In order to satisfy the needs of compliances and strengths of transmission parts in a variety of precision instruments,the flexure hinges with space curve notches that are intersecting lines of quadric surfaces and cylinders were studied in detail. Firstly, a general design equation for calculating the rotation compliance of this kind of hinge was deduced, and the effects of the design parameters on the compliance characteristics were discussed. Based on the analyses, a design method of this kind of hinge was proposed, and a design example was used to illustrate the usage of the method. The compliance and the strength of the example were verified by finite element analysis and experiments.Results show that the obtained compliances from the three methods are in a good agreement, and the maximum error is less than 5%, which indicates that the design method is effective and can be used for engineering design of this kind of hinge. In addition, the finite element model method illustrated in this paper and the proposed model testing method can be used to determine the mechanical properties of this kind of hinge.