Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic o...Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of.conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.展开更多
基金This project is supported by National Natural Science Foundation of China (No.50275017)Provincial Natural Science Foundation of Liaoning, China (No.20051019).
文摘Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of.conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.
