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

Static balance is the reduction or elimination of the actuating effort in quasi-static motion of a mechanical system by adding non-dissipative force interactions to the system. In recent years, there is increasing recognition that static balancing of elastic forces in compliant mechanisms leads to increased efficiency as well as good force feedback characteristics. The development of insightful and pragmatic design methods for statically balanced compliant mechanisms is the motivation for this work. In our approach, we focus on a class of compliant mechanisms that can be approximated as spring-loaded rigid-link mechanisms. Instead of developing static balancing techniques directly for the compliant mechanisms, we seek analytical balancing techniques for the simplified spring–loaded rigid–link approximations. Towards that, we first provide new static balancing techniques for a spring-loaded four-bar linkage. We also find relations between static balancing parameters of the cognates of a four-bar linkage. Later, we develop a new perfect static balancing method for a general n-degree-of-freedom revolute and spherical jointed rigid-body linkages. This general method distinguishes itself from the known techniques in the following respects: 1 It adds only springs and not any auxiliary bodies. 2 It is applicable to linkage shaving any number of links connected in any manner. 3 It is applicable to both constant(i.e., gravity type) and linear spring loads. 4 It works both in planar and spatial cases. This analytical method is applied on the approximated compliant mechanisms as well. Expectedly, the compliant mechanisms would only be approximately balanced. We study the effectiveness of this approximate balance through simulations and a prototype. The analytical static balancing technique for rigid-body linkages and the study of its application to approximated compliant mechanisms are among the main contributions of this thesis.