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In order to understand the kinematic properties of the tripod sliding universal joint, its kinematic model was established. First, the relation between the input and output angles and the relative displacements of the slide-rods to the input shaft and to the tripod were obtained by using coordinate transformation technology. And then, the expression of the fluctuation of the joint angle was derived from the cross product of the centerlines of the input and output shafts. The numerical results show that the output angle error, the angular velocity error of the output shaft, the joint angle and the relative displacements of the slide-rods to the input shaft and to the tripod are all periodic and similar to a sinusoid. In addition, the output angle error, the angular velocity error of the output shaft and the joint angle have a threefold frequency of the input shaft, whereas the relative displacements of the slide-rods to the input shaft and to the tripod have simple and twofold frequencies of the input shaft respectively. The gained results agree well with the main documents, and validate the present model.