Radial braiding machines are widely used in the preparation of complex preforms of high-performance fibers. However, the structural characteristics of a radial braiding machine inevitably cause axial clearance between the carrier base and horn gear, which affects the running speed of braiding machines and the stability of carrier exchanges. It is easy to create disadvantages of yarn fuzzing and poor continuity of preformed fibers. In order to solve these problems, this study compares and analyzes the coplanar horn gears in the industry and designs a kind of noncoplanar horn gear. Through the study, it is found that the trajectory of a carrier on a horn gear is divided into the linear phase and circular phase, based on which the mathematical model of the axial clearance between the carrier base and horn gear is established. The variation curve of the clearance with the horn gear rotation angle is plotted by using MATLAB software. A simulation model of the axial clearance between the carrier base and horn gear is established by using ABAQUS software, and carrier bases with different clearances are made to run on the braiding machine. The reliability of the theoretical calculation is verified by combining simulation and experiment, and it is proved that the use of the noncoplanar horn gear in radial braiding machines can effectively reduce the clearance and reduce vibration and shock.