This chapter focuses on the dimensional synthesis of four-bar mechanisms specifically for function generation and crank-rocker applications. It revisits Freudenstein’s equations, a mathematical framework used to relate input and output angles for precise motion control. By applying trigonometric identities and algebraic manipulations, readers learn how to derive links dimensions that fulfill a specific angular function. The chapter also delves into crank-rocker mechanisms, explaining how to design systems that convert continuous input rotation into controlled oscillatory motion. Practical criteria such as the Grashof condition, transmission quality, and mechanical advantage are discussed to evaluate mechanism viability. Analytical procedures are supplemented by graphical interpretations to enhance intuition. The content bridges theory and application, equipping readers with tools to synthesize mechanisms that accurately perform specified mathematical functions.