Springs are commonly used in mechanisms and robotics for imparting stiffness into it or balancing out the gravitational effects. Usually, some kind of design optimization would be performed on the static model of such systems to arrive at a set of suitable spring parameters and its mounting locations. However, in the static model, only the stiffness and free-length parameters of the spring appear explicitly. Thus, only their values would be determined in the design process. But, such a spring may not be practically realizable due to its operation range exceeding the elastic deformation limits or its geometry not satisfying some necessary conditions. Such issues can be avoided only by accounting for the spring design in its entirety (material, geometry, etc.) while designing the mechanical system. This work presents a method that accounts for the above features and derives the complete feasible design space for an extension spring. A parametric representation of this feasible design space has been obtained with two variables. This process has been illustrated for springs mounted on the two sides of a remotely actuated antiparallelogram (X) joint. Finally, a scheme for design optimization of the X-joint considering its geometry, spring, and cable forces, has been proposed using the parametric representation for springs.