In articulated vehicle, the importance of adjustment or confinement of the side slip angle has not yet been investigated. However, their proper dynamic behavior is of great significance. In this research, based on a planar model of articulated vehicle and adopting a proper method, the significance of this quantity is examined. In this article, after a review of the literature, the articulated vehicle model is clarified. The selected model is a validated model of articulated vehicle with 14 degrees of freedom that simulates the vehicle’s directional dynamics. In the analysis of the stability, phase plane method based on the nonlinear model of articulated vehicle with three degrees of freedom is used, which includes the major degrees of freedom in planar motion. In this section, the traction phase plane is drawn via two variables, the side slip angle and the rotational velocity of the articulated vehicle by terms of constant longitudinal velocity of the vehicle as the critical condition and then stable and unstable zones are separated. Fuzzy estimator systems have been based on the Takagi-Sugeno fuzzy model and offer a stable range for the articulated vehicle’s motion according to the results from the phase plane. Finally, the application of phase plane in studying the stability would be magnified by designing two control systems based on the stable range, in order to control the articulation angle and the side slip angle. Eventually, the results are analyzed, and the method is tested based on the vehicle’s full model.