Symmetrical four-bar coupler curves, containing three cusps

Symmetrical coupler curves are easier to analyse than non-symmetrical ones. This is particular true if one diseres to find the double points or the cuspidal points of such curves. It appears that symmetrical coupler curves containing three cusps are governed by one parameter only, which happens to be the coupler-angle. The dimensions of the generating four-bar then meet very simple formulas, enabling the designer of these linkages to face other requirements as well; such as the requirement of a straight-stretch in the coupler curve.