To address the problem of elastic contact discrepancies between a variable-diameter internal drive device and a non-continuous surface during the transition, caused by the vibrations resulting from elastic collision impact when the motion speed of the elastic body increases, the following steps were taken. First, we established models for elastic collision, impact, and vibration during the inter-stage transition to analyze how motion speed and preload affect the elastic contact characteristics between the two components. Subsequently, we employed the finite element method to further analyze the elastic contact state, using identical loads but varying motion speeds and radial preloads as boundary conditions. Finally, an experimental prototype was developed to validate the elastic contact state of the elastic body during the inter-stage transition. The results indicated that the amplitude of elastic body vibration increased with higher motion speed, while it decreased with higher radial preload. Therefore, it is necessary to adjust radial preload at different times to ensure effective elastic contact between the elastic body and the non-continuous surface during the inter-stage transition. This approach not only enhances deployment speed but also guarantees the stability of the inter-stage transition.