Real inflections of hinged planar four-bar coupler curves

Abstract

Plücker's and Klein's equations provide an upper bound on the number of real inflections on the coupler curve of a hinged planar four-bar mechanism. Generally, for any configuration of the four-bar, the coupler points whose trajectories exhibit inflections lie on a circle. The coupler plane is partitioned by the envelope of the inflection circles into connected regions within which every coupler point has the same number of inflections on its trajectory. This enables us to locate coupler curves exhibiting the maximum possible number of inflections.