This thesis presents a technique for the optimal synthesis of planar five-link mechanisms that produce a desired mechanical advantage function over a specified path. Since a five-bar linkage has two degrees of freedom, small deviations from the specified path are possible without significantly altering the mechanical advantage function. The research shows one potential application, the design of strength machines, where it is important to control force while allowing the user freedom of motion. In the past, closed-form analytical synthesis techniques have been used to design mechanical-advantage-generating linkages. This method is time consuming and case specific. However, optimal synthesis techniques apply to the general case and present a robust solution procedure. This thesis uses the non-linear pattern search technique of Hooke and Jeeves to synthesize five-bar linkages. The search technique matches user strength curves and mechanism resistance curves to produce a five-link mechanism. This mechanism produces the desired mechanical-advantage function and serves as the basis for strength training machines. Unlike analytical synthesis, optimization allows direct incorporation of a greater number of design constraints, thus resulting in solutions that are more practical. The pattern search technique aims to minimize a given objective function that depends primarily on the force generating capabilities and kinematic constraints on of the linkage. / Master of Science