Optimizing 4-bar crank-rocker mechanism

Closed form equations are developed for the synthesis of the 4-bar crank-rocker mechanism in which the angle between dead-centre positions of the rocker and the corresponding angle turned by the crank are prescribed. All the four different situations are considered and the minimum transmission angle, for the complete rotation of the crank, is obtained for each case. The upper and lower bounds on the crank angle, corresponding to a dead centre position of the rocker, are obtained by using Grashof's criterion. The design is optimized by maximizing the minimum transmission angle. Each case is illustrated by providing a numerical example.