A rotational parallel mechanism is proposed that can perform rotational output motion around two axes and fine translational motion to compensate for position error of a target point, the center of rotation of the output link. This mechanism is composed of three connecting chains: one is a constraint chain without actuation and two are actuation chains, each with two actuators. The structures of the constraint and actuation chains were synthesized so that the mechanism can perform fine translational motion for position compensation while achieving a rotational output motion within a large workspace. Dimensional synthesis was carried out taking into account singularity with respect to actuation torque and output velocity, and rotational output motion coupled with translational compensation motion for position error. Based on the synthesis results, a prototype mechanism was designed and built. Experimental results regarding compensation for position error of the target point are shown to support our structural and dimensional syntheses.