The universal joint or Hooke joint, or U-joint is the main unit of the cardan transmission, which consists of two joints connected by an intermediate shaft. Cardan gears are widely used in various industries when creating machines with power transfer from the output shaft of the gearbox to the crank shaft in the absence of their coaxiality. A sufficiently large number of works are devoted to the study of the kinematics of the universal joint, and there are no works on its dynamics. Such a description became possible due to the use of matrix and quaternion formalism in describing the movement of the universal joint. In this paper, a complete description of the kinematics of the universal joint in its working cycle in terms of analogues of angular velocities is obtained and, on this basis, the dynamics of the joint is studied, taking into account its inertial characteristics. It is shown that taking into account the inertial characteristics of the U-joint cross can lead to a significant increase in the magnitude of the torque, the effectiveness on the spikes, in contact with the fork of the driven shaft.