摘要
本文应用微分几何理论和画法几何的图示与图解方法,研究等倾角变螺距圆锥螺旋线的几何特性及其投影图的绘制方法,并得出如下结论:(1)等倾角变螺距圆锥螺旋线展开后是对数螺线,只需计算一个参数值,即可用几何作图方法画出展开图;(2)它的切线与H面相交的轨迹也是对数螺线,而且切线与H面的夹角为常数,即sinθ=cosγcosα;(3)等倾角变螺距圆锥螺旋线的主法线与OZ轴垂直相交。
The geometric characterastic and drawing method of equiangular conie helix is futher ivesti-gated. From the investigation the following conclusions have been reached for this kind conic helix ; 1. After spreading out it becomes a logarithomic sprial, therefore, only one parameter value is needed for obtaining its spreading drawing by geometric construction method ; 2. The locas of the intersection points of its tangents with the H-plane is a logarithemic spiral too, Bisides, the angle between these tangents and the H-plane is constant, i. e. sinθ=cosα·cosγ; 3. Its principle normal is perpendicular to the Z-axe.
出处
《合肥工业大学学报(自然科学版)》
CAS
CSCD
1992年第4期138-144,共7页
Journal of Hefei University of Technology:Natural Science
关键词
等角变距圆锥
螺旋线
对数螺线
The cohic helix of equiangular and change pitch
logrithmic Spiral
locus
principal normal