根据圆柱螺旋线理论,分析了形成圆环螺旋线的要素,并运用解析几何方法建立了圆环螺旋线的参数方程。基于圆柱螺旋面和圆环螺旋线的形成原理,构建了圆环直纹螺旋面的数学模型,讨论了圆环直纹螺旋面的两种表示方法。在AutoCAD环境下,用VisualLisp语言编程,绘制了圆环螺旋线的投影图和三维立体图,并给出了圆环正螺旋面和斜螺旋面的三维CAD造型方法。

According to the helix theories of cylinder,the essential factors of helix with torus are analyzed,and the parametric equation of helix on torus is given based on analytic geometry.The mathematical model of ruled helicoids on torus is constructed and two expression methods of ruled helicoids are discussed.The projective view and 3D solid view of helix on torus are drawn by AutoCAD VisualLisp,and the method of 3D modeling about vertical helicoids and oblique helicoids is given.

Formating and Drawing of Helicoids on Torus Based on AutoCAD

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