A mathematical model of a robot manipulator is described by a set of ordinary, coupled non-linear differential equations. Present theory is insufficient to obtain the exact solution of the equations to control the manipulator. We reduce the complexity of the problem by proposing a model reference system where the Coriolis terms are ignored and where the system of non-linear differential equations is almost decoupled by a careful selection of input torques. We show that the proposed control scheme for the model reference system is stable about a known equilibrium point. We present the simulation study for a two-link rotary manipulator where a model reference system and a control scheme are developed. The simulation results indicate that the solution is stable around a predetermined equilibrium point and that the addition of Coriolis terms in the non-linear differential equation does not change the overall stability of the system. The simulation results indicate that the robot manipulator tracks the desired trajectory.