The handling stability of a vehicle is a crucial performance aspect. In this study, the focus is on investigating the impact of the universal gearing of the steering shaft on the handling stability of the vehicle. The research involves a theoretical analysis of how the structural parameters of universal gearing affect the handling stability of the vehicle, which is then validated through a series of simulation experiments including swept-sine steering input simulation, constant radius cornering simulation, and cornering with steer release. Evaluation is based on objective indices such as the steering wheel angle, yaw rate, and lateral acceleration. Moreover, the trends of these indices with respect to the phase angle and initial angle of universal gearing are determined. The findings reveal that the steering ratio of the vehicle varies significantly for varying phase angle and initial angle, resulting in different handling performance. The relationship between the phase angle and fluctuation magnitude of steering ratio is particularly noteworthy, while the impact of initial angle is primarily on the phase of steering ratio. Furthermore, within a certain range, changing the structural parameters of the universal gearing has the potential to enhance the handling performance of the vehicle.