This paper designs and analyzes the hybrid flexure hinge composed of half a hyperbolic flexure hinge and half a corner-filleted flexure hinge. As it is transversely asymmetric, it has different performance when the fixed and free ends switch. Considering the diversion of rotation center from midpoint, closed-form equations are formulated to characterize both the active rotation and all other in-plane parasitic motion by the Castigliano's second theorem. The maximum stress is evaluated as well. These equations are verified by the finite element analysis and experimentation. The compliance precision ratios are proposed to indicate flexure hinges' ability of preserving the rotation center when they have the same displacement at the free end. The hybrid flexure hinges are compared with five kinds of common notch flexure hinges (circular, corner-filleted, elliptical, hyperbolic, and parabolic flexure hinges) quantitatively based on compliance, precision, compliance precision ratios, and the maximum stress. Conclusions are drawn regarding the performance of these six kinds of flexure hinges.