Triangular nomograms for symmetrical spherical four-bar linkages generating symmetrical coupler curves

The purpose of this paper is to present triangular nomograms for symmetrical spherical four-bar linkages, which provide a simple means to search for the desired symmetrical coupler curves. The dimensional parameters of a symmetrical spherical four-bar linkage are the lengths of the fixed link, turning link, coupler link, and coupler point position. Four types of spherical Grashof linkages tracing symmetrical coupler curves are discussed. Seven kinds of special symmetrical coupler curves are investigated, and the corresponding geometric relations are used to derive the implicit equations consisting of four dimensional parameters. Then, four triangular nomograms for symmetrical spherical four-bar linkages are presented for the selection of dimensional parameters of a linkage generating the desired curve without further calculation.