At present, there are few reports on the profiling mechanism that can achieve surface envelope profiling along the surface of a shaft whose radius is constantly changing. Existing profiling mechanisms cannot achieve this function. To this end, a novel deployable arc profiling mechanism is presented in this paper. The mechanism can realize centering deployment along the shaft with a changing radius. The radius of the deployable arc can be adapted to the continuous change of shaft radius, and its surface can always maintain the arc shape for surface envelope profiling. The mechanism is mainly composed of compound cams. Each cam contains multiple grooves, and each groove connects to an arc support linkage. The arc support linkage is controlled by the compound motion of cams in different layers. The pitch curve of each groove is designed by applying the method of relative motion and inverse solution and obtained various parameter equations of the mechanism. The feasibility of this mechanism is verified by analysis, experiment, and application test. The results show that the proposed deployable arc profiling mechanism can achieve the design purpose and the profiling accuracy is kept above 96.425%.