可展面的实现方法与应用

Method of designing developable surfaces and its application

为解决工程实际中按照已知条件构造可展面的问题,以微分几何学中单参数平面族包络理论为基础,提出了实现可展面的包络方法,即利用单参数平面族的包络来获得可展面,据此发展出按照已知可展面上一条曲线及可展面在该曲线上的法线构造可展面的方法.研究表明,该方法在按照已知条件设计可展的工程曲面方面具有创新性,操作简便,易于被工程所接受,将该方法应用于工程实际,解决了螺旋输送器的核心部件———铰龙的设计问题,使其在平面上的展开成为可能.

The paper discusses the method of designing developable surface to meet en gineering requirements.On basis of the principle of envelope of one-parameter plane family,the method of envelope for designing developable surfaces is prese nted.In addition,a method of designing developable surfaces based on one curve on it and its perpendicular is developed.The method is useful in designing de velopable surfaces to meet engineering requirements.It is a simple and convenie nt method for engineering.As an example of application,an involute helicoid ,which is widely applied in engineering,is designed,and the surface is develo ped for the spiral,which is the central part of helical transfer.