A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage

Abstract

Abstract This paper presents a closed-form polynomial equation for the path of a point fixed in the coupler links of the double butterfly linkage. The revolute joint that connects the two coupler links of this planar eight-bar linkage is chosen to be the coupler point. A systematic approach is presented to obtain the coupler curve equation, which expresses the Cartesian coordinates of the coupler point solely as a function of the link dimensions; i.e., the equation is independent of the angular joint displacements of the linkage. From this systematic approach, the polynomial describing the coupler curve is shown to be, at most, forty-eighth order. This result is believed to be an original contribution to the literature on coupler curves of a planar eight-bar linkage.