Second order Lagrange equations are used for describing dynamics of planar mechanism with rotation joints. For calculating kinetic energy of the links local coordinates of velocity vectors are used as well as recursive matrix transformations. Kinetic energy quadratic form coefficients are represented by linear combinations of seven independent trigonometric functions of generalized coordinates, i.e. basis functions. A number of these functions are connected to number of links by quadratic dependence. Constant coefficients in expansions in basic functions are determined from linear equation systems, representing kinetic energy of the mechanism in its several nonrecurring configurations with non-zero values for one or two generalized velocities. The resulting system of dynamics differential equations is integrated numerically with Runge-Kutta method in software environment Mathcad. Efficiency of the proposed method of creating and solving dynamic equations is demonstrated by example of numerical solution the direct dynamic problem of three-link mechanism.
| Published in | Applied and Computational Mathematics (Volume 3, Issue 4) |
| DOI | 10.11648/j.acm.20140304.20 |
| Page(s) | 186-190 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Flat Multilink Mechanism, Lagrange Equations, Basis Functions, Direct Dynamic Problem
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APA Style
Bagautdinov Ildar Nyrgaiazovich, Pavlov Alexander Ivanovich, Zhuravlev Evgeny Alekseevich, Bogdanov Evgeny Nikolaevich. (2014). Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators. Applied and Computational Mathematics, 3(4), 186-190. https://doi.org/10.11648/j.acm.20140304.20
ACS Style
Bagautdinov Ildar Nyrgaiazovich; Pavlov Alexander Ivanovich; Zhuravlev Evgeny Alekseevich; Bogdanov Evgeny Nikolaevich. Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators. Appl. Comput. Math. 2014, 3(4), 186-190. doi: 10.11648/j.acm.20140304.20
AMA Style
Bagautdinov Ildar Nyrgaiazovich, Pavlov Alexander Ivanovich, Zhuravlev Evgeny Alekseevich, Bogdanov Evgeny Nikolaevich. Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators. Appl Comput Math. 2014;3(4):186-190. doi: 10.11648/j.acm.20140304.20
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author = {Bagautdinov Ildar Nyrgaiazovich and Pavlov Alexander Ivanovich and Zhuravlev Evgeny Alekseevich and Bogdanov Evgeny Nikolaevich},
title = {Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators},
journal = {Applied and Computational Mathematics},
volume = {3},
number = {4},
pages = {186-190},
doi = {10.11648/j.acm.20140304.20},
url = {https://doi.org/10.11648/j.acm.20140304.20},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.20},
abstract = {Second order Lagrange equations are used for describing dynamics of planar mechanism with rotation joints. For calculating kinetic energy of the links local coordinates of velocity vectors are used as well as recursive matrix transformations. Kinetic energy quadratic form coefficients are represented by linear combinations of seven independent trigonometric functions of generalized coordinates, i.e. basis functions. A number of these functions are connected to number of links by quadratic dependence. Constant coefficients in expansions in basic functions are determined from linear equation systems, representing kinetic energy of the mechanism in its several nonrecurring configurations with non-zero values for one or two generalized velocities. The resulting system of dynamics differential equations is integrated numerically with Runge-Kutta method in software environment Mathcad. Efficiency of the proposed method of creating and solving dynamic equations is demonstrated by example of numerical solution the direct dynamic problem of three-link mechanism.},
year = {2014}
}
TY - JOUR T1 - Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators AU - Bagautdinov Ildar Nyrgaiazovich AU - Pavlov Alexander Ivanovich AU - Zhuravlev Evgeny Alekseevich AU - Bogdanov Evgeny Nikolaevich Y1 - 2014/09/20 PY - 2014 N1 - https://doi.org/10.11648/j.acm.20140304.20 DO - 10.11648/j.acm.20140304.20 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 186 EP - 190 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20140304.20 AB - Second order Lagrange equations are used for describing dynamics of planar mechanism with rotation joints. For calculating kinetic energy of the links local coordinates of velocity vectors are used as well as recursive matrix transformations. Kinetic energy quadratic form coefficients are represented by linear combinations of seven independent trigonometric functions of generalized coordinates, i.e. basis functions. A number of these functions are connected to number of links by quadratic dependence. Constant coefficients in expansions in basic functions are determined from linear equation systems, representing kinetic energy of the mechanism in its several nonrecurring configurations with non-zero values for one or two generalized velocities. The resulting system of dynamics differential equations is integrated numerically with Runge-Kutta method in software environment Mathcad. Efficiency of the proposed method of creating and solving dynamic equations is demonstrated by example of numerical solution the direct dynamic problem of three-link mechanism. VL - 3 IS - 4 ER -
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