In this article, a novel method for the systematic design of a planar three-degrees-of-freedom compliance device with desired compliance characteristics is presented. For the realization of desired compliance, the synthesis method of stiffness of a planar mechanism is first derived. The compliance device may be directly realized by means of parallel connections of the synthesized springs. However, the use of several mechanical elements such as joints and guides for spring assemblies for the realization may cause significant complexity in manufacturing the compliance device with high precision and in compact size. In order to resolve the problem, the form of serial connections of three torsional springs which has the same compliance as the form of parallel connections of the synthesized line springs is proposed. The serial form of torsional springs can be physically realized by designing proper shape of the circular flexure hinge corresponding to each of the torsional springs. For the illustration of the proposed design method, a planar serial compliance device with high compliance to the normal contact force is designed and verified by finite element method analysis.