Abstract: Function symmetry exists widely in mechanical systems. It plays an important role in the accomplishment of design requirements. The fundamental concept of the function symmetry is studied systematically, the generalized function symmetry architecture which is composed of the function symmetry, performance symmetry and constraint symmetry is put forward, and the function symmetry elements which consist of symmetry body, symmetry unit and symmetry criterion are defined. The function symmetry is divided into effect symmetry and space-time symmetry according to the difference of its symmetry criterion, and it will also be divided into other types according to the difference of its symmetry body, unit and transformation operation. Thereby, the hierarchical tree of the function symmetry architecture is established. At last, based on the analysis of a large number of mechanical instances, the relationships among those kinds of function symmetries are discussed, and the rudimentary knowledge for the application of function symmetry are summarized.

Key words: Effect symmetry, Function symmetry, Generalized function, Space-time symmetry, Symmetry