Computerized determination of curvature relations and contact ellipse for conjugate surfaces

Abstract

A general approach is proposed for determination of direct relations between: (i) the principal curvatures and directions of two surfaces being in continuous tangency along a line at every instant, (ii) the normal curvatures and torsions of two surfaces with conditions of tangency mentioned above. The surface of relative normal curvature, its principal curvatures and directions, and the torsions are determined as well. The instantaneous contact ellipse for two elastic surfaces is determined. The proposed approach is illustrated with a numerical example of hypoid gears.