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This paper introduces an augmented adjacency matrix with the connectivity of links, the types of joint and its axis-orientation. The configuration transformation matrix for the link-annexing process is presented based on the augmented adjacency matrix operation. The metamorphic operations are only focused on elements of the annexed-link and the corresponding un-functional joints after the metamorphic process. The paper further provides examples to illustrate that the proposed topological representation and configuration transformations of mechanisms from planar motion to spatial motion.