Remote Center Compliance (RCC) devices are passive devices used in automated assembly. For round peg-in-hole insertions, initial misalignments of the peg can cause heavy radial loadings on the corresponding hole in arbitrary direction. RCC devices with rotational symmetry property are therefore desirable. This paper discusses how such devices may be designed and shows that circular periodic structures satisfy this property. The elastic part of the RCC device is formulated as a compliant mechanism and a systematic design methodology is proposed based on structural optimization. A smooth optimal design is achieved with distributed compliance and numerical simulation is conducted to illustrate the feasibility. The proposed method is expected to be used to design a novel device for assembling fragile plastic parts, which is a challenge to 3C industry.