A complex number approach to generating the cubic of stationary curvature (CSC) has been developed. The approach provides a closed form solution for generating points on the curve. The new approach eliminates the need for considering the Euler-Savary equation and centrode curvature as intermediate steps for obtaining points on the curve. Furthermore, the method guarantees that the points will be generated in their natural sequence and it simultaneously produces points on the centerpoint and circlepoint curves. The method can be applied to analyze an existing linkage or to synthesize a linkage to produce a coupler curve with specified stationary curvature at one position. Two analysis and one synthesis examples are provided.