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During the engaging process of sleeve and teeth ring in mechanical transmissions, their rotational speed and position differences cause multiple engaging ways and trajectories, and casual impacts between them will delay the engaging process and cause a long power off time for a gear shift. In order to reveal the engaging mechanism of the sleeve and the teeth ring, it is essential to build a high-fidelity model to cover all of their engaging ways and capture their speed changes for an impact. In this work, our contribution is that their impact process is modeled as a precise, continuous and nonlinear damping model, and then a hybrid automaton model is built to connect the system dynamics in different mechanical coupling relationships.