机械制图第三章立体的投影（机械制图基本立体投影）

今天我们学习《机械制图》——立体的投影第四部分的内容。今天的主要内容是两回转体表面相交。Today we are studying Mechanical Drawing - Projection of three dimensions part 4. Today's main topic is the intersection of two revolving body surfaces.

1.（1）两立体表面的交线称为相贯线。

（2）相贯线不仅出现在两立体外表面相交的情况下，有时还常常见到由于在立体上穿孔，而形成的孔口交线，或孔与孔的孔壁交线。

2.由于立体分为平面立体和曲面立体，因而两立体表面的交线可以有以下几种情况：

（1）两平面立体相交（2）平面立体与曲面立体相交（3）两曲面立体相交。

相贯线的基本性质：

（1）共有性：相贯线是两立体表面的共有线。

（2）分界性：相贯线是两立体表面的分界线。

（3）封闭性：相贯线一般是封闭的空间曲线，特殊情况下为平面曲线或直线。

其作图实质是找出相贯的两立体表面的若干共有点的投影。

3.影响相贯线形状的因素：

（1）两立体的形状

（2）两立体的大小

（3）两立体的相对位置

求相贯线的方法：

两曲线立体的相贯线是两曲面立体表面的共有线，相贯线上的点是两曲面立体的共有点。

求作两曲面立体表面的相贯线时，应在可能方便的情况下，作出相贯线的一系列共有点，并表明其可见性，再光滑连线即可。

1. (1) The intersection line of two three-dimensional surface is called the coherent line.

(2) The intersection line not only appears in the case of two three-dimensional outer surface intersection, sometimes also often see due to the perforation on the stereo, and the formation of the hole intersection line, or hole and hole wall intersection line.

2. As the stereo is divided into flat stereo and curved stereo, and thus the two stereo surface intersection line can have the following cases.

(1) two plane stereo intersection (2) plane stereo and surface stereo intersection (3) two surface stereo intersection.

Basic properties of coherent lines.

(1) Commonality: The coherent line is the common line of two three-dimensional surfaces.

(2) Demarcation: The coherent line is the demarcation line between two three-dimensional surfaces.

(3) Closure: The coherent line is generally a closed space curve, or a plane curve or a straight line in special cases.

The essence of the drawing is to find out the projection of a number of common points of the two three-dimensional surfaces.

3. Factors affecting the shape of the coherent line.

(1) The shape of the two dimensions

(2) The size of the two dimensions

(3) The relative positions of the two dimensions

Method of finding the coherence line.

The coherence line of two curves is the common line of two surfaces, and the point on the coherence line is the common point of two surfaces.

To find the coherent line of two surfaces, a series of common points of the coherent line should be made, if possible and convenient, and its visibility should be shown, and then the smooth line can be connected.

No.1 利用积聚性作图

当相交的两回转体中有一个是轴线垂直于投影面的圆柱时，由于圆柱面在该投影面上的投影具有积聚性（积聚为圆），因此相贯线在该投影面上的投影就积聚在圆柱面有积聚性的投影上。这时，可以将相贯线看成是另一回转面上的曲线，利用回转面上取点的方法作出相贯线的其它投影。

注意：利用积聚性作图的方法只适用于相交两回转体中至少有一个是圆柱，并且其轴线与投影面垂直的情况下。

When one of the two intersecting gyrations is a cylinder whose axis is perpendicular to the projection plane, the projection of the coherent line on that projection plane accumulates on the projection of the cylinder with accumulation (accumulates as a circle). In this case, the coherent line can be considered as another curve on the rotary surface, and other projections of the coherent line can be made by using the method of taking points on the rotary surface.

Note: The method of drawing with cumulants is only applicable when at least one of the two intersecting gyrations is cylindrical and its axis is perpendicular to the projection plane.

No.2简化画法

用三点法绘制两不等径圆柱相贯线的方法。

条件：

（1）两圆柱正文

（2）两圆柱直径不相等

作图：

（1）作出两圆柱体转向线上的相贯线点（三点）。

（2）连接a’，b’，作a’b’的中垂线，与小圆柱的轴线相交于o’。

（3）以o’为圆心，以o’a’半径为半径画圆弧，即得相贯线。

The method of drawing two unequal cylindrical coherent lines by the three-point method.

Conditions.

(1) two cylinders body

(2) the two cylinders are not equal in diameter

Drawing.

(1) Make two cylinders turning line of coherence points (three points).

(2) Connect a', b', make a perpendicular to a' b', and intersect the axis of the small cylinder at o'.

(3) Take o' as the center and draw an arc with the radius of o'a' as the radius to get the coherence line.