Carbon fiber yarn circular braiding is a composite manufacturing process for producing tubular preforms, widely applied in industrial fields such as aerospace. Before circular braiding, it is essential to inversely calculate the takeup speed of the mandrel based on the expected braid angle of the braided composite. However, the traditional inversesolution method relying solely on kinematics has a large error. To address this issue, this paper proposes an inverse-solution algorithm for the mandrel take-up speed in circular braiding that incorporates yarn friction. Firstly, through the mechanical analysis of the interaction between yarns in the convergence zone, the equivalent braid angle under the ideal kinematic model was calculated according to the expected braid angle. Then, by conducting a kinematic analysis of the circular braiding process, the corresponding mandrel take-up speed was obtained based on the equivalent braid angle. To verify the effectiveness of the inverse-solution algorithm, a circular-braiding finite element simulation model and a circular-braiding physical experimental platform were established for simulation and physical experiments. The experimental results indicate that, compared with the traditional inverse-solution method based only on kinematics analysis, the proposed algorithm can effectively reflect the influence of the interaction between yarns during the braiding process. The average error between the obtained braid angle and the expected braid angle is less than 1°, which is significantly reduced compared to traditional kinematic methods.