**1. Introduction**

Today, world has seen a marked increase in the variety of techniques used in all areas of human activity, in terms of their functionality. Therefore working out of working bodies expanding their functionality is one of the major problems of modern engineering and design activity. This has become especially important in the context of the transition of the Republic of Uzbekistan to a new stage of development, where fundamental reforms of management in agriculture are taking place, grandiose projects in construction are being implemented, as well as great attention is being paid to the development of settlements [1]. Decision of these problems is straight connected with geometric modeling on which modern problems of design engineering and manufacturing are based. Extending the functional

possibilities of agricultural machines is one of the main ways for design engineering and manufacturing of modern agricultural machines, which can be realize by design engineers. Particularly, it actually in modern agricultural production, which based on precision agriculture technologies, where using such machines must provide: reduction of cost, conservation of ground fertility, saving energy-resources, improvement labor conditions, and increase machines capacity. One of the efficient ways to decide these problems is using geometric modeling in design engineering of agriculture machines' tools. Geometric modeling, as one of varieties synthetic methods' of designing, is a theoretical base for production design and CAD technologies, which widely use in design engineering and manufacturing [2–4].

The development of agricultural tools mankind has been engaged for centuries. In 1830, the Italian abbes Lambruschini and Ridolfi were prompted by the helical surface (helix) to plow's moldboard. In the late nineteenth century, Russian academician V.P. Goryachkin laid the foundation of the science "Agricultural Mechanics". Since then, many scientists from America, Europe, and other countries have developed various methods of research and modeling in the mechanization of agriculture. These methods mainly solve problems by analytical and experimental methods, although synthetic methods have a number of advantages in solving some problems. The reason that synthetic methods, as geometric modeling, until recently used rarely, was the advantage of the use of information technology in analytical methods. However, the widespread use of information technology in synthetic methods since the end of the twentieth century, their capabilities have become much more effective. The advantage of geometric modeling is its simplicity and clarity. It as a basis of synthetic methods of development of technical objects has innovative character that modern production demands increase in a variety of production, reduction of terms of their development, and also automatization of these processes [5–8].
