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Shock and Vibration
Volume 18, Issue 1-2, Pages 365-375

Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

Qingkai Han, Xueyan Zhao, Xingxiu Li, and Bangchun Wen

School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China

Received 4 February 2010; Revised 2 May 2010

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.