A Screw-Based Dynamic Balancing Approach, Applied to a 5-Bar Mechanism

  • Jan de JongEmail author
  • Johannes van Dijk
  • Just Herder
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 4)


Dynamic balancing aims to reduce or eliminate the shaking base reaction forces and moments of mechanisms, in order to minimize vibration and wear. The derivation of the dynamic balance conditions requires significant algebraic effort, even for simple mechanisms. In this study, a screw-based balancing methodology is proposed and applied to a 5-bar mechanism. The method relies on four steps: (1) representation of the links’ inertias into point masses, (2) finding the conditions for these point masses which result in dynamic balance in one given pose (instantaneous balance), (3) extending these conditions over the workspace to achieve global balance, (4) converting the point mass representation back to feasible inertias. These four steps are applied to a 5-bar mechanism in order to obtain the conditions which ensure complete force balance and additional moment balance over multiple trajectories. Using this methodology, six out of the eight balancing conditions are found directly from the momentum equations.


Dynamic balance 5-bar mechanism Screw theory Inertia decomposition 


  1. 1.
    Berkof, R., Lowen, G.: A new method for completely force balancing simple linkages. J. Eng. Ind. 91(1) (1969)Google Scholar
  2. 2.
    Foucault, S., Gosselin, C.: On the development of a planar 3-DOF reactionless parallel mechanism. In: ASME 2002 IDETC, pp. 1–9 (2002)Google Scholar
  3. 3.
    Jonker, J.B., Meijaard, J.P.: SPACAR — computer program for dynamic analysis of flexible spatial mechanisms and manipulators. Multibody Systems Handbook, pp. 123–143. Springer, Berlin (1990).
  4. 4.
    Ouyang, P., Li, Q., Zhang, W.: Integrated design of robotic mechanisms for force balancing and trajectory tracking. Mechatronics 13(8–9), 887–905 (2003)CrossRefGoogle Scholar
  5. 5.
    Ricard, R., Gosselin, C.M.: On the development of reactionless parallel manipulators. In: ASME 2000 DECTC, Baltimore, Maryland, vol. 1, pp. 1–10 (2000)Google Scholar
  6. 6.
    Stramigioli, S., Bruyninckx, H.: Geometry of dynamic and higher-order kinematic screws. In: Proceedings 2001 IEEE ICRA, pp. 3344–3349 (2001)Google Scholar
  7. 7.
    Van der Wijk, V.: Shaking-moment balancing of mechanisms with principal vectors and momentum. Front. Mech. Eng. 8(1), 10–16 (2015)CrossRefGoogle Scholar
  8. 8.
    Van der Wijk, V., Herder, J.: Guidelines for low mass and low inertia dynamic balancing of mechanisms and robotics. Advances in Robotics Research, pp. 21–30. Springer, Berlin (2009)CrossRefGoogle Scholar
  9. 9.
    Van der Wijk, V., Krut, S., Pierrot, F., Herder, J.L.: Design and experimental evaluation of a dynamically balanced redundant planar 4-RRR parallel manipulator. Int. J. Robot. Res. 32(6), 744–759 (2013)CrossRefGoogle Scholar
  10. 10.
    Wu, Y., Gosselin, C.M.: Synthesis of reactionless spatial 3-DoF and 6-DoF mechanisms without separate counter-rotations. Int. J. Robot. Res. 23(6), 625–642 (2004)CrossRefGoogle Scholar
  11. 11.
    Wu, Y., Gosselin, C.M.: On the dynamic balancing of multi-DOF parallel mechanisms with multiple legs. J. Mech. Design 129(2), 234 (2007)CrossRefGoogle Scholar
  12. 12.
    Zoppi, M., Zlatanov, D., Molfino, R.: On the velocity analysis of interconnected chains mechanisms. Mech. Mach. Theory 41(11), 1346–1358 (2006)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.University of TwenteEnschedeNetherlands

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