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A new approach for dynamic modeling of n-viscoelastic-link robotic manipulators mounted on a mobile base

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Abstract

In this article, the mathematical modeling of a robotic system composed of n flexible links and a mobile platform has been considered. Most of the mechanical systems including the nonholonomic constraints are analyzed by Lagrangian formulation and its associated “Lagrange multipliers.” Eliminating these variables from the obtained equations is a time-consuming and cumbersome task. So, the Gibbs–Appell formulation and the assumed mode method are used to make the derivation of motion equations easier. Also, to model the system thoroughly and accurately, the dynamic interactions between the manipulator and the mobile platform and the coupling effects arising simultaneously from large motions and small deflections are taken into consideration. The links (assumed as 3D Timoshenko beams) undergo tension-compression, torsion and spatial bending (in two directions), while the effects of internal and external damping (as dissipative forces) are also considered in the mathematical modeling. A systematic approach is developed based on the derived formulation to establish the dynamic equations of motion. In order to alleviate the computational complexity of the suggested method, all the mathematical operations are carried out through \(3\times 3\) and \(3\times 1\) matrices only. Finally, this method is applied to a mobile manipulator with two flexible links to demonstrate the ability of the proposed method in deriving the equations of motion of such complex systems.

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Authors and Affiliations

  1. Robotic Research Laboratory, Mechanical Engineering Department, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, P.O. Box 16846-13114, Tehran, Iran

    M. H. Korayem & A. M. Shafei

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  1. M. H. Korayem
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  2. A. M. Shafei
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Correspondence to A. M. Shafei.

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Korayem, M.H., Shafei, A.M. A new approach for dynamic modeling of n-viscoelastic-link robotic manipulators mounted on a mobile base. Nonlinear Dyn 79, 2767–2786 (2015). https://doi.org/10.1007/s11071-014-1845-8

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  • DOI: https://doi.org/10.1007/s11071-014-1845-8

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