# New Construction Solutions of Gear Using in Space Vehicle Control Systems
###### Abstract
Its exceptional way of working the wave gear allows one to achieve a very large gear ratio, usually to a single degree, from 40:1 to 100:1 and, in some cases, even 300:1 [24; 25]. Hence, one of the most important advantages of toothed wave gears is their high kinematic accuracy. A disadvantage of wave gears is their manufacturing difficulties, especially concerning the flexspline, which requires special equipment during processing. Moreover, the very small modules used in these types of gears can be a problem when performing them using traditional methods. The basic problem of harmonic drives is their durability, which is based on the fact that endurance is the most loaded element, hence the flexspline. Computational and experimental work has been performed for years to increase the durability of harmonic drives by changing the design of flexsplines or using new materials. Figure 1: Scheme of harmonic drive: (1) flexspline, (2) circular spline, (3) wave generator. The vast majority of research so far has referred to typical harmonic drives with the flexspline with bottom and collar [26; 27; 28; 29]. The geometric parameters of the constructions encountered most often are presented in Figure 2. These gears are long parts with a toothed rim on one side and a bottom or flange on the other side. The harmonic drive has a standard shape of the thin-walled sleeve, and a slightly thicker bottom or collar is used to fix it to the shaft or body (Figure 2a). The classical bodies can have external (Figure 2b) or internal (Figure 2c) flanges. Their overall dimensions, especially the overall length (L), are significant relative to the width of the toothed wheel rim. Introducing new drives with such complicated construction and principles of operation must be preceded by a cautious analysis of the initial stages of design. The standard shapes of the flexspline of the harmonic drives shown in Figure 2 are solutions based on the cylindrical sleeve. The chamfers or rounding introduced are small, resulting from technological limitations that occur when making wheels using traditional processing methods. In a classical flexspline, the flat bottom stiffens the structure, causing high stress levels in the sleeve, which directly results in its destruction. Therefore, there is still the need for new construction and material solutions [20; 30] which will allow lowering the maximum stress values in this element by changing the shape of its body. However, only contemporary production possibilities, including numerically controlled machines (CNC) or incremental methods, can handle many restrictions in this range and allow one to make a flexspline with an unprecedented shape. The aim of the presented analysis is to fix the shape of the flexspline to improve it in terms of its durability and reliability. During the design of flexsplines intended for application in precise control and regulation of space vehicles, it is necessary to pay attention to maintaining their high kinematic accuracy and reliability that allow for working in space. Figure 2: Selected constructions of flexsplines of harmonic drives with: (**a**) bottom, (**b**) outer flange, (**c**) inner flange. Where: d\({}_{1}\)-pitch diameter, L-flexsplinength, d\({}_{w}\)—inside diameter, d\({}_{n}\)—diameter of the neutral layer circle, d\({}_{2}\)—thickening diameter, d\({}_{x}\)—diameter of the outer flange, d\({}_{x}\)—diameter of the inner flange, h\({}_{1}\)—sleeve body thickness, h\({}_{2}\)—body thickness without toothed ring, R\({}_{1}\)—radius of toothed rim, R\({}_{2}\)—filtel radius. Own study based on [21]. Hence, an attempt was made to establish the best shape of the flexspline which would improve the durability of the harmonic drive considering the lack of possibility of servicing it over a long period of time. To accomplish this research task, over a dozen construction variants were designed and researched, from which a few of the characteristics are presented in the next part of this study.