Unified Spherical Curvature Theory of Point-, Plane-, and Circle-Paths

Abstract

This paper presents a unified treatment on the spherical curvature theory of point-, plane-, and circle-, paths or direct and inverse kinematics. It features the use of spherical inverse Euler-Savary equation to identify the kinematic loci such as return cone, double cusp axes, center-axis cone, and Burmester center axes. These results are then applied to the curvature theory of plane-path or circle-path to identify return plane, center plane, Ball’s plane, and Burmester plane. It explains satisfactorily the duality between point- and plant-paths.