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Dynamic characteristics of a 3-RPR planar parallel manipulator with flexible intermediate links

Published online by Cambridge University Press:  13 May 2014

Amirhossein Eshaghiyeh Firoozabadi ,
Saeed Ebrahimi  and
Ghasem Amirian
Amirhossein Eshaghiyeh Firoozabadi
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran
Saeed Ebrahimi*
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran
Ghasem Amirian
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran
*
*Corresponding author. E-mail: ebrahimi@yazd.ac.ir
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Summary

This paper presents the dynamic modeling of a 3-RPR planar parallel manipulator with three flexible intermediate links in order to investigate the effects of the intermediate links flexibility on the undesired vibrations of the end-effector. For this purpose, the intermediate links are modeled as Euler--Bernoulli beams with two types of fixed-pinned and fixed-free boundary conditions based on the assumed mode method (AMM). The equations of motion of the 3-RPR manipulator are formulated using the augmented Lagrange multipliers method in the form of differential algebraic equations (DAEs) by incorporating the elastic and rigid coordinates in the set of generalized coordinates. After defining the initial conditions and imposing external forces to the manipulator, the equations are then solved numerically using the Modified Extended Backward-Differentiation Formula Implicit (MEBDFI) approach. Comparison of the simulation results for two different boundary conditions shows clearly the effects of flexibility of the intermediate links on the vibration of the end-effector trajectory. Results of this work can be used for the dynamic modeling of other manipulators or to design a controller for reducing the undesired vibrations.

Keywords

Flexible manipulatorsParallel manipulatorsAssumed mode methodEuler–Bernoulli beam
Type
Articles
Information
Robotica , Volume 33 , Issue 9 , November 2015 , pp. 1909 - 1925
Copyright
Copyright © Cambridge University Press 2014 

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