## 1 Introduction  
Cantilever workpieces on aerospace products have characteristics that include a complex structure, poor stiffness, and high precision requirements, and often require special fixtures to reduce their machining vibration [1]. Moreover, the diversity of cantilever workpiece types poses a high challenge to the selection of fixtures. Industrial robots have been widely used in the manufacturing of aerospace products with low costs, high mobility and strong adaptability [2, 3, 4, 5], and have gradually become an important choice for fixed large-size structure and cantilever workpieces. For example, the cantilever workpieces on the space station have poor stiffness, making it easy to produce vibration under the action of external forces and thus affecting the machining quality. Enhancing the stiffness through the mobile clamping robot can effectively suppress the vibration, and avoid the disadvantages of traditional processes such as repeated assembly, which entails a complex process, and long cycle. However, the operation performance of the robot will change with the configuration [6, 7, 8], resulting in the unstable vibration suppression effect of different clamping robot configuration on the workpiece, and cannot meet the requirements of machining quality [9, 10]. Consequently, optimizing the configuration of the clamping robot is very important to improve the machining quality of the clamped workpiece. Extensive studies on robot configuration optimization based on kinematics [11, 12, 13], stiffness [14, 15, 16], and dynamic performance [17, 18] have been carried out to date. Generally,the robot configuration optimization based on kinematic performance is mainly used to ensure the track smoothness and task accessibility of large-range machining such as milling and welding [13; 19; 20]. However, in order to improve the machining quality of the workpiece, the robot stiffness is necessary to be considered in the configuration optimization [21; 22]. When the external excitation frequency is not close to the natural frequency of the robot system, the configuration optimization effect based on static stiffness is enough [15; 23]. For example, [PERSON] [24] and [PERSON] et al. [25] built a robot static stiffness model based on the robot six-joint stiffness and Jacobian matrix, and guaranteed the drilling quality of the robot by analyzing and optimizing the stiffness at different configurations. Actually, there are six stiffness parameters on each joint of the robot. Accordingly, in order to accurately analyze the stiffness performance of the robot under different configurations, [PERSON] et al. [26] established a dynamic model including 36 stiffness parameters based on the transfer matrix method of the multibody system (MSTMM). In addition, for processing tasks such as drilling and milling, the machining quality is mainly affected by the stiffness in the axial direction and the feed direction [27]. [PERSON] [14] and [PERSON] et al. [28] ensured the optimal stiffness in the direction of the main machining load by using the robot orientation stiffness optimization model, and the experimental results proved that the optimization method could effectively improve the machining quality. The above methods are based on the redundant degree-of-freedom (DOF) of the six-joint robot when performing five DOF tasks. However, due to the fixed position relationship between the robot and the workpiece, the improvement effect of the configuration optimization is limited. Hence, [PERSON] et al. [29] first analyzed the optimal configuration in the working space according to the robot stiffness model, and then ensured that the robot is in the ideal configuration by adjusting the fixed position of the workpiece. Similarly, [PERSON] et al. [30] improved the stiffness performance of the robot by optimizing the fixed angle between the flange and the spindle, which ensured the quality of the robot drilling. [PERSON] et al.