圆柱族包络面的非等径重构问题的理论研究

在机械设计与制造中 ,常遇到由一圆柱面运动生成的包络面是否能由另一半径不同的圆柱面运动来重新生成的问题 ,即圆柱族包络面的非等径重构问题。本文以等距曲面和包络理论为工具对此问题进行了研究。在得出包络面、轴迹曲面、等效轴迹曲面互为等距曲面的结论的基础上 ,研究了轴迹曲面可展与不可展两种情况下的非等径 (一次 )包络重构问题 ,得到了一些有价值的结论。然后研究并提出了两重包络重构方法。这些结论和方法对指导圆柱族包络面的设计与制造具有重要价值

Theoretical Research on the Reconstruction of the Envelope surface of A Family of Cylinders With Unequal Diameter Ones

The problem that if the envelope surface generated by a family of cylinders can be reconstructed by a family of unequal diameter cylinders is always met during the machine design and manufacturing.By use of offset surface theory and envelope theory,the conclusion that the envelope surface,the axis track surface and the equivalent axis track surface are offset surfaces is derived.Based on that,the problem of reconstruction is studied according whether the axis track surface is developable or not,and some valuable conclusions are derived.Then the double envelope reconstruction method is proposed and studies.All these conclusions and methods are valuable in instructing the design and manufacture of envelope surface of cylinder family.