Higher path-curvature analysis in plane kinematics

Abstract

Classical kinematics furnishes us with powerful techniques for the determination of the motion cliaraclerislics of a rigid body, or “plane,” or link. The present analysis is concerned more with the motion cliaraclerislics of the path generated by a point on a link, rather ilian with the link as a whole. For four infinitesimal displacements, it is shown tliat the locus of all points on a link with a prescribed ratio of path-evolute curvature to path curvature is a higher algebraic curve, the “quartic of derivative curvature." For five infinitesimal displacements, five points on a moving link can in general be found liaving five-point contact with an arbitrary, prescribed curve. For circular motion, these results reduce to the classical theories ofBurmesler and Mueller. Equations have been derived for the first and second rates of cliange of path curvature in terms of the evolutes to the path. The results are applicable to the kinematic analysis and synthesis of mechanisms and are illustrated, specifically, for the generation of involute, parabolic, and elliptic arcs. © 1965 by ASME.