Universal joints, which transmit torque through the balls guided in such a manner that they always lie in the plane bisecting the angle between the driving-shaft and driven-shaft, are called ball-type constant-velocity joints. The authors presented papers on the analysis of this type of universal joint based on statics neglecting the friction force between their components. To obtain more precise estimations of the internal forces and the moments, it appears to be important to evaluate the effect of the friction between the parts. Furthermore, grasping the relative motions of the parts, such as rolling of the balls on the tracks, is beyond the scope of static analysis. In this study, the authors analyze the motions of each part based on dynamics, taking account of the friction between the parts. The analysis results in simultaneous differential equations, which can be solved numerically using an electronic computer.