A comprehensive stable control strategy has been proposed to address the control challenges of under-actuated robotic arms, which can ensure stable system operation in the presence of uncertain vibration disturbances. Firstly, based on the Denavit-Hartenberg (D-H) method and Lagrangian mechanics, a dynamic model is established to capture the uncertain nonlinear dynamics of the under-actuated manipulator. Secondly, a trajectory tracking controller is designed based on ANSTSMC (adaptive non-singular fast terminal sliding mode control) to address the uncertain disturbances experienced by robotic arms in complex environments. Under the proposed adaptive control law, external disturbances and inherent chattering effects can be estimated and compensated in real time. Meanwhile, based on the Lyapunov stability theory, a system stability analysis is conducted, with the analysis results showing that the designed controller can ensure rapid convergence of the system within a finite time. The simulation experiment results have verified the effectiveness of the proposed method. The results show that the control strategy can achieve precise trajectory tracking of the robotic arm in the unstable state of the system, effectively improve the overall performance of the system, and promote the rapid recovery of the robotic arm to a stable operating state.