A study of curvature for single point contact

The study of curvature focuses on the case of two bodies (e.g. gears) that touch in a single point, where additionally at least one virtual body is introduced that contains as fixed elements, the point of contact, its tangent, and the contact normal. The equations of relative motion as well as the new idea of higher-order reciprocity are used to investigate what happens between the gears and the virtual bodies in order to determine various curvature properties (to third-order).