###### Abstract  
Purpose: In the present work, different combinations of fits and accuracies, in relation to the profiles of mating parts, have been analysed in order to assess the degree of the engagement of transmissions that contain intermediate rolling elements. The aim of this work is to determine which fits have decreased accuracy, but nevertheless provide a minimum manufacturing clearance for the transmission engagement in order to reduce the cost of parts production. **Methods and materials:** Considering the normal probabilistic distribution law in relation to the obtained dimensions of the manufacturing equipment, a combination of fits were selected using the incomplete interchangeability method, taking into account the peculiarities of the cycloid engagement in transmissions with intermediate rolling elements (IRE). **Results:** Having studied various combinations of fits of parts that are engaged in transmissions with intermediate rolling elements and a free cage (IREFC), a combination of fits for a \"ring, rolling-element cam\" were determined, in which a technological clearance of 3 \(\upmu\)m is formed in the engagement. At the same time, cycloid disk profiles are manufactured according to the 9 th tolerance grade, which reduces the laboriousness and cost of the production. **Discussion**. When reducing the manufacturing accuracy of cycloid disks, it is possible to obtain both very ample tolerances and significant negative allowances. For example, having manufactured a ring with the H9 fit, rolling elements with h6 and a cam with j89, the maximum manufacturing clearance can reach 0.086 mm, while the clearance limits vary from 0.025 mm to 0.061 mm. Additionally, if mating parts are manufactured using a combination of K9-h6-j89 fits, a negative allowance varying from 0.014 mm to 0.026 mm will emerge in the engagement. Both described cases are unacceptable because both ample clearances and large negative allowances will negatively influence the working capacity of the mechanism. However, it is possible to select a combination of fits using the 9 th tolerance grade of the basic parts, by which the parts will contact in the range from a small negative allowance of 1 \(\upmu\)m to a clearance of 3-4 \(\upmu\)m. Furthermore, if this is considered, taking into account the machine settings, it is possible to obtain parts according to the 9 th accuracy tolerance grade and, at the same time, provide a clearance in the engagement that is almost equal to zero. Moreover, such a combination of fits is relevant for any transmission with IRE. This is a positive result because it reduces the laboriousness when manufacturing parts and, at the same time, provides high accuracy of the mechanism. **Conclusions:** It has been established that when lowering the accuracy of manufacturing transmission parts with IRE, both clearances and negative allowances may occur in the engagement, depending on the combination of fits. At the same time, it is possible to select such a combination of fits, by which the parts manufactured according to the 9 th tolerance grade, will provide almost zero clearance of the engagement of the transmission. In this way, it is possible to reduce the cost of manufacturing the parts for gears with intermediate rolling elements and, at the same time, maintain a high accuracy of the transmission mechanism.  
manufacturing accuracy; cycloidal transmission; kinematic parameters; tolerances; deviations; technological gap