Symmetrical Coupler Curve and Singular Point Classification in Planar and Spherical Swinging-Block Linkages

Abstract

The purpose of the present paper is coupler curve synthesis and classification in planar and spherical swinging block linkages for path generation problem. It is shown that the swinging block mechanism, which is an inversion of the slider crank mechanism, can be classified into two types. The first type generates Lemniscate coupler curves consisting one or two loops. In this case, two double points, namely cusp and crunode, occur depending on the mechanism's dimension. The second type generates Cardioid and Limaçon type coupler-curves consisting of one, two, three, and four loops. In this case, three kinds of double points, namely cusp, crunode, and tacnode, occur. For the spherical swinging-block linkages, a parametric coupler curve equation is derived. Using a trigonometric similitude between the planar and spherical linkages, a symmetrical coupler curve and singular point classification is accomplished.