Performing stable and safe lane changes can avoid collisions and improve traffic safety. In recent years, most of the research in automated ground transportation was focused on path planning and path tracking. However, this work emphasizes the importance of lane changing time point. Based on traditional safety distance, a novel concept, that is the synthesized safety distance for lane changing (SSDLC), is proposed to study lane changing time point. It consists of the reference safety distance and lane changing safety distance, and the weight coefficient between them is obtained by fuzzy logic control algorithm. Additionally, the joint model predictive control (JMPC) is proposed to follow the reference trajectory. This newly established algorithm not only considers the physical saturation of actuators but the yaw stability characteristics. To overcome the calculation difficulty to obtain the optimal results in the prescribed time, the algorithm adds a relaxation factor in the objective function. Finally, the lane changing time point and path tracking framework is modeled and simulated on a CarSim‐Simulink platform. Four scenarios are carried out to illustrate the feasibility of the proposed framework.