Path Curvature of the Single Flier Eight-Bar Linkage

Abstract

This paper presents a graphical technique to locate the center of curvature of the path traced by an arbitrary coupler point of the single flier eight-bar linkage. The first step is to locate the pole for the instantaneous motion of the coupler link; i.e., the point in the fixed plane coincident with the absolute instant center of the coupler link. Since the single flier is an indeterminate linkage, comprised of one four-bar and two five-bar chains, then the Aronhold-Kennedy theorem cannot locate this instant center. The paper presents a novel graphical technique which can locate this instant center in a direct manner. Then the paper focuses on a graphical method to locate the center of curvature of the path traced by the coupler point. The method locates six equivalent four-bar linkages for the two five-bar chains, investigates six kinematic inversions and obtains a four-bar linkage from each inversion. This systematic procedure produces a four-bar linkage with a coupler link whose motion is equivalent up to, and including, the second-order properties of motion of the single flier coupler link. The radius of curvature and the center of curvature of the path traced by the coupler point can then be obtained in a straightforward manner from the Euler-Savary equation.