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Mathematical Problems in Engineering
Volume 2012, Article ID 857064, 19 pages
Research Article

Vibration Analysis of a New Type of Compliant Mechanism with Flexible-Link, Using Perturbation Theory

1Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Center of Excellence in Design, Robotics, and Automation, Sharif University of Technology, Tehran, Iran
3School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 14588-89694, Iran

Received 6 December 2011; Revised 8 February 2012; Accepted 24 February 2012

Academic Editor: Slim Choura

Copyright © 2012 N. S. Viliani 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.


Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange’s equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg 4, 5th leads to highly accurate solutions, and the results are performed and discussed.