Helical gears are the most common type of drive that converts rotational motion into translational motion. Ball screw gears are the most widely used in precision instruments and machine tools. Currently, the issue of improving the reliability of the drive containing a ball screw transmission, according to the parameter “kinematic accuracy”, is relevant. The method of probabilistic estimation of the aftereffect of screw gears is considered. The method is based on the results of the analysis of the functioning of the transmission parts, followed by the synthesis of a model of the accuracy of screw gears. A comparative analysis of the magnitude of the aftereffect of some screw gear designs is performed. The prospect of using planetary mechanisms with threaded rollers and nonrack mechanisms with threaded rollers in three-dimensional hingerod structures such as: mobile reconfigurable robotic stations, robotic systems, collaborative and exoskeletal robots is shown.