Shaking Moment Balancing of a Four-Bar Mechanism Using Actuation Redundancy

  • Mario AcevedoEmail author
  • Teresa Orvañanos
  • Ramiro Velázquez
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Shaking moment balancing of force-balanced mechanisms is typically achieved by the use of counter-inertias that, in general, are very large. This leads to a substantial increase in the total mass of the linkage. In opposition to these traditional methods a novel, simple and direct method that takes advantage of actuation redundancy is proposed. The method can be generalized to any force balanced planar mechanism and is based on the solution of the inverse dynamics problem. The method is exemplified through the shaking moment balancing of a four-bar mechanism, previously balanced by force, following a didactic approach. Effectiveness of the method is verified by dynamic simulation.


Shaking moment balancing Dynamic balancing Actuation redundancy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gosselin, C.: Gravity compensation, static balancing and dynamic balancing of parallel mechanisms. Smart Devices Mach. Adv. Manuf., Springer International Publishing, pp. 27–48 (2008). doi:
  2. 2.
    Arakelian, V. H., Briot, S.: Balancing of Linkages and Robot Manipulators. Advanced Methods with Illustrative Examples. Springer (2015). doi:
  3. 3.
    Thmmel, T.T., Angeles, J. Nahon, M.A.: Active Control for the Complete Dynamic Balancing of Linkages. Proceedings of the ASME Design Engineering Technical Conference (1992).Google Scholar
  4. 4.
    Yu, Y.Q., Lin, J.: Active Balancing of a Flexible Linkage With Redundant Drives. J. Mech. Des. 125(1), pp. 119–123 (2003). doi:
  5. 5.
    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. Robotics Res. 32(6), pp. 744–759 (2013). doi:
  6. 6.
    Acevedo, M.: Design of Reactionless Mechanisms with Counter-Rotary Counter-Masses. Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots, Springer International Publishing, pp. 83–111 (2016). doi:
  7. 7.
    Shabana, A.: Computational Dynamics. Wiley, 3 ed. (2010).Google Scholar
  8. 8.
    Wang, L., Wu, J., Wang, J.: Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Robotics and Computer-Integrated Manufacturing 26, pp. 67–73 (2010). doi:
  9. 9.
    García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems - The Real-Time Challenge. Springer-Verlag, (1994).Google Scholar
  10. 10.
    Do Thanh, T., Kotlarski, J., Heimann, B., and Ortmaier, T.: On the Inverse Dynamics Problem of General Parallel Robots. Proceedings of the 2009 IEEE International Conference on Mechatronics. (2009).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mario Acevedo
    • 1
    Email author
  • Teresa Orvañanos
    • 2
  • Ramiro Velázquez
    • 2
  1. 1.Universidad Panamericana, Facultad de IngenieríaZapopanMéxico
  2. 2.Universidad Panamericana, Facultad de IngenieríaAguascalientes, AguascalientesMéxico

Personalised recommendations