Abstract
The design of shaking-moment-balanced linkages still is challenging. Considering moment balance in the very beginning of the design process of mechanisms is important for finding applicable solutions. For this purpose, the method of principal vectors is investigated, showing a compact notation of the angular momentum with respect to the center of mass. The moment-balance conditions are derived for three links in series from which balance solutions are synthesized and illustrated. The application for moment balancing of a 4R four-bar linkage is shown.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arakalian, V.H., Smith, M.R.: Design of planar 3-dof 3-RRR reactionless parallel manipulators. Mechatronics 18, 601–606 (2008)
Berkof, R.S., Lowen, G.G.: A new method for completely force balancing simple linkages. J. Eng. Ind. 91, 21–26 (1969)
Feng, G.: Complete shaking force and shaking moment balancing of 26 types of four-, five-, and six-bar linkages with prismatic pairs. Mech. Mach. Theory 25(2), 183–192 (1990)
Fischer, O.: Theoretische grundlagen für eine Mechanik der lebenden Körper. Teubner, Leipzig (1906)
Kochev, I.S.: General theory of complete shaking moment balancing of planar linkages: a critical review. Mech. Mach. Theory 35, 1501–1514 (2000)
Moore, B., Schicho, J., Gosselin, C.M.: Determination of the complete set of shaking force and shaking moment balanced planar four-bar linkages. Mech. Mach. Theory 44, 1338–1347 (2009)
Ricard, R., Gosselin, C.M.: On the development of reactionless parallel manipulators. In: Proceedings of DETC 2000, ASME (DETC2000/MECH-14098), Baltimore (2000)
Van der Wijk, V., Herder, J.L.: Guidelines for low mass and low inertia dynamic balancing of mechanisms and robotics. In: Kröger, T., Wahl F.M. (eds.) Advances in Robotics Research, Proceedings of the German Workshop on Robotics, pp. 21–30. Springer, Berlin/Heidelberg (2009). ISBN 978-3-642-01212-9
Van der Wijk, V., Herder, J.L.: Synthesis method for linkages with center of mass at invariant link point – pantograph based mechanisms. Mech. Mach. Theory 48, 15–28 (2012)
Van der Wijk, V., Herder, J.L.: The work of Otto Fischer and the historical development of his method of principal vectors for mechanism and machine science. In: Proceedings of the International Symposium on the History of Machines and Mechanisms, Amsterdam (2012, accepted)
Van der Wijk, V., Herder, J.L., Demeulenaere, B.: Comparison of various dynamic balancing principles regarding additional mass and additional inertia. J. Mech. Rob. 1(4), 04 1006 (2009)
Van der Wijk, V., Krut, S., Pierrot, F., Herder, J.L.: Generic method for deriving the general shaking force balance conditions of parallel manipulators with application to a redundant planar 4-RRR parallel manipulator. In: Proceedings of the 13th IFToMM World Congress on Mechanism and Machnine Science, Guanajuato (A12-523) (2011)
Wu, Y., Gosselin, C.M.: Design of reactionless 3-dof and 6-dof parallel manipulators using parallelepiped mechanisms. IEEE Trans. Rob. 21(5), 821–833 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
van der Wijk, V., Herder, J.L. (2013). The Method of Principal Vectors for the Synthesis of Shaking Moment Balanced Linkages. In: Viadero, F., Ceccarelli, M. (eds) New Trends in Mechanism and Machine Science. Mechanisms and Machine Science, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4902-3_43
Download citation
DOI: https://doi.org/10.1007/978-94-007-4902-3_43
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4901-6
Online ISBN: 978-94-007-4902-3
eBook Packages: EngineeringEngineering (R0)