A Simple Graphical Construction of the Centre of Curvature for a Point in the Plane of Symmetry during Regular Precession

Regular precession is a special case of spherical motion with circular-conical axoids and constant angular velocities. In a previously published graphoanalytical study, the determination of acceleration was developed by means of ellipses, and a simple construction of the centre of curvature was also given for a point lying in the plane of symmetry. The present note isolates that special construction. For the point B in the plane of symmetry, the acceleration components are obtained from the reference geometry of regular precession. The actual normal acceleration is constructed by the parallelogram rule, and the centre of curvature is obtained as the intersection of its direction with the semicircle whose diameter is OB.