National Natural Science Foundation of China [51575018, 51275015, 51175494]
; Foundation of State Key Laboratory of Robotics 
Metamorphic mechanisms are members of the class of mechanisms that are able to change their configurations sequentially to meet different requirements. The paper introduces a comprehensive symbolic matrix representation for characterizing the topology of one of these mechanisms in a single configuration using general information concerning links and joints. Furthermore, a matrix representation of an original metamorphic mechanism that has the ability to evolve is proposed by uniting the matrices representing all of the mechanism's possible configurations. The representation of metamorphic kinematic joints is developed in accordance with the variation laws of these mechanisms. By introducing the joint variation matrices derived from generalized operations on the related symbolic adjacency matrices, evolutionary relationships between mechanisms in adjacent configurations and the original metmaorphic mechanism are made distinctly. Examples are provided to demonstrate the validation of the method.