Conjugated symmetrical coupler curves, produced by 4-bar linkages having the same transmission angles

The focal properties of the 4-hour linkage are shown to be at the base of a family relationship between each time of four symmetrical coupler curves. Four-bars producing these related curves are conjugated. It appears that two such conjugate four-bars always form an overconstrained linkage mechanism through the admission of two particular chosen, binary links. It is shown that the four conjugated four-bar linkages develop the same diagonal function and have the same extreme transmission angles that occur in the frame aligned position of their crank.