The control of robotic manipulators traditionally relies on accurate knowledge of their dynamics, including link lengths, masses, geometric structure, and kinematic models. However, in this work, we propose a novel approach to robotic arm control that operates without any prior knowledge of these parameters. This study focuses on the control of a serial robotic manipulator using a neural network-based dynamic model, specifically a Nonlinear AutoRegressive with eXogenous inputs (NARX) network. Initially, traditional control methods and a Nonlinear Model Predictive Control (NMPC) strategy were successfully applied to the manipulator, demonstrating effective motion control. To develop the proposed model-free control framework, an experimental setup was established where only two joints and their respective links were utilized. A sequence of torque inputs was applied to the joints, and the corresponding joint angles and angular rates were recorded, effectively capturing the system’s forward dynamics. These input–output data pairs were then used to train an NARX-based neural network, which learned the system’s inverse dynamics and served as a computed torque controller. The developed neural network model was integrated into the control loop to generate torque commands necessary for trajectory tracking. Extensive simulations and experimental validations demonstrated that the proposed approach achieves highly satisfactory performance, comparable to model-based controllers, without requiring explicit knowledge of the robot’s physical parameters. Furthermore, the experimental platform facilitated direct torque control, leveraging actuators equipped with angular position, angular rate, and torque sensors. This study presents a significant advancement in model-free control of robotic manipulators, showcasing the potential of neural network-based approaches in environments where obtaining precise dynamic models is infeasible. The results highlight the robustness and generalizability of the proposed method, paving the way for future research in adaptive and intelligent robotic control.