Graphical Technique to Locate the Center of Curvature of a Coupler Point Trajectory

Abstract

This paper presents an original technique to locate the center of curvature of the path traced by an arbitrary point fixed in the coupler link of a planar four-bar linkage. The method is purely graphical and the center of curvature; i.e., the center of the osculating circle, can be located in a direct manner with few geometric constructions. The advantage of this technique, compared to the classical approach using the Euler-Savary equation, is that measurements of angles and distances between points are not required. Also, it is not necessary to locate inflection points or draw the inflection circle for the instantaneous motion of the coupler link. The technique is based on the concept of a virtual link which is valid up to, and including, the second-order properties of motion of the coupler link. The virtual link is coincident with the path normal to the coupler curve; i.e., the line connecting the coupler point to the velocity pole of the coupler link. The absolute instant center of the virtual link defines the ground pivot for the link and is, therefore, coincident with the center of the osculating circle. The authors believe that the graphical approach presented in this paper represents an important contribution to the kinematics literature on the curvature of a point trajectory.