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To obtain the three-rotational parallel mechanism with large bearing capacity and easy control, the connection between the motion coupling of the parallel mechanism and the spatial geometric conditions of the transmission wrench screws was established by analyzing the meaning of the singular vectors in the inverse Jacobian matrix, and then a configuration synthesis method for the weakly-coupled three-rotational parallel mechanisms was proposed. Firstly, according to the motion coupling requirements of the parallel mechanism in different directions,the inverse Jacobian matrix was constructed, and the spatial geometric conditions of all transmission wrench screws were derived based on the inverse Jacobian matrix. Secondly, according to the relationship between the transmission wrench screws and the twist screws of the passive joints and the relationship between the constraint screws and twist screws of the active and passive joints, the types and arrangement conditions of the joints in each branch chain were obtained. On this basis, many branch chains whose active joints were mounted on the fixed platform were synthesized. Furthermore, the principles of selection and combination of branch chains were formulated, and based on the above principles, the configuration synthesis of the weakly-coupled three-rotational parallel mechanism was completed. Finally, the correctness of the proposed method was verified by the analysis of the motion coupling of three examples.