The derivation of the valid contracted graphs (CGs) with pentagonal links P plus quaternary links Q and/or ternary links T is studied for the type synthesis of closed mechanisms by means of arrays. First, the concepts of CGs and arrays are explained, and the numbers of dots representing basic links and edges in the CGs are solved. Second, the relative criteria are determined for representing/deriving CGs and identifying isomorphic/invalid CGs by arrays. Third, some simple CGs are derived from associated linkages with P(Q, T) and are represented by arrays, and the isomorphic/invalid CGs are identified by arrays. Finally, many complex valid CGs with more P(Q, T) are represented and derived by arrays and their isomorphism are identified by arrays.
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