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A comparative study of elastic motions in trajectory tracking of flexible RPR planar manipulators moving with high speed

Published online by Cambridge University Press:  20 May 2016

Amirhossein Eshaghiyeh Firoozabadi ,
Saeed Ebrahimi  and
Josep M. Font-Llagunes
Amirhossein Eshaghiyeh Firoozabadi
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran. Email: Isaac_iut2004@yahoo.com
Saeed Ebrahimi*
Affiliation:
Department of Mechanical Engineering, Yazd University, Yazd, Iran. Email: Isaac_iut2004@yahoo.com
Josep M. Font-Llagunes
Affiliation:
Department of Mechanical Engineering and Biomedical Engineering Research Centre, Universitat Politècnica de Catalunya, Barcelona, Catalunya, Spain. Email: josep.m.font@upc.edu
*
*Corresponding author. Email: ebrahimi@yazd.ac.ir
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Summary

The study of inertial forces effects at high speeds in flexible parallel manipulators, which generate undesired deviations, is a challenging task due to the coupled and complicated equations of motion. A dynamic model of the Revolute Prismatic Revolute (RPR) planar manipulators (specifically 3-RPR, 2-RPR and 1-RPR) with flexible intermediate links is developed based on the assumed mode method. The flexible intermediate links are modeled as Euler-Bernoulli beams with fixed-free boundary conditions. Using the Lagrange multipliers, a generalized set of differential algebraic equations (DAEs) of motion is developed. In the simulations, the rigid body motion of the end-effector is constrained by some moving constraint equations while the vibrations of the flexible intermediate links cause deviations from the desired trajectory. From this analysis, the dynamic performance of the manipulators when tracking a desired trajectory is evaluated. A comparison of the results indicates that in some cases, adding each extra RPR chain in the n-RPR planar manipulators with flexible intermediate links reduces the stiffness and accuracy due to the inertial forces of the flexible links, which is opposite to what would be expected. The study provides insights to the design, control and suitable selection of the flexible manipulators.

Keywords

Accuracy performanceTrajectory trackingSerial and parallel manipulatorsFlexible manipulatorsAssumed mode method
Type
Articles
Information
Robotica , Volume 35 , Issue 7 , July 2017 , pp. 1523 - 1540
Copyright
Copyright © Cambridge University Press 2016 

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