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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 254547, 17 pages
Research Article

An Evolutionary Analytic Method of Multi-DOF Nonlinear Coupling Dynamic Model for Controllable Close-Chain Linkage Mechanism System

1College of Mechanical Engineering, Guangxi University, Nanning 530004, China
2Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology, College of Mechanical Engineering, Guangxi University, Nanning 530004, China

Received 26 December 2010; Revised 27 March 2011; Accepted 20 April 2011

Academic Editor: Angelo Luongo

Copyright © 2011 Ru-Gui Wang 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.


The 2-DOF controllable close-chain linkage mechanism is investigated in this paper. Based on the characteristics of the multi-DOF nonlinear coupling dynamic equation of the system established by the finite element method, an analytic method of multiple-scales Newmark is presented after thinking about the method of perturbation and the method of numerical analysis. Firstly, the first-order approximate solution of the dynamic responses of the system at the time of 𝑡 is calculated by the multiple scales method. Then, taken the first-order approximate solution as the initialization of the generalized coordinate of the system, the stable dynamic response of the system is obtained by the implicit Newmark method. The simulation and experimental results are given in the end. The studies indicate that the method of multiple-scales Newmark is correct and practicable to study the dynamic characteristics of such kind of multi-DOF nonlinear coupling system.