Abstract: The concept of curve-surface conjugated meshing is defined as that a smooth curve always maintaining continuous and tangent contact with a smooth surface on two bodies with given motions respectively. A general method which generates the conjugated meshing curve-surface by the engagement pair with the conjugate tooth surfaces is presented. A tubular surface is generated which conjugated contact with its conjugated tooth surfaces. A new tooth profile generation method is proposed. The tubular enveloping surface is generated by a sphere with an appropriate radius following a given equidistant-curve of the meshing curve; the equations of the tubular surface and the contact curves are derived; the conditions of the conjugated curves and the radii of the conjugated surfaces are presented. Based on this method and the theoretical derivations, the forming theory of the tubular conjugate tooth surfaces regarding the conjugate curve as the ridge line is established. An application for the cycloid planetary transmission is presented. The helical tube tooth profile of cylindrical pin tooth is constructed and the characteristics of curve-surface conjugated cycloid planetary transmission are discussed. The results show that the curve-surface conjugated has the property of point-contact. The nearly pure rolling engagement can be obtained by applying appropriate cure-surface conjugated pair which has the small sliding ratio and the high transmission efficiency.

Key words: Curve-surface conjugated, Cycloid planetary transmission, Gear geometry, Tubular tooth profile