Proposals for finite 5-dimensional atlases for all planar 4-bar linkage coupler curves

Abstract

The paper seeks to extend earlier work that makes proposals for an atlas of curves traced by coupler points on crank-rocker linkages. We now examine ways of providing atlases for coupler curves of other 4-bar linkages. Provided that every family of similar movable quadrilaterals are included it is found that, as a further consequence of Roberts' cognate theory, it is sufficient to confine attention to coupler points that lie on or within boundaries that demarcate half the area bounded by two arcs having centres at the coupler bearings. For non-Grashof linkages only one quarter of this area is needed. This leads to an alternative way of providing an atlas of curves traced by coupler points of crank-rocker linkages.