A closed-chain mechanism having redundancy in the force domain can produce a spring effect by proper internal load distribution. The so-called antagonistic stiffness is provided by redundant actuation in conjunction with nonlinear geometric constraints. In the paper, an optimal structure of a five-bar mechanism that can maximize efficiency in generation of antagonistic stiffness is evaluated and analyzed. A stiffness modulation index that represents isotropic characteristics in antagonistic stiffness generation is proposed. A gradient design index that shows rate of change of the isotropic index is also employed to distribute the isotropy of stiffness uniformly throughout the workspace. To deal with multi-criteria based design, a composite design index based on the max-min principle of fuzzy theory is used as an objective function. Two optimization results are obtained. One is optimizing the X-directional stiffness and the other corresponds to optimizing the Y-directional stiffness. The result of the former design is found suitable for antagonistic stiffness generation as well as for first-order kinematic performances.