Antenna panels of a satellite are usually deployed and supported by a deployable mechanism. The accuracy of the deployable mechanism is important because it directly affects the performance of the satellite. This article focuses on the accuracy analysis of a deployable antenna considering the coupled effects of joint clearances and link tolerances, and based on which, two accuracy synthesis methods are further discussed. A novel geometric error modeling method is proposed to estimate the error space of the outer panel of the antenna. The advantages of the proposed method are that it can handle the overconstrained constraints efficiently and decouple the positioning error and orientation error. Moreover, the error space is visualized using a sampling method. Based on the proposed error modeling method, the maximum orientation and positioning errors are computed, and following which, sensitives of the antenna accuracy to tolerances considering various sizes of clearances are analyzed. Finally, two optimization methods for accuracy synthesis are discussed, and instructive conclusions are drawn.