The detection of faults during an operational process constitutes a crucial objective within the framework of developing a control system to monitor the structure of industrial mechanisms. Even minor faults can give rise to significant consequences that require swift resolution. This research investigates the impact of overtension in the tooth belt transmission and heating of the screw transmission worm on the vibration signals in a robotic system. Utilizing FFT techniques, distinct frequency characteristics associated with different faults were identified. Overtension in the tooth belt transmission caused localized oscillations, addressed by adjusting the acceleration and deceleration speeds. Heating of the screw transmission worm led to widespread disturbances affecting servo stress and positioning accuracy. A fuzzy logic algorithm based on spectral analysis was proposed for adaptive control, considering the vibration’s frequency and amplitude. The simulation results demonstrated effective damage mitigation, reducing wear on the mechanical parts. The diagnostic approach, relying on limited data, emphasized the feasibility of identifying transmission damage, thereby minimizing maintenance costs. This research contributes a comprehensive and adaptive solution for robotic system diagnostics and control, with the proposed fuzzy logic algorithm showing promise for efficient signal processing and machine learning applications.