The computer-aided analyses of multibody mechanical systems emerged as an important scientific tool in the applied mechanics field. This is possible due to improvements of computer technology at the level of both hardware and software. Before the advent of computer-aided tools, the design of machines and their components was based on trial and error and graphical methods. These methods have almost been replaced by the algebraic methods. In the last four decades, a great number of the methods and techniques were developed to analyze the dynamic behavior of the mechanical systems. There is a great need to utilize these methods in the optimization to produce cost-effective solutions with high reliability and durability. To achieve this goal, analysis of complex mechanical systems which includes kinematic and dynamic analyses, synthesis, and optimization of the motion forces in mechanical systems shall be viewed in this book in an integrated manner. On the other hand, mechanical balancing is one of the crucial steps in design of high-speed machineries which is difficult due to interaction among various dynamic quantities like shaking force, shaking moment, bearing reactions, and driving torques/forces. To deal with such diverse quantities leads to an optimization problem. Reduction or elimination in the magnitude of the above quantities is useful for improved performance of a system at hand. It is important to note here that the definition of balancing refers to the vanishing of unbalanced forces/moments. However, when such elimination of unbalanced terms is not possible, one needs to resort to only reduction of those terms, which is nothing but minimization. This book develops a unified methodology for dynamic analysis and minimization of the inertia-induced forces occurring in high-speed multiloop planar as well as spatial mechanisms based on the multibody dynamic modeling. The dynamic quantities, such as shaking force, shaking moment, bearing reactions, and driving torques/forces are highly depended on the mass and inertia properties of the bodies in the system. By mass redistribution of the bodies, the complete balancing or minimization of these dynamic quantities is possible.