A fire fighting and rescue motorcycle fitted with a fire fighting and rescue vehicle cluster on the vehicle's suspension will change the vehicle's center of gravity, affecting the vehicle's stability during travel. By modeling the kinematics in the planar motion of a two-wheeled motorcycle with 4 degrees of freedom, the paper has built a system of differential equations for the planar motion of the vehicle. Investigate the influence of the installation position of the vehicle cluster, the road surface collision, and the vehicle's speed on the loading and unloading of the vehicle in the process of moving in a straight line. The test results evaluate the reliability of the theoretical model.