Permanent Magnet Synchronous Motors are used in military applications due to their numerous advantages, including high power density, high efficiency, low noise, and simple and inexpensive maintenance. This paper, a model-independent adaptive fuzzy robust controller is presented for a mechanical robot arm driven by permanent magnet synchronous motors. Although robust control methods have been proposed in order to overcome the uncertainties that include parametric uncertainty, unmodeled dynamics, and external disturbances, they face problems due to the complexity of robot dynamics. A fuzzy system can be used as a general approximator to approximate any nonlinear function. In this article, considering that the joints of the robot arm are the load torques of PMSMs, the uncertainties related to the dynamics of the robot arm have been transferred to the voltage equations of PMSMs. Uncertainties in the control law are estimated and compensated using fuzzy systems. Unlike many previous related works that ignore the electrical equations of PMSM, both electrical and mechanical equations are considered. Based on Barblat's lemma, the asymptotic convergence of the tracking error to zero is guaranteed. A case study is an artist robot arm driven by PMSMs. Compared to a robust controller for a single-joint robot arm actuated by PMSM, the proposed method is superior due to faster and smoother responses. The simulation results show that the regulation error quickly drops to zero (less than 1.2 sec).