圆柱与圆锥轴线相交时左侧相贯线上最右点的解析证明与图解  

Analytical Proof and Illustrations on the Ultra Right Point of Intersection Curve of Cylinder and Cone with Intersected Axes

作　　者：谷艳华[1] 侯洪生[1] 张秀芝[1] 

机构地区：[1]吉林大学机械科学与工程学院,吉林长春130025

出　　处：《工程图学学报》2010年第4期146-150,共5页Journal of Engineering Graphics

基　　金：吉林省重点教研资助项目

摘　　要：轴线相交的圆柱、圆锥两曲面立体相贯时,产生左右两条空间相贯线曲线。该文以左侧相贯线为研究对象,用数学方法证明圆柱立体的半径在一定范围内变化时,左侧相贯线上最右点的变化规律,由此提出了准确绘制左侧相贯线上最右点的图解方法。左侧相贯线上的最右点在两条特殊相贯线上,分别在锥和与锥相切的球的相贯线上及在柱和与锥相切的球的相贯线上。A left and a right spacial intersection curves are formed by a cylinder and a cone with their axes intersected.The research is focused on the left intersection curve,and the variation rule of its ultra right point is derived using mathematical method as the radius of the cylinder varying.Then a graphical method to draw the exact position of the ultra right point on the left intersection curve is provided.The ultra right point of the left intersection curve is on two particular intersection curves,namely,the intersection curve of the cone and its tangent sphere and the intersection curve of the cylinder and the sphere mentioned above.

关 键 词：工程图学 画法几何 相贯线 解析证明 图解方法 

分 类 号：O185.2[理学—数学]