Abstract <p>Variations in road adhesion conditions exert a significant influence on the dynamic performance of vehicles, primarily due to alterations in the maximum tire force achievable by the tires. In&#xa0;this paper, the transient dynamic behavior of vehicle braking on a road with sudden changes in road friction coefficient is studied. Particularly, the transient changes in tire force when crossing road boundaries are detailed during model establishment. Taking into account the asynchronous changes in tire force among individual wheels, the transient dynamic behavior and tire force characteristics of vehicle braking on mixed-μ road are analyzed. The tire force saturation and vehicle loss of control when tire total sliding occurs are discussed, and the calculation expression for the corresponding critical conditions are derived. The lateral motion, yaw motion, and trajectory deviation resulting from asynchronous changes in the longitudinal forces of the tires on both sides of the vehicle are analyzed. The conclusions of this paper provide theoretical reference for the analysis of vehicle braking performance in complex scenarios, and the derived critical condition of tire force saturation can be used as the boundary constraint of ABS control.</p>