Skip to main content

Balancing Conditions of Planar and Spatial Mechanisms in the Algebraic Form

  • Chapter
Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots

Abstract

This chapter deals with an approach to formulate balancing conditions for the shaking force and shaking moment of planar mechanisms and spatial mechanisms. In the Mechanism Theory, every Mechanism has p moving members and a non-moving frame. According to tradition, a planar 8R-eightbar mechanism is a multibody system with 7 moving bodies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dresig, H, Vulfson, JI: Dynamik der Mechanismen. Deutscher Verlag der Wissenschaften, Berlin (1989)

    Book  MATH  Google Scholar 

  2. Schiehlen, W, Eberhard, P: Technische Dynamik, 3rd edn. Vieweg + Teubner, Wiesbaden (2007)

    Google Scholar 

  3. Dresig, H, Holzweissig, F: Dynamics of Machinery. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  4. Huston, RL: Multibody Dynamics. Butterworth-Heinemann, Boston (1990)

    Google Scholar 

  5. Haug, EJ: Computer Aided Kinematics and Dynamics of Mechanical Systems, vol. 1: Basic Methods. Allyn and Bacon, Boston, MA (1989)

    Google Scholar 

  6. Chaudhary, H, Saha, SK: Dynamics and Balancing of Multibody Systems. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  7. Lowen, GG, Tepper, FR, Berkorf, RS: Balancing of linkages – an update. Mech Mach Theory 18, 213–220 (1983)

    Article  Google Scholar 

  8. Thümmel, T: Literaturbericht zum dynamischen Ausgleich schnellaufender Mechanismen. Wiss Schriftenreihe der TH Karl-Marx-Stadt. Mech Mater 7, 57–92 (1983)

    Google Scholar 

  9. Arakelian, VH, Smith, MR: Shaking force and shaking moment balancing of mechanisms: a historical review with new examples. ASME J Mech Des 127, 334–339 (2005)

    Article  Google Scholar 

  10. Shchepetilnikov, VA: The determination of the mass centers of mechanisms in connection with the problem of mechanism balancing. J Mech 3, 367–389 (1968)

    Article  Google Scholar 

  11. Berkof, RS, Lowen, GG: A new method for completely force balancing simple linkage. Trans ASME J Eng Ind 91(1), 21–26 (1969)

    Article  Google Scholar 

  12. Kaufman, RE, Sandor, GN: Complete force balancing of spatial linkages. Trans ASME J Mech Des 93B(2), 620–626 (1971)

    Google Scholar 

  13. Berkof, RS: Complete force and moment balancing of inline four-bar linkages. Mech Mach Theory 8, 397–410 (1973)

    Article  Google Scholar 

  14. Dresig, H, Rockhausen, L, Naake, S: Balancing conditions for planar mechanism. Flex Mech Dyn Anal ASME 47, 67–73 (1992)

    Google Scholar 

  15. Dresig, H, Rockhausen, L, Naake, S: Vollständiger und harmonischer Ausgleich ebener Mechanismen, Fortschritt-Berichte VDI, Reihe 18, Nr. 155. VDI Verlag, Düsseldorf (1994)

    Google Scholar 

  16. Kochev, IS: General theory of complete shaking moment balancing of planar linkages: a critical review. Mech Mach Theory 35, 1501–1514 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kochev, IS: General method for active balancing of combined shaking moment and torque fluctuations in planar linkages. Mech Mach Theory 25, 679–687 (1990)

    Article  Google Scholar 

  18. Ye, Z, Smith, MR: Complete balancing of planar linkages by an equivalence method. Mech Mach Theory 29(5), 701–712 (1994)

    Article  Google Scholar 

  19. Esat, I, Bahai, H: A theory of complete force and moment balancing of planer linkage mechanisms. Mech Mach Theory 34, 903–922 (1999)

    Article  MATH  Google Scholar 

  20. Arakelian, VH, Smith, MR: Design of planar 3-DOF 3-RRR reactionless parallel manipulators. Mechatronics 18(10), 601–606 (2008)

    Article  Google Scholar 

  21. Wu, Y, Gosselin, CM: On the dynamic balancing of multi-DOF parallel mechanisms with multiple legs. ASME J Mech Des 129(2), 234–238 (2007)

    Article  Google Scholar 

  22. Nguyen, VK: Über den Massenausgleich in Mehrkörpersystemen. Tech Mech 14(3–4),231–238 (1994)

    Google Scholar 

  23. Nguyen, VK, Nguyen, PD, Pham, VS: Balancing conditions of planar mechanisms with multi-degree of freedom. Vietnam J Mech 27, 204–212 (2005)

    Google Scholar 

  24. Nguyen, VK, Nguyen, PD: Balancing conditions for spatial mechanisms. Mech Mach Theory 42, 1141–1152 (2007)

    Article  MATH  Google Scholar 

  25. Nguyen, VK, Nguyen, PD: On the dynamic balancing conditions of planar multi-DOF parallel manipulators with revolute joints. In: Proceedings of the 1st IFToMM International Symposium on Robotics and Mechatronics, Hanoi, 21–23 Sept, 2009

    Google Scholar 

  26. Arakelian, VH, Smith, VH: Complete shaking force and shaking moment balancing of linkages. Mech Mach Theory 34, 1141–1153 (1999)

    Article  MATH  Google Scholar 

  27. Arakelian, V, Dahan, M: Partial shaking moment balancing of fully shaking force balanced linkages. Mech Mach Theory 36, 1241–1252 (2001)

    Article  MATH  Google Scholar 

  28. Arakelian, VH: Complete shaking force and shaking moment balancing of RSS’R spatial linkages. J Multibody Dyn 221, 303–310 (2007)

    Google Scholar 

  29. Chaudhary, H, Saha, SK: Balancing of shaking forces and shaking moments for planar mechanisms using the equimomental systems. Mech Mach Theory 43, 310–334 (2008)

    Article  MATH  Google Scholar 

  30. Feng, G: Complete shaking force and shaking moment balancing of four types of six-bar linkages. Mech Mach Theory 24(4), 275–287 (1989)

    Article  Google Scholar 

  31. Feng, G: Complete shaking force and shaking moment balancing of 17 types of eight-bar linkages only with revolute pairs. Mech Mach Theory 26, 197–206 (1991)

    Article  Google Scholar 

  32. Moore, B, Schicho, J, Gosselin, CM: Determination of the complete set of shaking force and shaking moment balanced planar four-bar linkages. Mech Mach Theory 44, 1338–1347 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  33. Kaufman, RE, Sandor, GN: Complete force balancing of spatial linkages. Trans ASME J Eng Ind 93, 620–626 (1971)

    Article  Google Scholar 

  34. Bagci, C: Complete balancing of space mechanisms – shaking force balancing. J Mech Trans Automat Des 105, 609–616 (1983)

    Article  Google Scholar 

  35. Chen, N-X: The complete shaking force balancing of a spatial linkage. Mech Mach Theory 19, 243–255 (1984)

    Article  Google Scholar 

  36. Yue-Qing, Y: Complete shaking force and moment balancing of spatial irregular force transmission mechanisms using additional link. Mech Mach Theory 23, 279–285 (1988)

    Article  Google Scholar 

  37. Abdel-Rahman, TM, Elbestawi, MA: Synthesis and dynamics of statically balanced direct-drive manipulators with decoupled inertia tensors. Mech Mach Theory 26, 389–402 (1991)

    Article  Google Scholar 

  38. Wang, J, Gosselin, CM: Static balancing of spatial four-degree-of freedom parallel mechanisms. Mech Mach Theory 35, 563–592 (2000)

    Article  MATH  Google Scholar 

  39. Arakelian, V., Smith, M.R: Shaking moment minimization of fully force-balanced linkages. In: Proceedings of the 11th World Congress in Mechanism and Machine Science, Tianjin, China (2004)

    Google Scholar 

  40. Park, J: Principle of dynamical balance for multibody systems. Multibody Syst Dyn 14, 269–299 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  41. Russo, A, Sinatra, R, Xi, F: Static balancing of parallel robots. Mech Mach Theory 40, 191–202 (2005)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgment

The work discussed in this chapter was completed with the financial support given by the National Foundation for Science and Technology Development of Vietnam.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nguyen Van Khang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Van Khang, N., Dien, N.P. (2016). Balancing Conditions of Planar and Spatial Mechanisms in the Algebraic Form. In: Zhang, D., Wei, B. (eds) Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots. Springer, Cham. https://doi.org/10.1007/978-3-319-17683-3_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-17683-3_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17682-6

  • Online ISBN: 978-3-319-17683-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics