## 1 Introduction  
With the rapid development of aerospace technology, the development of large spacecraft has become an inevitable trend. In the aerospace field, macro-micro robotic systems are typically used in assembling large components, where the wheeled mobile system composed of Mecanum wheels is used for long-distance component transport in the macromotion stage, while the docking mechanism is used to adjust the posture of components in the micro-motion stage. There are three types of docking equipment in common use, namely Pogo positioning platforms, rail-mounted platforms, and industrial robotic arms [1], all of which are composed of serial structures. Serial mechanisms can increase joint motion, thereby expanding the workspace of the end effector. However, serial mechanisms tend to accumulate deformation, which reduces the stiffness of the docking equipment [2, 3]. Since less stiffness is not conducive to carrying large and heavy components, parallel mechanisms (PMs) can be used [4, 5]. Parallel mechanisms support a single end effector with multiple kinematic limbs and offer several advantages over traditional serial mechanisms, such as a high load-to-weight ratio, greater stiffness, compact structure, low inertia, and good dynamic response [6, 7, 8]. However, compared to serial mechanisms, parallel mechanismshave a smaller workspace. Most parallel mechanisms are unable to improve performance such as working space while increasing stiffness. To enhance the performance of parallel mechanisms, many researchers have introduced redundancy actuation [9; 10; 11]. Redundant actuation can effectively eliminate certain singular configurations, increase the workspace, enhance stiffness, and improve the dynamic performance of the mechanism [12; 13; 14]. Furthermore, the performance of parallel mechanisms can vary significantly based on their configuration, structure, and parameters [15; 16]. Design optimization aims to enhance performance indicator by adjusting mechanism parameters [17; 18]. The primary objective of mechanism optimization is to meet diverse engineering requirements such as stiffness, mass, and workspace. Due to the complexity and variety of performance metrics, design optimization problems are typically characterized by constraints, nonlinearity, and multimodality, often lacking a closed-form solution [19]. Consequently, identifying optimal parameters that meet various task requirements is a significant challenge. In the optimization of PMs, performance indicators are typically treated as objectives, mechanism parameters as design variables, and constraints are dictated by design requirements. With these objectives, design variables, and constraints in place, advanced optimization algorithms can be utilized to determine the optimal parameters [20; 21; 22; 23]. The kinematic design mainly involves the determination of the geometric parameter sizes and the range of drive joint variables. Workspace plays a critical role in mechanism optimization, and the volume of the non-singularity workspace is commonly used to evaluate the performance of PMs [24]. [PERSON] and [PERSON] [25] proposed a method to determine the workspace, [PERSON] et al. [26] solved the maximum non-singularity workspace of a 6-UPS mechanism by convex optimization, and [PERSON] et al. [27] used a geometric method to solve the 3-PRR mechanism's maximum non-singular workspace. However, these methods often overlook the volume of the mechanism itself. This paper introduces the spatial occupancy function (volume ratio), which considers both the workspace volume and the mechanism's volume, to avoid an unlimited increase in the mechanism volume, which can evaluate the workspace utilization of the 4-SPPP mechanism more comprehensively. Currently, the primary optimization methods are divided into two categories: the objective function method [28; 29] and the performance atlas method [30; 31].