# Spatial Data-Based Automatic and Quantitative Approach in Analyzing Maintenance Reachability
## 2 Literature Review
However, the rock crusher repair platform was verified by the augmented maintenance technology and virtual maintenance technology by [PERSON] and [PERSON] [34]. As a result, virtual maintenance technology is more suitable for the evaluation and verification of visibility, reachability, and operability than augmented maintenance technology. In the maintenance reachability analysis, the inverse kinematics and dynamics analysis of the human body is required. However, the human body is a complex, non-linear, and multiple redundancy system, which is difficult to be modeled, solved, and simulated. Therefore, this issue has been a research hotspot. Feasible technical approaches have emerged in recent years, and one of the most widely used is the envelope-based approach, owing to the kinematic characteristics of the human arm. In terms of envelope establishment, various approaches for human reach envelopes were introduced by [PERSON] and [PERSON] [35], such as the experiment-based approach, voxel-based method, and closed-form method. [PERSON], [PERSON], and [PERSON] presented a general analytical method to determine the upper extremity workspace for any percentile virtual humans [36]. The upper extremity workspace and comfort index of the human body was obtained according to the changes in joint limits and limb length and the kinematics model. [PERSON] et al. analyzed the influencing factors of maintenance reachability [37], whereas a mathematical model for the continuous quantification of the maintenance reachability based on the kinematic model of a human arm was established. Only the arm in the free state was analyzed in this study, that is, the interference of objects in the surrounding environment was ignored. In terms of the envelope application, [PERSON], [PERSON], and [PERSON] examined the problem of pipeline maintenance in architecture [37], and a visual tool for pipeline maintenance design was proposed to evaluate the visibility, reachability, and operability of the pipeline. In the reachability analysis section, a cylinder is used to envelop the person, and the cylinder movement is used to represent the path of the person. Moreover, an immersive virtual maintenance simulation system built by the Cave Automated Virtual Environment was introduced [38], which is a motion capture system and virtual simulation software. Using this system, the visibility, reachability, and other factors in the maintainability of products can be evaluated. In this method, maintenance reachability analysis is realized with the help of a shoulder joint-based envelope. [PERSON] and [PERSON] investigated the design for the maintenance accessibility method [4], whereas the maintenance accessibility design was accomplished using a tool in building information modeling software, which was called the Solibri Model Checker (SMC). The ruleset used to check the reachability in SMC is \"free area in front of component\", whose essence is also a reach envelope. Moreover, optimization algorithms can be used in maintenance reachability analysis. [PERSON] and [PERSON] established a mathematical model for the layout optimization of the components in a small satellite cabin with maintenance reachability as one of the goals [39]. A multi-objective genetic algorithm was examined to solve this problem. According to the investigation, the physical prototype-based method is poor in timeliness because it can only be conducted after a design is finished, and the virtual prototype-based method is subjective because it requires the analyst to operate the virtual person during the whole analysis process. The calculation-based method has the limitation of the solution because only a limited set of solutions can be obtained for evaluation. Addressing the subjectivity and limitation of current maintenance reachability analyses based on virtual maintenance technology, the proposed methodology starts from the initial global solution set of the arm.