# Spatial Data-Based Automatic and Quantitative Approach in Analyzing Maintenance Reachability
## 1 Introduction  
Owing to usage, transportation, and storage, failures ultimately happen even if products were at a high reliability level. The increasing complexity and powerful function of products may bring high requirements in the maintenance process. Hence, the well-designed maintainability is of particular importance for enhancing maintenance convenience and decreasing maintenance cost and duration. Maintainability, as a vital element in product design, covers qualitative and quantitative factors. The qualitative section generally includes visibility, reachability, simplification, standardization, error proofing, ergonomics, and safety [1]. Among these elements, reachability is the major concern to users because \"reaching\" the target is always the first issue in maintenance steps. Reachability represents how easily an object can be reached and maintained, in which a rational and logical reachability design makes a repair man approach the maintenance spot rapidly and conduct maintenance work conveniently [1, 2]. The duration and cost can be effectively reduced further. A dissatisfactory reachability design not only increases maintenance difficulty, but also increases the cost and duration [3]. Consequently, evaluating reachability is extremely fundamental at the early stage of product design [4], and design flaw exposure is considerably ahead of its production under the support of the virtual prototype, whereas limitations, such as human position selection and human posturesetting, also bring subjective results [5]. The current reachability analysis methods can be roughly divided into three types: physical prototype-based, virtual prototype-based, and geometric calculation-based. First, the physical prototype-based approach is conducted by operating real physical prototypes under maintenance rules and analyzing the extent of reachability. Although the analysis result approximates actual specifications, this strong dependency on a physical prototype always leads to hysteresis [6]. Hence, reachability design flaws need to be exposed after a product is produced and assembled. Aside from the high cost and time required, this hysteresis always results in incomplete improvement at the design stage, in which even flaws are exposed. Thus, inconvenient maintenance always occurs after a product is in use. Second, the virtual prototype-based approach reveals a product in advance for users, and the corresponding reachability analysis can be conducted in a virtual environment on the basis of virtual reality technology and necessary analysis tools [7]. In this approach, design flaws are exposed and improved in a predictable manner. The procedure of reachability analysis based on virtual prototypes is summarized as follows. Digital human modeling technology [8; 9; 10], an essentially basic technology in virtual maintenance, is firstly introduced to generate different specifications of human body models [11; 12], and based on the digital model, a shoulder joint-based envelope that approximates a sphere is established to present the reachability scope [13]. This envelope moves along with the human position or posture changes. In the virtual environment, once the position or posture of the virtual human is confirmed, the corresponding envelope is generated to show the current reachability scope, and the objects in this envelope are treated as reachable. On the contrary, objects outside the envelope are regarded as unreachable. This envelope-based approach is widely used in virtual maintenance to verify reachability, owing to its intuitive visualization by means of this envelope. Although taken seriously, envelope establishment relies on a fixed posture, while the fixed posture also depends on the subjectivity of the analyst, in that even though the analyst has considered a number of scenarios, the generated envelopes remain limited. Thus, the reachability analysis results are also limited.