Determination of Linkage Parameters from Coupler Curve Equations

A fundamental problem in four-bar linkage synthesis is to determine linkage parameters from a given coupler-curve equation, which is essentially an inverse problem to the linkage analysis. For many decades, this synthesis problem has been considered as overdetermined, which yields only approximate solutions. This paper presents a new result, which shows that a determined system of coupler-curve coefficient equations can be formulated, which leads to exact solutions of the linkage parameters. A method of linkage parameter determination from known coupler-curve equation is further developed, demonstrated with examples.