Advertisement

Meccanica

, Volume 51, Issue 12, pp 3211–3225 | Cite as

Synthesis, optimization and experimental validation of reactionless two-DOF parallel mechanisms using counter-mechanisms

  • Thierry Laliberté
  • Clément GosselinEmail author
50th Anniversary of Meccanica

Abstract

The synthesis of reactionless mechanisms generally involves the force balancing of a mechanism using countermasses followed by the dynamic balancing of the inertia using counter-rotations. This approach requires that the force balanced mechanism have a constant equivalent moment of inertia for any configuration. Two of the main drawbacks of reactionless mechanisms are a significant increase in mass and actuation inertia. In this paper, a counter-mechanism is introduced in order to dynamically balance a force balanced two-DOF mechanism with variable inertia, which is expected to reduce the aforementioned drawbacks. The conditions for which the counter-mechanism matches the moment of inertia of the main mechanism for any configuration are derived. Then, in order to fairly compare the use of a counter-mechanism instead of counter-rotations, the balancing strategies are optimized regarding the addition of mass and actuation inertia using Lagrange multipliers. The results are optimal rules for the design of reactionless mechanisms and optimal mass-inertia curves which are akin to Pareto curves. These results allow to demonstrate the advantages of counter-mechanisms over counter-rotations, especially regarding added actuation inertia and compactness. Also, the significant influence of the radius of gyration of the counter-inertias on the optimal mass-inertia curves is revealed. Finally, examples of reactionless mechanisms are presented and prototypes are tested in order to validate the concepts.

Keywords

Dynamic balancing Parallel mechanism Pantograph Reactionless mechanism Planar mechanism 

Notes

Acknowledgements

The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. 89715) and the Canada Research Chair Program.

Supplementary material

Supplementary material 1 (mp4 25023 KB)

Supplementary material 2 (mp4 24265 KB)

References

  1. 1.
    Lowen GG, Berkof RS (1968) Survey of investigations into the balancing of linkages. J Mech 3:221–231CrossRefGoogle Scholar
  2. 2.
    Kochev IS (2000) General theory of complete shaking moment balancing of planar linkages: a critical review. Mech Mach Theory 35:1501–1514MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Arakelian VG, Smith MR (2005) Shaking force and shaking moment balancing of mechanisms: a historical review with new examples. ASME J Mech Des 127:334–339, 1035CrossRefGoogle Scholar
  4. 4.
    Arakelian V (2014) Shaking force and shaking moment balancing in robotics: a critical review. In: Ceccarelli M, Glazunov VA (eds) Advances on theory and practice of robots and manipulators. Springer, Heidelberg, pp 149–157Google Scholar
  5. 5.
    Arakelian V, Briot S (2015) Balancing of linkages and robot manipulators: advanced methods with illustrative examples, vol 27. Springer, HeidelbergGoogle Scholar
  6. 6.
    Van der Wijk V, Herder JL, Demeulenaere B (2009) Comparison of various dynamic balancing principles regarding additional mass and additional inertia. ASME J Mech Robot 1(4):041006CrossRefGoogle Scholar
  7. 7.
    Van der Wijk V, Demeulenaere B, Gosselin C, Herder JL (2012) Comparative analysis for low-mass and low-inertia dynamic balancing of mechanisms. ASME J Mech Robot 4:031008CrossRefGoogle Scholar
  8. 8.
    Van Der Wijk V, Krut S, Pierrot F, Herder J (2013) Design and experimental evaluation of a dynamically balanced redundant planar 4-RRR parallel manipulator. Int J Robot Res 32(6):743–758Google Scholar
  9. 9.
    Van der Wijk V (2015) Closed-chain principal vector linkages. In: Flores P, Viadero F (eds) New trends in mechanism and machine science. Springer, Heidelberg, pp 829–837Google Scholar
  10. 10.
    Foucault S, Gosselin CM (2002) Synthesis, design, and prototyping of a planar three degree-of-freedom reactionless parallel mechanism. In: Proceedings of DETC2002, ASME, Montreal, CanadaGoogle Scholar
  11. 11.
    Herder JL, Gosselin CM (2004) A counter-rotary counterweight (CRCW) for light-weight dynamic balancing. In: Proceedings of DETC2004, ASME, Salt Lake CityGoogle Scholar
  12. 12.
    Van der Wijk V, Herder JL (2009) Synthesis of dynamically balanced mechanisms by using counter-rotary countermass balanced double pendula. ASME J Mech Des 131:1110003Google Scholar
  13. 13.
    Acevedo M (2015) Conditions for dynamic balancing of planar parallel manipulators using natural coordinates and their application. In: Proceedings of the 14th IFToMM world congress, pp 419–427Google Scholar
  14. 14.
    Van der Wijk V, Herder JL (2010) Active dynamic balancing unit for controlled shaking force and shaking moment balancing. In: Proceedings of DETC2010, ASME, Montréal, CanadaGoogle Scholar
  15. 15.
    Laliberté T, Gosselin C (2013) Dynamic balancing of two-DOF parallel mechanisms using a counter-mechanism. In: Proceedings of DETC2013, ASME, PortlandGoogle Scholar
  16. 16.
    Song S-M, Lee J-K (1988) The mechanical efficiency and kinematics of pantograph-type manipulators. KSME J 2(1):69–78CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Département de Génie MécaniqueUniversité LavalQuébecCanada

Personalised recommendations