In order to design a micro-motion angle displacement mechanism for precision engineering,the degrees of freedom and constraint patterns of 3HSE and 3HSVR angle displacement mechanisms with three screws were analyzed,and it shows that the common angle displacement mechanisms designed via three point supports have the uncertainties of the orientation and motion. Therefore, an exact constraint angle displacement mechanism with double screws was presented. The mechanism is exactly constrained by six point constraints, so that the position and orientation are deterministic at the natural state. Moreover, the number of degrees of freedom of the mechanism are equal to the number of the inputs and its motion is also deterministic at the input state. Furthermore,the adjusting orientation principles under different inputs were proved and the sensitivity was analyzed via the relationship of kinematic geometry. The result indicates that the sensitivity of the mechanism is superior to 0.83 μrad. The analysis shows that the proposed angle displacement mechanism has good stability and is suitable for the angle adjustment involving two degrees of freedom in precision engineering.