This paper presents a novel model-free finite-time sliding mode control strategy for robotic manipulators that ensures accurate tracking, rapid error convergence, and smooth control signals while effectively handling system uncertainties and external disturbances. Unlike conventional control techniques requiring detailed dynamic models, the proposed method employs time-delay estimation (TDE) to approximate system dynamics in real-time, enabling model-independent implementation. A new nonsingular sliding surface and finite-time reaching law are introduced to enhance stability, convergence speed, and chattering mitigation. The controller’s performance is validated through simulations on a 3-DOF SAMSUNG FARA AT2 robot arm, demonstrating superior tracking accuracy, robustness, and control smoothness compared to Computed Torque Control (CTC), Sliding Mode Control (SMC), and Nonsingular Terminal SMC (NTSMC).