今天我们学习《机械制图》——立体的投影第三部分的内容。今天的主要内容是平面与回转体表面相交。Today we are studying Mechanical Drawing - Projection of the three dimensions part 3. Today's main topic is the intersection of a plane with the surface of a rotary.
1.在一些零件上，常常见到平面与回转体表面相交。曲面立体的截交线通常是一条平面曲线，也可能是由截平面上的曲线和直线所围成的平面图形或多边形。
2.影响截交线形状的因素：
（1）曲面立体的几何性质
（2）曲面立体与截平面的相对位置
3.求截交线的方法：截交线是截平面和曲面立体表面的共有线，截交线上的点是他们的共有点。当截平面为特殊位置平面时，截交线的投影就积聚在截平面有积聚性的同面投影上，可用在曲面立体表面上取点和线的方法作截交线。
作截交线的步骤：
（1）求特殊点：特殊点是一些能确定截交线形状和范围的点，包括转向线上的点，截交线在对称轴上的顶点，极限位置点。
（2）求一般点：为了能光滑地作出截交线的投影，还需在特殊点之间再作一些中间点。
（3）判别可见性并光滑连线
4.组合回转体的表面截交线
组合回转体是指由多个基本回转体组合而成的立体。求组合回转体被截平面截切后的表面截交线的作图步骤：
（1）分析组合回转体由哪些基本回转体组成以及它们的连接关系。
（2）分别求出这些基本回转线的截交线，，并依次将其连接。
（3）正确作出两基本回转体间的分界线的投影
1. On some parts, it is common to see planes intersecting the surface of a rotary. Curved three-dimensional intercept line is usually a plane curve, may also be by the intercept plane on the curve and line surrounded by a plane figure or polygon.
2. Factors affecting the shape of the intercept line.
(1) the geometric properties of the surface
(2) the position of the surface in relation to the plane of intersection
3. The method of finding the intersection line: The intersection line is a common line between the surface of the plane of intersection and the surface of the surface, and the point on the intersection line is their common point. When the intercept plane is a special position plane, the projection of the intercept line accumulates on the same surface projection as the intercept plane, and the intercept line can be made by taking points and lines on the surface.
Steps for making an interceptor line.
(1) Special points: Special points are points that determine the shape and extent of the intercept line, including the point on the steering line, the vertex of the intercept line on the axis of symmetry, and the limit position point.
(2) Finding general points: In order to make a smooth projection of the interceptor, some intermediate points between the special points are also required.
(3) Discriminate the visibility and smoothly connect the lines
4. Combined rotary surface intersection line
A combined slalom is a three-dimensional combination of several basic slaloms. To find the surface intersection line of the combined slalom after being truncated by the truncated plane, the following steps are required.
(1) Analyse which basic rotors make up the combined slalom and how they are connected.
(2) Find the intercepts of each of these elementary rotations and connect them in turn.
(3) Make the correct projection of the line of intersection between the two basic rotaries
No.1 平面与圆柱相交
当截平面与圆柱体相交时，若截平面平行于柱轴，则与顶面，底面分别交得一段直线，与圆柱面上的两段直线交线围成矩形截交线；截平面垂直于柱轴，截交线为垂直于柱轴的圆；截平面倾斜于柱轴，若截平面只截到圆柱面，截交线是椭圆，若截平面既截到圆柱面，又截到顶面和底面，截交线由两段直线和两段椭圆弧所围成，若截平面既截到圆柱面又只截到顶面或底面之一时，则截交线由一段直线和一段椭圆弧所围成。
When the intercept plane intersects with the cylinder, if the intercept plane is parallel to the column axis, it intersects with the top surface and the bottom surface respectively, and the intersection of the two straight lines on the cylindrical surface is enclosed by a rectangular intercept line; the intercept plane is perpendicular to the column axis, and the intercept line is a circle perpendicular to the column axis; the intercept plane is inclined to the column axis, and if the intercept plane intercepts only the cylindrical surface, the intercept line is an ellipse; if the intercept plane intercepts both the cylindrical surface and the top and bottom surfaces, the intercept line is enclosed by If the intercepting plane intercepts both the cylindrical surface and only one of the top or bottom surfaces, the intercepting line is an ellipse; if the intercepting plane intercepts both the cylindrical surface and the top and bottom surfaces, the intercepting line is a straight line and an ellipse.
No.2平面与圆锥面的交线
当截平面与圆锥相交时，若截平面垂直于锥轴，截交线为垂直于锥轴的圆。若截平面倾斜于锥轴：θ>φ，未截到底圆，截交线为椭圆，截到底圆，截交线为椭圆弧和直线段；θ=φ，截交线为抛物线段和直线段；θ<φ，截交线为双曲线段和直线段。若截平面通过锥顶，截交线为三角形。
When the intercept plane intersects with the cone, if the intercept plane is perpendicular to the cone axis, the intercept line is a circle perpendicular to the cone axis. If the intercept plane is inclined to the cone axis: θ>φ, the intercept line is an ellipse if the plane is not intercepted to the base circle, an elliptic arc and a straight line segment if the plane is intercepted to the base circle; θ=φ, the intercept line is a parabolic segment and a straight line segment; θ<φ, the intercept line is a hyperbolic segment and a straight line segment. If the intercept plane passes through the top of the cone, the intersecting line is a triangle.
参考资料：文字：百度；图片：微博；翻译：百度翻译
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