Vast steppes of Kazakhstan mainly consist of stubble and sandy loam soils, as well as salt marshes with solid surface. Therefore, it is possible to drive on them on conventional vehicles with pneumatic wheels. Where the land is developed for grain crops, the surface of the soil is soft, and where fodder crop rotations are cultivated, the surface of the soil is as solid as stubble. Wherever land is used for economic needs, wheeled cars, tractors and agricultural machinery drive there. Unfortunately, they deteriorate a lot. Service life time of trucks and cars in off-road conditions compared with service lifetime of them in urban environments is reduced by almost four times. Tractor trucks, tractor cultivators and all types of self-moving wheeled agricultural machinery are annually subjected to seasonal repairs as a result of agricultural harvesting. Moreover, their maintenance is expensive. Accordingly, we cannot say that all goes well, but this happens unwillingly. What shall we do if there are no other types of progressive machinery? Mechanicians rush to answer the question if there is a need to introduce something new. They say-"What else could you ask for? All machines work. " In fact, according to scientifi c forecasting, the design of these machines are supposed to be completely different in off-road conditions. Relief irregularities of soil supporting surface affect outrigger wheels with round cover disk strongly. In such cases not only a lot of energy is expended, but all the components and assemblies of undercarriage undergo vibrations, which causes severe wear to occur.

This work o ers a new chassis design, namely the wheel-track, presents a mathematical model of this chassis, and also proves the advantage of the proposed design when driving the vehicle on arbitrary terrain, a rough o-road. The proposed approach is applied to design unmanned research mechanisms for other planets (Mars rovers, lunar rovers, etc.) and, also, to design robots and transport of rescuers at liquidation of consequences of natural or technological disasters. This article analyzes the requirements of the chassis design of the extraterrestrial unmanned research mechanism and demonstrates the high compliance of the proposed approach with results. This study proposes and investigates a mathematical model of wheel-track, demonstrates the optimization of the proposed mathematical model to machine computing, and shows the exibility and scalability of the mathematical model. The proposed design is an attempt to combine the advantages of walking and wheel types of travel through one mechanism.