可展面展开方法及其应用

为解决工程实际中的曲面展开问题，以微分几何学中可展面展开的基本原则等相关理论为基础，提出锥面和切线曲面展开的理论方法。锥面的展开是利用单位球方法，确定直母线与平面上过定点射线之间的映射关系，进而展开曲面；切线曲面的展开则利用准线曲率在展开中的不变性，确定准线在平面上的展开曲线，再作与之相切的直母线，从而实现曲面的展开。两类可展面的展开方法均被应用于工程实际问题。其一是钣金工中方－圆类接头的展开问题。该问题的解决是锥面展开方法的成功应用；其二是螺旋输送器的核心部件－铰龙的展开问题，它是切线曲面展开方法应用的典型实例。

Method of development for developable surface and its application

This paper discusses the method of development for developable surface in order to solve the development problem in engineering. Based on the principle of surface development in differential geometry, the method of development for cone and tangent surface is given. Cone is developed in the unit ball way. Tangent surface is developed on the basis of unvarying curvature of ridge line. As the application of the methods given, involute helicoid, which is widely applied in engineering, is developed into plane. And the problem in plate metalwork, which is the development of square circle tie in, is also solved by the method.