## 1 Introduction  
Technologically advanced devices place increased demands on precise and reliable positioning in industrial applications, especially in robotics and high-precision machines. These requirements lead to the increased use of high-precision cycloidal and harmonic propulsion systems. The reducer, as part of the actuator drive unit, significantly influences its properties (the properties of the entire propulsion system). Reducers used in robotic joints are the most complex subsystems of robots [1, 2, 3]. Recently, these cycloidal, harmonic and planetary reducers have been brought to perfection to ensure that the robotic system has the properties required. In addition to the requirements for accuracy and reliability, a high gear ratio, high kinematic accuracy, high tilting rigidity, backlash-free operation, high torque capacity, compact size, low weight and high load capacity are also expected [4]. High-precision gear mechanisms (reducers) are used in combination with actuators and form a mechatronic node. The mechatronic node can be described as a coupling member between the non-power (information) control part, and the power control part of the system. Energy conversion occurs in the power section. The mechatronic node can be understood as a complex system consisting of a servomotor, a reducer, a feedback sensor and possibly also a brake or a redundant position sensor. Such a device of precision mechanics, in combination with control electronics, enables precise control of the position, speed, simplification of kinematic structures and increase in dynamics while reducing the demands on the assembly of individual sub nodes [5, 6, 7]. Typical for today is highly automated and flexible production aligned with the principles of Industry 4.0. Progressive automation is a fundamental pillar of the modern production process, which requires accuracy, repeatability and minimal deviations. These factors are a prerequisite for efficient operation. An overview of high-precision reducers for industrial robots that operate in accordance with the principles of Industry 4.0 is given in the paper by the team of authors of [PERSON] et al. [8]. Many research institutes and development centers work on the continuous development and innovation of high-precision reducers. The new design proposal is addressed by authors of several studies, an example being the paper of [PERSON] et al. [9], or the paper by [PERSON] et al. [10]. In their study, [PERSON] et al. [11] present an innovative cycloidal planetary reducer, utilizing the principle of internal engagement instead of an external one between the cycloidal wheel and the pins of the traditional reduction wheel. Its results prove that the proposed transmission power of the reducer is competitive compared to traditional RV reducers. Prototype testing is performed, parameters in individual phases of product life are analyzed, and stress tests are conducted. In their paper, [PERSON] et al. [12] focus on the analysis of a new method of modifying the parabolic profile to improve the transmission accuracy, where the result was a difference of up to 5% between the errors measured and the results calculated, thus proving the correctness of this system. The engagement stiffness of the level gears in the transmission of the rotational level vector was described in the study by [PERSON] et al. [13], which helps researchers to better understand the influence of various parameters on the analysis of the dynamic characteristics of transmission systems. In their paper, the authors of [PERSON] et al. focused on the analysis of the efficiency of cycloidal reducers with tolerance achieved by means of an approximate force distribution of an ideal cycloidal reducer [14]. The experimental work was carried out by a team of authors ([PERSON] et al.) in order to clarify the optimal input formula for precise rotation using a prototype of a motor designed by them [15]. In their publication, a team of authors ([PERSON] et al.)