Abstract: The metamorphic mechanism is defined by three characteristics in multi-stage, multi-topological structure and multi-degree of freedom. The properties and boundary of metamorphic mechanism are discussed and clarified for the mechanism with multi-degree of freedom, combined symmetrical mechanisms, and kinematropic mechanisms. A way to describe a metamorphic mechanism is proposed. A new concept of the work-stage mechanism and the origin mechanism for metamorphic mechanism, which can be expressed by metrics, are presented. Meanwhile, a mathematic model of a metamorphic mechanism is set up by a metamorphic equation, which indicates the relationship among a work-stage matrix, an origin metamorphic matrix and a metamorphic matrix. The type synthesis of metamorphic mechanism can be converted into solving the group of metamorphic equations, which leads to form all work-stage matrices, an origin metamorphic matrix and metamorphic matrices. Therefore, the metamorphic mechanism, including the series work-stage mechanism and origin mechanism, is readily located by the corresponding matrices. An example is given to demonstrate the process of the synthesis of a metamorphic mechanism. A groundwork for the theoretical basis of synthesis of metamorphic mechanisms is presented.

Key words: Matrix, Mechanisms synthesis, Metamorphic mechanisms, Topology