A Classification of Coupler-Line Envelopes from Hinged Four-Bar Linkages

The loci of straight lines (attached to moving links in mechanisms) call for further study, because translation along a line can be identified with the movement at a sliding pair. The paths of points (identifiable with turning pairs) have been examined in considerable depth, almost to the exclusion of loci of lines. A line fixed on the coupler of a four-bar linkage generates an envelope, the line-counterpart of the well-known coupler-point curve. Such envelopes are here classified into 27 patterns, with the objects of both providing a broad geometrical base for further study and assisting towards practical applications in mechanism design. The classification is, in the main, limited to those linkages displaying greatest generality, but means of extending the classification are mentioned.