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等倾角变螺距圆锥螺旋线的几何特性及其作图方法 被引量:4

THE GEOMTRIC CHARACTERISTIC OF THE COHIC HELIX OF EQUIANGULAR AND CHANGE PITCH AND THE DRAWING OF ITS PROJECTIVE VIEW
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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.
作者 夏鼎立
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
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