Regarding the image rotation happened on the rotation direction of large astronomical cameras, a system of fast adjustment mechanism was designed with the flexible hinge shafting which was characterized by zero friction, non-abrasion, free of lubrication, easy maintenance and high resolution. This system could directly drive the camera for a mechanically despun. The flexible shafting was composed of 8 flexible units which were rounded off and evenly distributed. According to the structure of each flexible unit, a theoretical model was also set up for the system guided by applied mechanics theories, by which we analyzed the relationship between the rigidity and the structural parameters, carried out the finite element simulation and made experiments for test. The results showed: The maxim error between the finite element simulation and the theoretical analysis was 3.215%. The maxim error between the testing result and the theoretical analysis was 4.875%. It verified that the theoretical formula is correct and reliable. The mathematical model was built up according to theoretical formula, so that we could define the optimized structural parameters efficiently for the fast adjustment mechanism, and realize the design goal to meet the technical requests and minimize the working moment.