This paper “describes” the investigation of the stability of a single Degree of Freedom (DOF) flexible robotic arm by the diagrams shown below. The derived model is based on Euler- Lagrange approach. Exploration of a flexible robotic arm with using state-of-the-art controllers is essential for intelligent applications. These robot arms have joints that work independently of each other in order to create a smooth connection between joints. They still ensures the natural properties like a real human arm. The use of polarity assignment method “helps” the system to achieve desired output signals which has not been thoroughtly studied before for this system. The author can also compare the effectiveness of control methods for this system to find the most effective method for control strategies. In particular, ANN ( artificial neural network) is the most modern technique currently applied to this system to investigate the security and stability of the system through this program. This is new and it has never been used before for a system of this type. Neural networks strategy has been implemented in this paper as an application of artificial intelligence. It has successfully performed a mission in re-simulating functions of another control method: Polarity assignment method. Simulation results are done by Matlab.