<p>In this paper, a calculation model for accurately determining the results of the multi-tooth meshing-in impact force of cycloidal pin gear transmission in rotate vector reducer was proposed. Firstly, the principle of multi-tooth meshing-in impact of cycloidal pin gear transmission mechanism under load was explained, and meshing-in velocity was derived. Secondly, a meshing-in impact force model considering damping force and the meshing-in impact coefficient was proposed based on the Hunt-Crossley contact collision model and the Hertz contact collision curve. The study investigated the influence of different modification methods, eccentricity and cycloidal revolution speed on the impact force. Subsequently, an optimization mathematical model was constructed to optimize the basic design parameters of cycloidal gear, with the meshing-in impact coefficient of cycloidal pin gear transmission as the objective. Finally, the impact force model and the optimal mathematical model were verified using finite element analysis. The maximum error of impact force between the theory and simulation results is 3.53%, which is within the allowable range and proved the feasibility of the meshing-in impact model. The results demonstrate that the optimized cycloidal pin gear transmission effectively reduces the impact coefficient.</p>