The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the RK-eight stage seventh order limiting formulas. The parameters governing the arm model of a robot control problem have also been discussed through RK-eight stage seventh order limiting 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. Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. Based on the numerical results a thorough comparison is carried out between the numerical algorithms.