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A parallel mechanism with coupling kinematic chain was proposed. The moving platform of the parallel manipulator with two rotations and two translations was connected to the fixed base through three kinematic limbs. Mobility of the parallel mechanism was analyzed based on Lie group theory. The moving platform of the mechanism can output two rotations and two translations. Position analysis was conducted through closed-loop vector approach, and inverse position solutions were obtained. The mechanism had two positive singular cases. Singularity analysis was conducted based on Jacobian matrix. Jacobian matrix of the mechanism was derived based on velocity analysis. Singularity analysis was carried out according to the rank reduction conditions of the Jacobian matrix. Workspace and singularity curves were analyzed. The principle of virtual work was used to establish stiffness model for the mechanism, and stiffness performance evaluation was conducted. To avoid stiffness degeneration caused by internal singularities, a redundant limb was added to the mechanism. Performance comparison in terms of stiffness and workspace between the mechanisms with and without redundant limb was carried out. Optimal design of the redundantly actuated mechanism was conducted to improve the average stiffness throughout its workspace. The variation law of the optimized target with the scale parameters can be obtained through numerical calculation. The results show that the stiffness performance of the optimized redundantly actuated mechanism is significantly improved.