Please wait a minute...

Frontiers of Mechanical Engineering

Front Mech Eng    2013, Vol. 8 Issue (1) : 10-16
Shaking-moment balancing of mechanisms with principal vectors and momentum
V. van der WIJK()
University of Twente-Engineering Technology, Enschede 7500 AE, Netherlands
Download: PDF(213 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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 elements in series from which balance solutions are synthesized and illustrated. From the application for moment balancing of a 4R four-bar linkage it is shown that the moment balancing of closed kinematic chains remains challenging.

Keywords shaking-moment balancing      principal vector linkage      angular momentum     
Corresponding Author(s): WIJK V. van der,   
Issue Date: 05 March 2013
 Cite this article:   
V. van der WIJK. Shaking-moment balancing of mechanisms with principal vectors and momentum[J]. Front Mech Eng, 2013, 8(1): 10-16.
E-mail this article
E-mail Alert
Articles by authors
V. van der WIJK
Fig.1  The common CoM of three elements in series is in joint of a principal vector linkage with principal dimensions , , , and for all motion. Element CoM is defined w.r.t. by a parallelogram with sides and as illustrated
Fig.2  Moment-balance configurations for (a) with ; (b) and
Fig.3  Moment-balance configuration for for <1 in which joints and , and and coincide, respectively, and also elements 2 and 3 coincide for all motion
Fig.4  (a) Force-balanced 4R four-bar linkage derived from principal vector linkage with base link 4; (b) two moment-balance configurations of the 4R four-bar linkage
1 van der Wijk V, Herder J L. Guidelines for low mass and low inertia dynamic balancing of mechanisms and robotics. Advances in Robotics Research , 2009, 21–30
2 Kochev I S. General theory of complete shaking moment balancing of planar linkages: a critical review. Mechanism and Machine Theory , 2000, 35(11): 1501–1514
doi: 10.1016/S0094-114X(00)00015-X
3 van der Wijk V, Herder J L, Demeulenaere B. Comparison of various dynamic balancing principles regarding additional mass and additional inertia. Journal of Mechanisms and Robotics , 2009, 1(4): 041006
4 Arakelian V H, Smith M R. Design of planar 3-DOF 3-RRR reactionless parallel manipulators. Mechatronics , 2008, 18(10): 601–606
doi: 10.1016/j.mechatronics.2008.05.002
5 Feng G. Complete shaking force and shaking moment balancing of 26 types of four-, five-, and six-bar linkages with prismatic pairs. Mechanism and Machine Theory , 1990, 25(2): 183–192
doi: 10.1016/0094-114X(90)90120-9
6 Wu Y N, Gosselin C M. Design of reactionless 3-DOF and 6-DOF parallel manipulators using parallelepiped mechanisms. IEEE Transactions on Robotics , 2005, 21(5): 821–833
doi: 10.1109/TRO.2005.847573
7 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 World Congress on Mechanism and Machine Science , Guanajuato, Mexico, 2011
8 van der Wijk V, Herder J L. Synthesis method for linkages with center of mass at invariant link point-pantograph based mechanisms. Mechanism and Machine Theory , 2012, 48: 15–28
9 Fischer O. Theoretische grundlagen für eine mechanik der lebenden k?rper. Teubner , Leipzig, 1906
10 van der Wijk V, Herder J L. The work of Otto Fischer and the historical development of his method of principle vectors for mechanism and machine science. Explorations in the History of Machines and Mechanisms , 2012, 521–534
11 van der Wijk V, Herder J L. Inherently balanced 4R four-bar based linkages. Latest Advances in Robot Kinematics , 2012, 309–316
12 Papadopoulos E, Abu-Abed A. Design and motion planning for a zero-reaction manipulator. In: Proceedings of IEEE International Conference on Robotics and Automation , 1994, 1554–1559
13 Ricard R, Gosselin C M. On the development of reactionless parallel manipulators. In: Proceedings of ASME 2000 Design Engineering Technical Conferences and Computers and Information in Engineering Conference , Baltimore, Maryland, 2000
14 Moore B, Schicho J, Gosselin C M. Determination of the complete set of shaking force and shaking moment balanced planar four-bar linkages. Mechanism and Machine Theory , 2009, 44(7): 1338–1347
doi: 10.1016/j.mechmachtheory.2008.10.004
15 Berkof R S, Lowen G G. A new method for completely force balancing simple linkages. Journal of Engineering for Industry , 1969, 91(1): 21–26
Full text



  Shared   0