Algebraic-geometric properties of the coupler curves of the RCCC spatial four-bar mechanism

Abstract

This paper uses an analytical approach, based on (3×3) orthogonal transformation matrices with dual number elements and the principle of transference, to obtain three parametric equations for the coupler curves of the RCCC four-bar mechanism. The equations express the Cartesian coordinates of an arbitrary point fixed in the coupler link as a function of a single variable; namely, the input angle. From this systematic approach, the curve describing the path of the coupler point is shown to be 16th-order. The coupler curve equations for the spherical four-bar and the Bennett linkage are deduced as special cases. The paper then presents plots of coupler curves of a general geometry and a special geometry RCCC mechanism. The latter example has a branch extending to infinity which is directly related to the limiting positions of the mechanism. Finally, the paper includes plots of typical coupler curves of the spherical four-bar and the Bennett linkage.