The characteristics of a coupler curve

Deriving the characteristics, order and circularity, of a coupler curve efficiently is presented. The derivation is based on two major concepts. One is the order of a curve is related to the number of the intersection points between this curve and a straight line. The other is the correlation between circularity and intersection with a circle. The coupler curves of some four-bar were used as the basic tool. The developed technique can be applied to figure out the characteristics of a coupler curve and to estimate the maximum number of configurations for linkage with multi-links. Several examples are given for illustration.