This paper proposes an analytical approach to the robust design of mechanisms, to achieve motion and accuracy requirements given a desired transmission ratio and allowable geometrical variations. The focus is on four-bar and slider-crank mechanisms, which are common elements for the transmission of rotary motion, especially over distances, which are too big for the use of conventional elements such as gears, and motion along a predefined guide-curve, which often is a straight line. For many power transmission applications, a constant relation between the motions of an input and corresponding output element is required. For a four-bar linkage, a value of 1 is the only possible constant transmission ratio—achieved when the mechanism has a parallelogram configuration. In the case of a slider-crank linkage a constant transmission ratio can be achieved with a properly designed circular guide-curve, which makes the slider-crank essentially equivalent to a four-bar. In practice, however, as a result of variations in link lengths due to manufacturing tolerances and load-induced or thermal deformations, the transmission ratio for a parallelogram four-bar linkage will deviate substantially from its ideal theoretical value of 1. Even small changes in link lengths due to deformations or joint backlash can cause unacceptable instantaneous transmission ratio variations. The concepts presented are not limited to the design of four-bars and slider-cranks but can also be applied universally in the design of other mechanisms.