Abstract: Three basic problems of the theory for the variable topology mechanisms are explored: the definition of the variable topology mechanism, basic changing topology ways of the variable topology mechanisms and their correlativity. The new concept of the variable topology mechanisms is put forward based on the graph theory and vertex-figure graph theory after the new concepts such as the topological structure of a mechanism, the mechanism idea-lization, the ideal mechanism, the element of a mechanism and the variable set etc. are defined. And the strict mathematical definition of the variable topology mechanism is given. Three basic changing topology ways of the variable topology mechanisms are represented accurately. It is one of the funda- mental principles of the topological structure changing of the variable topology mechanisms. According to that, two correlativity theorems and three corollaries of basic changing topology ways of the variable topology mechanisms are discovered, put forward and proved strictly.

Key words: Basic changing topology way, Correlativity theorem, Variable topology mechanism