## 1 Introduction  
The development trend of various aircraft emphasizes longer range, smaller size, and reduced weight. The constraints of space and weight necessitate a compact design for functional mechanisms. For instance, applying folding wing technology significantly reduces the radial dimensions of aircraft before flight [1, 2]. Folding wings typically unfold from a stowed position through the action of deployment mechanisms, providing aerodynamic lift [3, 4, 5]. Scholars have made substantial progress in the design of folding wing deployment mechanisms, most of which are planar linkages, such as the link-slider and rocker-slider mechanisms [6, 7]. For folding wings used in aircraft, the deployment mechanism must meet technical requirements to automatically unfold to the designated position, fulfilling the specified design criteria of the mechanism. However, as aircraft design diversifies, the demand for folding wing deployment mechanisms is increasing. Tominimize the weight of the folding wing deployment mechanism and the number of actuators, it is particularly important to achieve the synchronized deployment of multiple wings using a single actuator within a confined and enclosed space [8]. There is a particular need to achieve synchronous deployment of multiple wings using a single drive within confined spaces. This necessitates the development of new linkage configurations. Moreover, the design process of existing deployment mechanisms fails to account for their impact on performance, leading to systems that, while functional, exhibit suboptimal efficiency. Such challenges hinder the application and advancement of folding wings in aircraft design. Configuration synthesis is a critical method for studying folding and deployment mechanisms and serves as a key approach to achieving innovative designs for folding wing deployment mechanisms. To achieve innovative designs for folding wing deployment mechanisms, it is essential to select an appropriate link mechanism suitable for such applications. The synthesis and optimization of linkages aim to design a mechanism that meets the intended functional requirements while exhibiting favorable motion and dynamic characteristics [9; 10; 11]. Scholars have researched the configuration synthesis of deployable mechanisms [12; 13; 14; 15; 16]. For instance, [PERSON] and [PERSON] [17] successfully combined [PERSON]'s theory with graphical tools for adding two-joint linkages, synthesizing 16 types of eight-bar, one-degree-of-freedom (1-DOF) motion chains. Additionally, [PERSON] et al. [18] proposed an automated process for synthesizing planar 1-DOF motion chains with varying link types. This research established a database of 1-DOF motion chains with six, eight, ten, twelve, and fourteen links, demonstrating the effectiveness of the method. The above studies on planar mechanism synthesis primarily concentrate on the methods of motion chain synthesis. Nonetheless, they often overlook the subsequent optimization and selection processes. As research progresses, scholars have made significant theoretical advancements in configuration optimization [19; 20; 21; 22; 23]. [PERSON] et al. [24] proposed a configuration design method that takes constraint forces into account. In this approach, unit masses are assigned to simulate rotational joints drawing on a specified number of degrees of freedom. This approach analyzes the dynamic characteristics resulting from the combination of unit mass and constraint forces. While this method allows for topological optimization of planar rigid-body mechanisms, it focuses solely on the impact of constraint forces, lacking other performance impacts. [PERSON] et al. [25] established a constraint model for motion generation and a dynamic model for four-bar mechanisms, thereby linking the synthesis of linkages with their dynamic performance. This approach allows for the identification of optimal configurations for four-bar mechanisms.