Design and Dynamic Modeling of Planar Parallel Micro-Positioning Platform Mechanism with Flexible Links Based on Euler Bernoulli Beam Theory

Document Type : Research Paper


1 Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University

2 Center of Excellence in Design, Robotics, and Automation, Sharif University of Technology; Fellow, The Academy of Sciences of Iran,

3 School of Mechanical Engineering, Sharif University of Technology


This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane’s methods. Euler-Bernoulli beam theory is considered for modeling the intermediate flexible link. Based on the Assumed Mode Method theory, the governing differential equations of motion are derived and solved using both Runge-Kutta-Fehlberg4, 5th and Perturbation methods. The mode shapes and natural frequencies are calculated under clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg4, 5th leads to same results. The mode frequency and the effects of geometry of flexure hinges on intermediate links vibration are investigated and the mode frequency, calculated using Fast Fourier Transform and the results are discussed.


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