Similarity and scaling assessments of mechanical parts using adjacency relation matrices

This paper presents a mathematical model-based approach for similarity and scaling assessments of 3D mechanical parts. Similarity and scaling assessments are based on geometric and topological information represented within adjacency relation matrix (ARM). The approach relies on the standard for the exchange of product data model (STEP) file of a Boundary Representation (B-Rep) model for construction of the ARM. The algorithm is conducted in three main stages. In the first stage, the CAD model of a part is translated into the STEP file, and the entities represented in the STEP file are mapped into the adjacency relation matrix. In the second stage, all geometric and topological information except dimensional information represented in the new and candidate matrices are matched. If the matrices are completely matched, the approach calculates a scaling factor between two parts by using the dimensional information. In the final stage, the closest matrix corresponding to matrix of the new design is retrieved and found from the database. A similarity factor between the most similar part representations is calculated. The similarity and scaling assessments can be helpful for many CAD/CAM applications. The approach is implemented to some simple, intermediate and complex parts designed in a CAD environment to demonstrate its efficiency and capabilities.