Structural synthesis plays an important role in the conceptual design of mechanisms. Based on the link assortment array, links are divided into binary links and multi-vertex links. From the relation of binary links and multi-vertex links, a new form of the adjacency matrix is introduced to illustrate planar kinematic chain. It enriches the representative form of the adjacency matrix, which can provide a new direction for rigid-chain detection and structural synthesis. Without auxiliary graph models, based on the link-path adjacency matrix, characteristic code, and Sudoku Crosswords, a computer-aided digitization method is proposed to synthesize the whole family of planar non-fractioned kinematic chains. Compared with most existing methods of structural synthesis, isomorphic kinematic chains and some rigid chains are identified and deleted in the generation of link-path adjacency matrix, which can improve the efficiency of structural synthesis. By synthesizing planar non-fractioned kinematic chains with up to 10 links and 5 degrees of freedom, results confirm that the proposed method is available.
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