Curvature theory for the double flier eight-bar linkage

Abstract

This paper presents a graphical technique to obtain the radius of curvature of the path traced by a coupler point of a planar, single-degree-of-freedom, indeterminate eight-bar linkage commonly referred to as the double flier linkage. The first step is to find the pole for the instantaneous motion of the coupler link; i.e., the point coincident with the absolute instant center of the coupler link. Since the double flier is a linkage with kinematic indeterminacy then the Aronhold–Kennedy theorem cannot locate this instant center. The paper, therefore, begins with a novel technique, which requires few geometric constructions, to locate this instant center. Then the paper focuses on the graphical technique to determine the radius of curvature of the path of an arbitrary coupler point for a given position of the input link. The technique begins by obtaining an equivalent five-bar linkage and four kinematic inversions of this linkage. A four-bar linkage is obtained from each inversion. Finally, the systematic procedure provides a four-bar linkage in which the motion of the coupler link is equivalent up to, and including, the second order properties of motion of the coupler of the original double flier linkage. The radius of curvature of the path traced by the coupler point is then obtained from the well-known Euler–Savary equation.