This paper deals with the extension of a preshaping input method to the flexibility control of a cartesian robot. The method is the original one recently proposed by the authors and already modeled and discussed for a polar robot geometry. Besides the above extension, the method has been numerically simulated to analyze the behavior of a one link robot under different model parameters conditions. This activity allowed the characterization of the method for what concerning the robustness: the effectiveness of the method under structural damping factors and modal frequencies variations. The observed behavior has been physically interpreted and presented in quantitative terms.