%0 Journal Article
%T System of second order robot arm problem by an efficient numerical integration algorithm
%A R. Ponalagusamy
%A S. Senthilkumar
%J Archives of Computational Materials Science and Surface Engineering
%D 2009
%I 
%X 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 ¨B¦Ã=¦Ë¦Ã (¦Ë 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 ¦Ëh (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 ¦Ëh 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.
%K RK-Sixth-Order algorithm
%K Ordinary differential equations
%K System of second order
%K Robot arm problem
%U http://www.archicmsse.org/vol09_1/0916.pdf