A new approach for curvatures of conjugate surfaces is provided in this paper. The main characteristic of the approach is that relative curvatures and geodesic torsions of the conjugate surfaces are directly calculated in terms of the normal curvatures and geodesic torsions of the generating surface on two nonorthogonal tangents of surface curvilinears in the global surface system. Based on the curvature equations, sliding velocities and sliding ratios of the conjugate surfaces are studied. The approach is illustrated by a numerical example of a plane enveloping globoidal worm-gear drive.

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