System of second order robot arm problem by an efficient numerical integration algorithm

• Autorzy: Ponalagusamy R. , Senthilkumar S.
• Języki publikacji: EN

Abstrakty

EN

Purpose: The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the Runge-Kutta Sixth order algorithm. Design/methodology/approach: The parameters governing the arm model of a robot control problem have also been discussed through RK-sixth-order algorithm. The precised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Findings: Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. The stability polynomial for the test equation γ=λγ (�γ is a complex Number) using RK-butcher algorithm obtained by Murugesan et. al. [1] and Park et. al. [2,3] is not correct and the stability regions for RK-Butcher methods have been absurdly presented. They have made a blunder in determining the range for real parts of �λh (h is a step size) involved in the test equation for RK-Butcher algorithms. Further, they have abruptly drawn the stability region for STWS method assuming that it is based on the Taylor's series technique. Research limitations/implications: It is noticed that STWS algorithm is not based on the Taylor�'s series method and it is an A-stable method. In the present paper, a corrective measure has been taken to obtain the stability polynomial for the case of RK-Butcher algorithm, the ranges for the real part of �λh and to present graphically the stability regions of the RK-Butcher methods. Originality/value: Based on the numerical results and graphs, a thorough comparison is carried out between the numerical algorithms.

Słowa kluczowe

EN

RK-Sixth-Order algorithm; ordinary differential equations; system of second order; robot arm problem

PL

równanie różniczkowe zwyczajne; system drugiego rzędu; ramiona robota

• Wydawca: International OCSCO World Press
• Czasopismo: Archives of Computational Materials Science and Surface Engineering
• Rocznik: 2009
• Tom: Vol. 1, nr 1
• Strony: 38--44
• Opis fizyczny: Bibliogr. 21 poz., tab., wykr.

Twórcy

autor

Ponalagusamy R.

autor

Senthilkumar S.

• Department of Mathematics, National Institute of Technology, Tiruchirappalli-620 015, Tamilnadu, India,

Bibliografia

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