Chapter 9 is focused on the design of mechanisms. The principal aim is to create mechanisms in such a way that they provide a desired input–output response. These mechanisms are called function generators. Computing the dimensions of such mechanisms (i.e., designing them) can be achieved by using the Freudenstein’s equations. In this chapter, Freudenstein’s equations are derived for both four-bar linkages and slider-crank mechanisms and they are used for mechanism design. Furthermore, cognate linkages that have identical coupler curves are introduced. Roberts-Chebyshev Theorem, discussed in this chapter, shows that for each four-bar linkage there are two more four-bar linkages (a total of three) that have the same coupler curves. Therefore, if in a particular application one of these solutions is not a proper choice due to constraints like space limitations, we can try any of the other two solutions that can provide an identical coupler curve.