Transactions of the ASME. Journal of Mechanical Design 130, 065001 (2008)CrossRefGoogle Scholar
  23. 23.
  24. 24.
    Hoberman, C.: Radial Expansion/Retraction Truss Structures, U.S. Patent 5024031 (1991)Google Scholar
  25. 25.
    You, Z.: Deployable structure of curved profile for space antennas. Journal of Aerospace Engineering 13, 139–143 (2000)CrossRefGoogle Scholar
  26. 26.
    Bennett, G.T.: Deformable octahedra. Proceeding of London Mathematics Society, 2nd series 10(1), 309–343 (1911)zbMATHCrossRefGoogle Scholar
  27. 27.
    Baker, E.J.: Limiting positions of a Bricard linkage and their possible relevance to the cyclohexane molecule. Mechanism and Machine Theory 21(3), 253–260 (1986)CrossRefGoogle Scholar
  28. 28.
    Chai, W.H., Chen, Y.: The line-symmetric octahedral Bricard linkage and its structural closure. Mechanism and Machine Theory 45, 772–779 (2010)zbMATHCrossRefGoogle Scholar
  29. 29.
    Bennett, G.T.: The skew isogram mechanism. Proceedings of the London Mathematical Society, 2nd series 13, 151–173 (1914)CrossRefGoogle Scholar
  30. 30.
    Baker, J.E.: The Bennett, Goldberg and Myard linkages–in perspective. Mechanism and Machine Theory 14, 239–253 (1979)CrossRefGoogle Scholar
  31. 31.
    Huang, C.: The cylindroid associated with finite motions of the Bennett mechanism. Journal of Mechanical Design 119, 521–524 (1997)CrossRefGoogle Scholar
  32. 32.
    Baker, J.E.: On the motion geometry of the Bennett linkage. In: Proceeding 2 of Eighth International Conference on Engineering Computer Graphic and Descriptive Geometry, Austin, USA, pp. 433–437 (1998)Google Scholar
  33. 33.
    Perez, A., McCarthy, J.M.: Dimensional synthesis of Bennett linkages. Journal of Mechanical Design 125, 98–104 (2003)CrossRefGoogle Scholar
  34. 34.
    Chen, Y., You, Z.: Mobile assemblies based on the Bennett linkage. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 461, 1229–1245 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Chen, Y., You, Z.: On mobile assemblies of Bennett linkages. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 464, 1275–1283 (2008)CrossRefGoogle Scholar
  36. 36.
    You, Z., Chen, Y.: Motion Structures: Deployable Structural Assemblies of Mechanisms. Taylor and Francis (2011) ISBN: 978-0-415-55489-3Google Scholar
  37. 37.
    Bennett, G.T.: The parallel motion of Sarrus and some allied mechanisms. Philosophy Magazine, 6th series 9, 803–810 (1905)CrossRefGoogle Scholar
  38. 38.
    Baker, E.J.: An analysis of Bricard linkages. Mechanism and Machine Theory 15, 267–286 (1980)CrossRefGoogle Scholar
  39. 39.
    Schatz, P.: U.S. Pat. No. 2,302,804 (1942)Google Scholar
  40. 40.
    Altmann, P.G.: Communications to Grodzinski, P. and M’Ewen, E, Link mechanisms in modern kinematics. Proceedings of the Institution of Mechanical Engineers 168(37), 889–896 (1954)Google Scholar
  41. 41.
    Mavroidis, C., Roth, B.: Analysis and synthesis of overconstrained mechanisms. Mechanism Synthesis and Analysis 70, 115–133 (1994)Google Scholar
  42. 42.
    Chen, Y., You, Z.: An extended Myard linkage and its derived 6R linkage. Journal of Mechanical Design 130, 052301 (2008)CrossRefGoogle Scholar
  43. 43.
    Song, C.Y., Chen, Y.: A spatial 6R linkage derived from subtractive Goldberg 5R linkages. Mechanism and Machine Theory 46, 1097–1106 (2011)zbMATHCrossRefGoogle Scholar
  44. 44.
    Song, C.Y., Chen, Y.: A family of mixed double-Goldberg 6R linkages. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, 871–890 (2012)CrossRefGoogle Scholar
  45. 45.
    Baker, J.E.: Screw replacements in isomeric variants of Bricard’s line-symmetric six-bar. Proceedings of the Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Science 223, 2391–2398 (2009)CrossRefGoogle Scholar
  46. 46.
    Baker, J.E.: Using the single reciprocal screw to confirm mobility of a six-revolute linkage. Proceedings of the Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Science 224, 2247–2255 (2010)CrossRefGoogle Scholar
  47. 47.
    Chen, Y., You, Z.: Spatial 6R linkages based on the Combination of two Goldberg 5R linkages. Mechanism and Machine Theory 42, 1484–1498 (2007)zbMATHCrossRefGoogle Scholar
  48. 48.
    Pellegrino, S. (ed.): Deployable Structures. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  49. 49.
    Guest, S.D., Fowler, P.W.: A symmetry-extended mobility rule. Mechanism and Machine Theory 40, 1002–1014 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    Guest, S.D., Fowler, P.W.: Symmetry conditions and finite mechanisms. Journal of Mechanics of Materials and Structures 2(2), 293–301 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Netherlands 2012

Authors and Affiliations

  • Yan Chen
    • 1
  • Zhong You
    • 2
  1. 1.School of Mechanical and Aerospace EngineeringNanyang Technological UniversityNanyangSingapore
  2. 2.Department of Engineering ScienceUniversity of OxfordOxfordUnited Kingdom

Personalised recommendations