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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 986319, 15 pages
Research Article

Periodic and Chaotic Motions of a Two-Bar Linkage with OPCL Controller

1School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
2School of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, UK

Received 16 December 2009; Accepted 25 June 2010

Academic Editor: Irina N. Trendafilova

Copyright © 2010 Qingkai Han et al. 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.


A two-bar linkage, which is described in differential dynamical equations, can perform nonlinear behaviors due to system parameters or external input. As a basic component of robot system, the investigation of its behavior can improve robot performance, control strategy, and system parameters. An open-plus-close-loop (OPCL) control method therefore is developed and applied to reveal and classify the complicated behaviors of a two-bar linkage. In this paper, the conception and stability of OPCL are addressed firstly. Then it is applied to the dynamical equations of two-bar linkage. Different motions including single-periodic, multiple-periodic, quasiperiodic, and chaotic motions are unfolded by numerical simulations when changing the controller parameters. Furthermore, the obtained chaotic motions are sorted out for qualitative and quantificational study using Lyapunov exponents and hypothetic possibilities of surrogate data method.