## 1 Introduction  
Industrial robots are a cornerstone of modern automated manufacturing, spanning various industries. Their extensive and diverse applications, such as assembly lines, transportation, and complex and costly processes, underscore their indispensable role in contemporary society [1, 2]. However, the precise and uninterrupted operation of these mechanisms depends on the seamless functioning of all their systems, including power components, control systems, and mechanical connections. Disruptions to any of these parts can lead to production failures and the loss of material and energy resources [3, 4].  
Typically, diagnostic systems embedded in robot controllers are oriented toward monitoring the condition of the power components and control systems of the robot. While such systems allow for monitoring the operation of the robot's main units and detecting malfunctions, they often overlook smaller mechanical connections, such as gearboxes, hinges, and other elements. The inability to track the behavior of mechanical connections makes these robot parts the most challenging for fault detection, potentially resulting in serious consequences, including complete robot failure [1, 3].  
The diagnosis of faults in robots uses many methods [3, 5, 6]:  
1. Mathematical methods (fast and short-time Fourier transform, continuous wavelet transforms) [7, 8];Modeling methods (fuzzy logic, machine learning, and other artificial intelligence methods) [8; 9];  
Condition monitoring methods (control currents, temperature of mechanical parts, noise control, etc.) [10; 11].  
Therefore, for diagnostics, each of the methods presented has its own scope of application and is used to achieve various goals [1; 6; 7]. The mathematical methods are a powerful tool for evaluating and analyzing data, thereby identifying anomalies in the behavior of the mechanism. The modeling methods offer predictive and control capabilities, assessing discrepancies in the data obtained [11; 12]. The condition monitoring methods enable real-time data acquisition, constantly evaluating possible deviations from normal operation, thereby allowing problems to be detected before a failure occurs.  
The application of fuzzy logic-based diagnostic and control methods is of particular interest in the context of identifying faults in the mechanical parts of the robot. This approach avoids the use of precise mathematical models and ensures operation even if the integrity of the input data is compromised, in conditions in which other methods are least effective. The fuzzy logic algorithm processes information in such a way as to create a reliable system for diagnosing, controlling, and rectifying faults in challenging operating conditions [13; 14].  
The use of fuzzy logic principles allows for the adequate and adaptive adjustment of the robot's operating characteristics, taking into account uncertainties. This enables the maintenance of operational reliability, timely detection of damage, and determination of preventive measures for preserving structures and for their maintenance. Integrating such a system based on fuzzy logic is a way to enhance the stability and reliability of mechanisms, reduce equipment downtime, and improve performance in changing conditions [15; 16].  
This article is organized as follows: Section 2 of this article is a description of a Cartesian robot and its diagnosis system with a controller. The main faults detected by the controller are shown. Section 3 illustrates the gearbox structure of the Cartesian robot and includes the benefits and limitations of each part. Based on this information, the main gearbox faults are described. Section 4 describes the methodology used for generating the results of this article. Section 5 presents the specification of the test bench, the diagnosis results, and their description. Based on these results, the fuzzy logic algorithm was built. This section also shows the fuzzy logic algorithm modeling results for control parameters and fault type diagnosis.