A large component flexible manufacturing system provides more application scenarios for industrial robots, and, in turn, these robots exhibit competitive advantages in machining applications. However, the structural characteristic of low stiffness is the main obstacle for the industrial robot. Aiming at obtaining sufficient stiffness in the whole machining process, this paper focuses on robot placement optimization in the flexible manufacturing of large components. The geometric center of the machined feature is selected as, firstly, the base point, and the center-reachable placement space of the robot base is obtained by establishing the kinematic model considering a variety of motion constraints. Then, according to the reachability of the machining feature contour, the global placement space meeting all machining boundaries is further extracted. The mapping relationship between joint force and posture is established, and the most suitable robot placement is selected based on the criterion of global stiffness optimization. A series of numerical and finite element simulations verify the correctness and effectiveness of the proposed optimization strategy. The developed stiffness-oriented placement planning algorithm can provide beneficial references for robotic machining applications.