# Design and Lateral Stability Analysis of an Attitude Adjustment Tractor for Moving on Side Slopes
## 1 Introduction
On the other hand, the design continuity requires that the new locomotion system should inherit the general structure of the previous tractor, and the changes should be as small as possible. To avoid lateral overturns, this work designs a four-wheeled tractor that integrates the advantages of the mechanisms mentioned above. Inspired by the traditional tractor, this one is modified by the rear and front axles, respectively. For the rear axle, equipping the attitude adjustment mechanism composed of a pair of gears on both sides, thereby changing the height on both sides. For the front axle, it can cooperate with the rear axle to actively adjust the tractor's attitude. Additionally, both the rear and front axles transmit power while ensuring that all four wheels can provide power. This tractor has two modes of locomotion, while the traditional one only has one mode; a new mode of changing the attitude/configuration enables the tractor to work on side slopes. This locomotion system does not require real-time control to keep all wheels in contact with the ground and reduces the complexity of the control system similar to the traditional tractor. It can also adjust its roll angle/configuration when necessary to enhance its stability. Generally, as a four-wheel-drive tractor, it can work on various terrains, especially the side slopes and uneven terrains. Therefore, taking the tractor's attitude into consideration, a mathematical model of a tractor on lateral slopes is developed. This general model is formulated, describing the relationship between wheel-soil contact forces as a function of overturn parameters. The designed tractor can adjust its roll angle by attitude adjustment mechanisms. Combining the model of specific attitude adjustment mechanisms and a complete tractor model, the lateral stability analysis associated with the active input of the attitude adjustment mechanism is conducted. Meanwhile, the instability indicator of tractor lateral overturns is obtained for an arbitrary configuration with attitude adjustment mechanisms. Thus, one main contribution of this study is the description of the design concept of a tractor with attitude adjustment mechanisms. Inspired by the traditional tractor, both front and rear axles are modified to achieve the three functions: attitude adjustment, steering, and power transmission. The designed tractor can also level itself when the angle of the lateral slope is less than 15\({}^{\circ}\). Then, a prototype is manufactured, which is the practical contribution of this study. Another main contribution is to formulate a general mathematical model for the tractor while taking the attitude into consideration and to develop the relationship between the input of the adjustment mechanisms and the tractor's lateral stability. Attitude adjustment parameters are also designed. This is the scientific contribution. The approach developed here provides an effective way to avoid lateral overturns, which are fatal to drivers. In the present paper, the design concept of the tractor is described in more detail. In addition, a mathematical model representing the relationship between the posture/configuration and the tractor's lateral stability is also built, and verification of the model is discussed based on experiments. The remainder of this paper is organized as follows. Section 2 discusses the design concept of the proposed hillside tractor. Section 3 develops the kinematic model of the adjustment mechanism equipped on the rear wheels. In Section 4, the effects of posture change on lateral stability are based on a mathematical model. Section 5 includes case studies and experiments that validate the lateral stability model. Finally, Section 6 concludes and describes the future works of this paper.