A new alternative way named modified improved Runge-Kutta fifth-order five stage (MIRK(5,5)) technique is employed to compute a second-order robot arm problem and also for variations in angles of a robot arm joints model, which needs less number of function evaluations per time step, is the main focus of this paper. Numerically computed outputs match with the exact solution of the industrial robot arm problem which in turn shows that MIRK(5,5) algorithm are better to solve real-time problems practically.