平面与圆锥面截交线的投影解析法分析  

Analytic Method by Using Projections of the Intersection Line of Plain and Circular Cone

作　　者：韦俊[1] 葛常清[2] 熊仲明[3] 

机构地区：[1]苏州科技学院基础实验中心,江苏苏州215009 [2]上海第二工业大学机电工程学院,上海201209 [3]西安建筑科技大学土木学院,陕西西安710055

出　　处：《淮海工学院学报（自然科学版）》2006年第3期12-14,共3页Journal of Huaihai Institute of Technology:Natural Sciences Edition

基　　金：陕西省教育厅专项科研计划项目(06JK260)

摘　　要：通过解析法分析研究了平面与圆锥面的截交线投影的变化规律,确定平面与圆锥面的截交线为椭圆时的投影,通过运算表明,截交线的投影在一定位置可以为圆,并分析和确定了截平面与圆锥轴线夹角θ和圆锥母线与圆锥轴线夹角α的内在联系,同时明确各种情况下截平面与轴线的相对位置,以及在不同投影面上投影的几何特征。This paper probes into the projection variations of the intersection line between a plane and a cone through analytic method, determines the projection when the intersection line is an ellipse, proves by calculation that the projection could be a circle at certain positions, analyzes and determines the internal relations between the angle θ, formed by the plane and the cone, and α, formed by the cone＇s generator and its axis. Meanwhile, it makes clear the relative positions of the intersecting plane and its axis under various circumstances, and the geometric features of projections on different projecting planes.

关 键 词：解析法 投影特性 圆锥面截交线 

分 类 号：TH126[机械工程—机械设计及理论]