## 1 Introduction  
Over the last few decades, cycloid speed reducers have found a wide application in engineering practice. They are generally used as reducers, while their applications as multipliers or two-way power transmission systems have not been sufficiently studied yet. Cycloid speed reducers have a great number of good performance characteristics, such as a wide range of transmission ratios, extremely compact design, low noise and vibration, lightweight concerning the torque they transmit, ability to transmit high torques, reliable operation under intensive dynamic loads, high efficiency, etc. All these good operating characteristics together with a good price range, give them an advantage over conventional speed reducers. These gear trains have found application in robots, satellites, manipulation devices, crane machines, large industrial mixers, conveyors, and renewable energy sources (wind generators, mini hydro power plants). The cycloid speed reducer force analysis and stresses in reducer elements caused by internal forces is a very complex task. For that reason, the cycloid speed reducer elements are often over-dimensioned, considering the possible problems that can be encountered in the cycloid speed reducer operation. The first analysis of the cycloid speed reducer internal forces was performed by [PERSON] in his book _Planetary Gear Train_[1]. His model was further improved by [PERSON] [2] in his doctoral thesis. [PERSON] and [PERSON] [3] developed a detailed model for determining the forces on all the elements of the cycloid speed reducer, which they later used to calculate the efficiency. The further published research about cycloid reducer dynamic analysis can be divided into two main groups: the papers that deal mainly with analytical models and simulations and the papers with dynamic simulations compared with experimental testing. One of the first papers from the first group of research was performed by [PERSON] and [PERSON] [4], showing the detailed dynamic simulation in CAD software of a cycloid speed reducer without a theoretical background. On the other hand, [PERSON] and [PERSON] [5] gave the analytical method of excitation force creation and its transformation into internal reducer forces. Furthermore, [PERSON] et al. [6] analyzed sliding speed in cycloid speed reducers. [PERSON] [7] did a static analysis of the stress state in cycloid discs interacting with other reducer meshing elements. [PERSON] [8; 9] did both simulation and experimental analysis in classic cycloid speed reducers and non-pin wheel cycloid speed reducers, comparing their results. [PERSON] et al. [10] did a dynamic analysis of cycloid speed reducers with special attention to their vibrations. Other authors in this field [11; 12; 13; 14; 15; 16; 17] did various dynamic simulations of cycloid speed reducer working using different software for its analysis, such as SolidWorks, ANSYS, MSC NASTRAN, etc. Two papers [18; 19; 20] in this field have been different because they described the simulation of contact stresses in cycloid discs all along their width. One of the most influential factors in the cycloid speed reducer dynamic is its machining and manufacturing tolerances [21]. Very accurate research about forces and stress calculation was performed by [PERSON] et al. [22], which can be used as a starting point for further experimental analyses. Papers from the second group of papers related to cycloid reducer dynamics involve investigations with experimental testing. These papers were not published often because of the experiments' complexity and their costs. One of the first papers related to cycloid reducer dynamics was written by [PERSON] [8], and the part related to the experiment was conducted in an open power circuit. In that research, the output torque was measured in two types of reducers: classic cycloid reducer and non-pin wheel concept. Another publication that had an experiment was by [PERSON] et al. [23].