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.