We address the synthesis of serial chain spatial mechanisms with revolute joints in which the rotations about the joints are coupled via cables and pulleys. Such coupled serial chain mechanisms offer a middle ground between the more versatile and compact serial chains and the simpler closed chains by combining some of the advantages of both types of systems. In particular, we focus on the synthesis of single degree-of-freedom, coupled serial chains with two revolute joints. We derive precision point synthesis equations for two precision points by combining the loop closure equations with the necessary geometric constraints in terms of the unknown mechanism parameters. This system of equations can now be solved linearly for the link vectors after a suitable selection of free choices. We optimize over the free choices to generate an end effector trajectory that closely approximates a desired end effector trajectory for motion generation and path following applications.

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