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Shock and Vibration
Volume 2017 (2017), Article ID 1582547, 13 pages
Research Article

Dynamic Model and Vibration Characteristics of Planar 3-RRR Parallel Manipulator with Flexible Intermediate Links considering Exact Boundary Conditions

School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, China

Correspondence should be addressed to Wei Li

Received 11 January 2017; Revised 28 March 2017; Accepted 24 May 2017; Published 12 July 2017

Academic Editor: Tai Thai

Copyright © 2017 Lianchao Sheng 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.


Due to the complexity of the dynamic model of a planar 3-RRR flexible parallel manipulator (FPM), it is often difficult to achieve active vibration control algorithm based on the system dynamic model. To establish a simple and efficient dynamic model of the planar 3-RRR FPM to study its dynamic characteristics and build a controller conveniently, firstly, considering the effect of rigid-flexible coupling and the moment of inertia at the end of the flexible intermediate link, the modal function is determined with the pinned-free boundary condition. Then, considering the main vibration modes of the system, a high-efficiency coupling dynamic model is established on the basis of guaranteeing the model control accuracy. According to the model, the modal characteristics of the flexible intermediate link are analyzed and compared with the modal test results. The results show that the model can effectively reflect the main vibration modes of the planar 3-RRR FPM; in addition the model can be used to analyze the effects of inertial and coupling forces on the dynamics model and the drive torque of the drive motor. Because this model is of the less dynamic parameters, it is convenient to carry out the control program.