In this work a method for the kinematic synthesis of structure topologies for modular metamorphic serial manipulators is presented. A detailed description of this class of robot manipulators is presented, in order to clarify their basic elements and their basic structural definitions. Based on these, the metamorphic structure representation (MSR) is proposed for the systematic representation of this type of metamorphic manipulator structures. A thorough examination of the possible metamorphic links that can be constructed is presented and used for the definition of the manipulator's structure evaluation criteria, to formulate a multicriteria evaluation index. The problem of the optimal kinematic synthesis of metamorphic structures is formulated and the process of automated generation of structures according to the specified requirements is presented. The results are presented in detail, in order to reflect their validity and the advantages that the proposed process for the kinematic synthesis of topologies for the modular metamorphic manipulator provides to the designer.