| 正螺面上的圆柱螺线网 |
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| 引用本文： | 吴德元. 正螺面上的圆柱螺线网[J]. 中国石油大学学报(自然科学版), 1990, 0(1) |
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| 作者姓名： | 吴德元 |
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| 作者单位： | 石油大学机械系 |
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| 摘 要： | 正螺面和圆柱螺线是几何学及运动学中最重要的曲面和曲线,可以用简明的公式表示,并和其它曲面和曲线有一定关系。目前关于正螺面方程是用常规的圆柱螺线方程表示,而正螺面上任意两点间的连线(短程线)只能用微分方程表示,并无实际意义。本文研究证明,正螺面上的短程线就是一根圆柱螺线,可根据正螺面的参数准确计算出其数值。由于正螺面有对称性,其上任何方向上两点间的短程线均可求出。形成正螺面的可以是与轴线相交的任何一组圆柱螺线族,它们的导程相同,而螺旋角不同。
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| 关 键 词： | 螺旋面 螺旋线 圆柱螺线族 解析法 图解法 |
CYLINDRICAL SPIRALS ON THE POSITIVE SPIRAL SURFACE |
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| Wu Dcyuan. CYLINDRICAL SPIRALS ON THE POSITIVE SPIRAL SURFACE[J]. Journal of China University of Petroleum (Edition of Natural Sciences), 1990, 0(1) |
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| Authors: | Wu Dcyuan |
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| Affiliation: | Dept.of Mechanical Engineering |
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| Abstract: | The positive spiral surface and cylindrical spiral arc the most important curved surface and curve in kinematics and geometry, which can be expressed with simple equations and related to other curved surfaces and curves. The equation of the positive spiral surface are expressed with the conventional cylindrical spiral equation. The line connecting two points on the positive spiral surface (geodesic) can only be expressed with differential equation, which his no practical meaning. This paper proves that the geodesic on the positive spiral surface is a cylindrical spiral, which can be calculated with the parameters on the positive spiral surface. Since the positive spiral surface is symmetric, all the geodesies in any direction can be calculated. The positive spiral surfaca may be formed by a group of cylindrical spirals which intersect with their axes. The thread pitches of cylindrical spirals but the spiral angles are different. |
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| Keywords: | Spiral surfaces Spiral curves Cylindrical spirals Analytic method Diagram method |
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