This paper presents a new way of structure composition of single-driven metamorphic mechanisms to develop a systematic and modularized structure synthesis methodology of metamorphic mechanisms based on augmented Assur groups (AAGs). Planar metamorphic mechanisms can hence be constructed based on the developed AAGs by applying the structure composition rule of general planar mechanisms formed by Assur groups (AGs). First, the one-mobility AAGs are introduced based on class II and class III AGs; the structure formulation and composition methodology of planar metamorphic mechanisms are then proposed based on the AAGs, and the basic problems including mobility and synthesis of constrained metamorphic working mobility-configuration are investigated. This leads to the investigation of the degenerated equivalent AGs of AAGs in the metamorphic process and the corresponding kinematic characteristics, providing references for kinematic synthesis of metamorphic mechanisms. Further, a typical spatial metamorphic group is introduced based on the concept of AAGs, and the structure formation and composition of spatial metamorphic mechanisms are presented. Examples show that both planar and spatial metamorphic mechanisms can be constructed by utilizing the one-mobility blocks extended from the AGs.