Abstract: China possesses vast reserves of thin coal seams, rendering their efficient exploitation of significant economic value. To accommodate the demands of excavation within confined environments—such as low-height roadways and thin seam coal mines—and to enhance the operational agility of integrated excavation-anchoring machines in underground settings, a novel “dual-wheel and single-track” system is proposed. This study begins by delineating the structural composition of the proposed locomotion system, with particular attention given to the dimensional and material optimization of the track plate, facilitating subsequent three-dimensional modeling. To ensure adaptability to adverse floor conditions, force analyses under two representative working conditions—gradient climbing and directional turning—are conducted. A theoretical model for calculating the optimal tractive force matching is developed and applied to both scenarios. Comparative analysis with empirical data reveals that the required uniaxial driving force is significantly higher under turning conditions. The theoretical torque values derived from the model show a deviation of merely 5.9% from those obtained via hydraulic gauge measurements, thereby affirming the model’s predictive accuracy and practical viability. Furthermore, finite element analysis is employed to validate the structural integrity of the track plate. Under equivalent loading conditions, the maximum stress observed along the X-axis reaches 244.3 MPa, remaining within permissible limits, thus verifying compliance with the strength requirements under optimal loading. The findings demonstrate that the “dual-wheel and single-track” locomotion system effectively reduces the chassis height and enhances maneuverability. The derived tractive force model exhibits high congruence with empirical measurements, offering a robust theoretical and engineering reference for the future design of similar mobility systems.