The invention discloses a flexible transmission mechanism of a non-closed type annular rotator and an application method of the flexible transmission mechanism. The flexible transmission mechanism comprises the non-closed type annular rotator, three pinch rollers, six tensioning wheels, a toothed belt, a housing and a gear, wherein the pinch rollers, the tensioning wheels and a central spindle of the gear are fixed on a base plate of the housing; the gear, the second tensioning wheel, the first tensioning wheel, the third tensioning wheel, the fourth tensioning wheel, the sixth tensioning wheel and the fifth tensioning wheel are arranged clockwise; the inner side of the toothed belt is fitted with the outer sides of the five tensioning wheels to form a closed ring; the outer side of the toothed belt is meshed with the gear and the outer tooth shape of the non-closed type annular rotator; the three pinch rollers are fitted with the inner side of the non-closed type annular rotator. The flexible transmission mechanism of the non-closed type annular rotator and the application method of the flexible transmission mechanism, disclosed by the invention, can enlarge the meshing area of the flexible transmission mechanism, the gear and the non-closed type annular rotator, so as to increase the meshing force, and meanwhile avoid interference and clamping between the flexible transmission mechanism, the gear and the rigid tooth shape of the non-closed type annular rotator.