Abstract: This study develops a coupled dynamic model and MATLAB/Simulink simulation framework for a shallot planter union consisting of a tractor, a working machine, a planting head, and an elastic coupling joint operating on soft soil. An eight-degree-of-freedom formulation is established using the Euler–Lagrange method and converted into a state-space representation with 16 state variables and 10 terrain-induced excitation inputs. Soil reaction is described via the Bekker pressure–sinkage relationship and linearized around the operating range for efficient simulation. The eigenvalue analysis confirms asymptotic stability of the coupled system (maxR(λ)=−2.8782), and time responses under initial perturbations remain bounded. Simulations indicate that pulse-type excitation governs peak responses, particularly in coupling yaw motion and planting head displacement, while harmonic and random excitations mainly contribute to sustained vibration levels. Frequency response analysis shows dominant low-frequency amplification of the main-body vertical motions in the range of approximately 0.5–2 Hz. The proposed framework supports preliminary vibration assessment and parameter tuning of shallot planting machinery under weak-soil field conditions.

Keywords: Shallot planter union, tractor-implement dynamics, Euler-Lagrange formulation, state-space modeling, MATLAB/Simulink, Bekker pressure-sinkage, soft-soil interaction, vibration and peak-load assessment

Pages: 91-99