The space optical camera is a high-precision system， and its primary mirror is supported by the repeatable development and collapse mechanism to achieve system imaging. To improve the accuracy of a space optical camera's repeatable development and collapse mechanism， the folding method of the membrane protective cover is proposed， and a parameter analysis is conducted based on the Miura origami principle. The NX/SST simulation software is used to calculate the temperature field of the repeatable development and collapse mechanism with and without the membrane protective cover. Further， the deformation law of the primary mirror mounting surface under different temperature gradients is studied. The extension mechanism membrane protective cover prototype is used to perform the repeatable development and collapse experiment of the extension mechanism. The results show that when the expansion angle of the repeatable expansion and collapse film protective cover， designed in this study， is 120°， the structure has completed nearly 85% of the expansion. Moreover， the shape of the model is still regular at this time， which verifies the passively repeatable development and collapse function of the protective cover. Through thermal analysis， it is found that the maximum temperature of the camera’s internal extension mechanism with a protective cover is 12℃， and the minimum temperature is 3.5 ℃. Compared with the no protective cover case， the maximum temperature is reduced by 22 ℃， and the minimum temperature is increased by 51.5 ℃. The protective cover effectively reduces the temperature gradient of the extension mechanism. The experimental results show that after 10 repeated development tests of the extension mechanism， the average repeatability accuracy absolute value in the X， Y， and Z direction are 0.002 16 mm， 0.005 96 mm， and 0.003 48 mm， respectively. The extension mechanism designed in the study has a high repeatable expansion accuracy， and the film protective cover designed based on the origami principle has good repeatable development and collapse， shading， and thermal control effects， which can effectively ensure the application of the optical cameras in space environments.