Skip to main content
SpringerLink
Log in

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

  • 50th Anniversary of Meccanica
  • Published:
Meccanica Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Lowen GG, Berkof RS (1968) Survey of investigations into the balancing of linkages. J Mech 3:221–231

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  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, 1035

    Article  Google Scholar 

  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 149–157

    Google Scholar 

  5. Arakelian V, Briot S (2015) Balancing of linkages and robot manipulators: advanced methods with illustrative examples, vol 27. Springer, Heidelberg

    Google Scholar 

  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):041006

    Article  Google Scholar 

  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 4:031008

    Article  Google Scholar 

  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):743–758

    Google Scholar 

  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 829–837

    Google Scholar 

  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, Canada

  11. Herder JL, Gosselin CM (2004) A counter-rotary counterweight (CRCW) for light-weight dynamic balancing. In: Proceedings of DETC2004, ASME, Salt Lake City

  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 131:1110003

    Google Scholar 

  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 419–427

  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, Canada

  15. Laliberté T, Gosselin C (2013) Dynamic balancing of two-DOF parallel mechanisms using a counter-mechanism. In: Proceedings of DETC2013, ASME, Portland

  16. Song S-M, Lee J-K (1988) The mechanical efficiency and kinematics of pantograph-type manipulators. KSME J 2(1):69–78

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Département de Génie Mécanique, Université Laval, Québec, QC, G1V0A6, Canada

    Thierry Laliberté & Clément Gosselin

Authors
  1. Thierry Laliberté
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Clément Gosselin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Clément Gosselin.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 25023 KB)

Supplementary material 2 (mp4 24265 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Laliberté, T., Gosselin, C. Synthesis, optimization and experimental validation of reactionless two-DOF parallel mechanisms using counter-mechanisms. Meccanica 51, 3211–3225 (2016). https://doi.org/10.1007/s11012-016-0582-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-016-0582-0

Keywords

Search

Navigation