The use of delivery drones is currently hindered by the inability of transported objects to maintain a steady position, which can result from roll-, pitch-, and heave-induced vibrations. This paper proposes a novel parallel manipulator for stabilizing the platform of unmanned aerial vehicles. The proposed mechanism builds upon an existing study of a 3-SRR/SRU parallel stabilizing mechanism by incorporating the dynamical properties of the system into the control model. The resultant control technique is then applied to both the 3-RRS and 3-SRR mechanisms, and a comparative study is conducted to identify the most reliable stabilizer for regulating the platform’s orientation. The results demonstrate that the 3-SRR mechanism exhibits superior robustness and stability characteristics compared to the other two mechanisms. Additionally, the 3-SRR mechanism is controlled using artificial neural networks, which significantly improves the accuracy and stability of the system. Overall, this research presents a novel and effective solution for stabilizing the platform of unmanned aerial vehicles, with significant implications for the development of delivery drone technology.