In the field of aviation and astronautics, large complex surface parts such as aircraft cabin cover are complex, varying in model, and produced in small batch. In order to reduce fixture cost and improve production efficiency, a variable multipoint and multi-DOF supporting fixture is designed. The coordinate system of the complex structure fixture is defined, and the kinematics of the multibody structures driven by air cylinders are modeled according to the topological principle. With the help of this data structure, fast and optimal search for clamping state can be realized. With the dichotomy method, the driving amount of the electric cylinder of the suction cups and the two rotation angles of two rotation axes at the end of the linkages are solved accurately. Based on the digital twin simulation method, the precise clamping motion of flexible fixture is calculated for an aircraft cockpit cover with a software developed by the authors in C++ language on the Visual studio platform. The distance between the clamping point and the surface was verified with a laser tracker. Finally, the practical experiment of a real cockpit cover clamping proves the practicability and effectiveness of the proposed method.