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Comparison of Kane’s and Lagrange’s Methods in Analysis of Constrained Dynamical Systems

Published online by Cambridge University Press:  10 February 2020

Amin Talaeizadeh ,
Mahmoodreza Forootan ,
Mehdi Zabihi  and
Hossein Nejat Pishkenari Open the ORCID record for Hossein Nejat Pishkenari [Opens in a new window]
Amin Talaeizadeh
Affiliation:
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran. E-mails: amtalaiezadeh@gmail.com, mahmood.foroutan@yahoo.com, mehdizabihi@yahoo.com
Mahmoodreza Forootan
Affiliation:
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran. E-mails: amtalaiezadeh@gmail.com, mahmood.foroutan@yahoo.com, mehdizabihi@yahoo.com
Mehdi Zabihi
Affiliation:
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran. E-mails: amtalaiezadeh@gmail.com, mahmood.foroutan@yahoo.com, mehdizabihi@yahoo.com
Hossein Nejat Pishkenari*
Affiliation:
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran. E-mails: amtalaiezadeh@gmail.com, mahmood.foroutan@yahoo.com, mehdizabihi@yahoo.com
*
*Corresponding author. E-mail: nejat@sharif.edu
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Summary

Dynamic modeling is a fundamental step in analyzing the movement of any mechanical system. Methods for dynamical modeling of constrained systems have been widely developed to improve the accuracy and minimize computational cost during simulations. The necessity to satisfy constraint equations as well as the equations of motion makes it more critical to use numerical techniques that are successful in decreasing the number of computational operations and numerical errors for complex dynamical systems. In this study, performance of a variant of Kane’s method compared to six different techniques based on the Lagrange’s equations is shown. To evaluate the performance of the mentioned methods, snake-like robot dynamics is considered and different aspects such as the number of the most time-consuming computational operations, constraint error, energy error, and CPU time assigned to each method are compared. The simulation results demonstrate the superiority of the variant of Kane’s method concerning the other ones.

Keywords

Kane methodLagrange’s methodSnake robotConstrained dynamical systemsDerivation of motion equations
Type
Articles
Information
Robotica , Volume 38 , Issue 12 , December 2020 , pp. 2138 - 2150
Copyright
Copyright © Cambridge University Press 2020

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