This thesis is a study in the application of kinematics coupled with elastic body mechanics. Most studies in kinematics assume all mechanism links to be inelastic. Furthermore, the methods of kinematic synthesis have generally been developed to meet requirements of displacement, velocity and acceleration. The work presented in this thesis differs in two important aspects. First, one grounded link of a four-bar linkage is replaced by a cantilevered beam in flexure to produce a force generating mechanism. Second, the synthesis method presented here allows the generation of these mechanisms in closed form for prescribed force generation. A compound archery bow that incorporates four-bar linkages has been developed as an example. This design relies on the non-linear mechanical advantage of the four-bar linkage and the bow mechanics to provide a resistance curve that is more compatible with the human strength curve. In addition, by modifying the bow kinematics, more potential energy can be stored, and thus potentially more kinetic energy can be transferred to the arrow than with previous bows. / Master of Science