Research on Concept System of Mechanical Scaling-Translation Symmetry

Abstract

Scaling-translation symmetry is combined by translation symmetry and scaling symmetry, it widely exists in mechanical systems, and plays an important role in realizing the technical, economic and social performances of mechanical products. Based on the concept system of translation symmetry, and according to the research on a lot of instances, the concept system of scaling-translation symmetry classified by the directivity and alternations of symmetry components, the dimensionality and closed circle of symmetry benchmark, and the variable type of scaling was established. The concept system can completely contain all kinds of existence of scaling-rotation symmetry in mechanical systems, and can provide a theoretical basis for the further research on the application of scaling-translation symmetry in mechanical systems.