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The method called Single-Open-Chain (SOC) proposed in the literature is a very effective one for structural synthesis of mechanisms; in particular the method suits the synthesis process with the computer. In this paper, a new representation for mechanisms, called Double-Color-Graph (DCG) is introduced. Application of the SOC concept with the help of DCG representation, a new procedure for type synthesis for multiple joints and multiple-joint links, is presented. Baranov Trusses are extensively studied, which results in the finding of 158 independent types of Baranov Trusses with the number of loops being (1–4). A computer program system has been developed to generate all these types.