MATHEMATICAL MODELING OF THE KINEMATIC AND DYNAMIC PARAMETERS OF THE RUNNING GEAR OF A THREE-WHEELED MINI-TRACTOR

Compact three-wheeled mini-tractors — comprising a single steered front wheel and two driven rear wheels — are increasingly used on small private (dekhkan) farms, in orchards and in greenhouse rows because of their small turning radius and high manoeuvrability in confined plots. Systematic, self-contained mathematical descriptions of the coupled kinematics and dynamics of this specific running-gear layout are, however, less commonly available in an accessible form than models developed for four-wheel or articulated tractor-implement systems. This paper develops a combined kinematic–dynamic model of the running gear of a three-wheeled mini-tractor. The kinematic sub-model, based on the classical tricycle (Ackermann-equivalent) formulation, relates the front-wheel steering angle to the turning radius, the yaw rate of the machine and the individual angular velocities of the two rear wheels. The dynamic sub-model, derived from Newton's second law, expresses the longitudinal equation of motion in terms of the adhesion-limited tractive force, the rolling-resistance force and the draft resistance of a towed implement, and is complemented by a lateral-stability (rollover) criterion based on the static stability factor and a critical cornering speed. Because no physical prototype or experimental data set was available at the time of the study, every numerical input is explicitly declared as a design assumption, calibrated against published data for comparable mini-tractor classes. The model was evaluated numerically for a front-wheel steering-angle range of 5–35° and for three draft-resistance scenarios (unloaded travel, light cultivation and mouldboard ploughing). The results show the turning radius decreasing from about 16.0 m to 2.0 m while the critical rollover speed falls from about 43 km/h to 15 km/h over the same steering range, revealing a direct manoeuvrability–stability trade-off inherent to the three-wheeled layout; the longitudinal-dynamics simulation shows the time needed to reach 90% of the steady travel speed increasing from 2.7 s (unloaded) to 9.0 s (ploughing) as the draft resistance approaches the adhesion limit of the driven wheels. On this basis, practical recommendations are proposed for the choice of track width, centre-of-gravity height and maximum permissible steering angle in the design of three-wheeled mini-tractor running gear.