The curvature stagnation point curve would degenerate in two straight lines, when the given Ball point was located on the fixed bar and an instantaneous center coincided with a fixed pivot. A random bar laid on the vertical straight line would produce an approximate straight line mechanism. The synthesis formulae and figures of crank linkages solution region on the coordinate plane, based on crank linkages analysis, were presented. Some useful conclusions were obtained by analyzing special points in the solution regions. According to different design demands, the corresponding evaluating functions were adopted in order to calculate the feasible solution region and the optimal mechanism solution automatically. The proposed method was visual and automatic. Both the blindness of choosing optimal mechanism and the lowness of design efficiency were overcome observably.