The study addresses the challenge of accurately simulating and visualising the kinematics of agricultural machinery during field operations. The research is motivated by the current lack of comprehensive guidelines for selecting optimal movement and turning modes under varying forward speeds, working widths, and field geometries. A spreadsheet-based environment was utilised to perform simultaneous kinematic simulation and trajectory visualisation. Turning manoeuvres were modelled using smooth composite curves, consisting of straight segments, clothoids, and circular arcs, with trajectories represented in a Cartesian coordinate system through geometric transformations including translation, rotation, and mirror symmetry. Continuity between curve elements was ensured by dimensional chains linking abscissas, ordinates, and direction angles at their start and end points. The influence of key operational factors—forward speed, angular turning velocity, working direction, and field boundaries—was evaluated for a range of turn types, including semicircle, pear-shaped, figure-eight, side exit, U-turn, and P-turn manoeuvres. Field experiments conducted on selected patterns confirmed that the proposed approach can reproduce actual trajectories with sufficient practical accuracy. These results demonstrate that spreadsheet-based kinematic modelling is a robust and accessible tool for optimising tractor–implement movement, enhancing operational planning, and providing a reliable framework for further research into machinery performance under complex field conditions.
Hristov et al. (2026) studied this question.