This paper presents the structure synthesis of a special class of parallel manipulators with motion decoupleability. The manipulator is synthesized by grouping a motion constraint leg and a set of constraint-free legs. The desired motion, i.e., the output degrees of freedom (DOFs), of the end-effector is expressed by a projective angle representation. It was found that the fully decoupled design for parallel manipulators with any DOFs is achievable when the output motion is described by the projective angles. A synthesis procedure is proposed based on the reasoning of the screw systems and reciprocal screws of the decoupled motion. Several design examples of fully decoupled 2-, 3-, 4-, 5-, and 6-DOF parallel manipulators are provided.

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