This paper shows the Lagrangian-based modelling of a fully actuated three-axis robot and a control application using a variant of Super Twisting Sliding Mode Control (STSMC) in which the robot is subject to disturbances and model uncertainties to demonstrate the robustness of the proposed method. The stability of the control system is proven with the help of the direct Lyapunov method. In particular, the robustness of the results is validated through computer simulations in which impulsive disturbances are simulated together with a model mismatch due to an uncompensated mechanical friction.