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In this paper, the idea of using cable differentials in the architecture of planar cable-driven parallel robots is introduced. Cable differentials are a type of mechanisms with several outputs driven by a single input. Using them in cable parallel manipulators can decrease their cost and control complexity. However, due to their kinematic constrains, cable differentials cannot be arbitrarily used in the design of these manipulators. Thus, a synthesis method is proposed to tackle this issue. First, the general requirements and characteristics of differentially driven planar cable mechanisms are reviewed. Then, the advantages of using these differentials instead of typically actuated cables are shown through a comparison between differentially actuated planar cable robots and fully actuated ones. The results reveal that with the same number of actuators, using differentials may lead to larger workspaces and improved kinetostatic properties. Subsequently, the systematic synthesis of differentially driven planar cable mechanisms is presented. For this, a method to find the different arrangements of q cables in a differential is proposed. Then, valid arrangements with 2, 3, and 4 cables are investigated. Finally, several differential actuation schemes are considered and all possible differentials with q=2, 3, and 4 cables are found.