第七章 轴测图   CHAPTER  THREE  AXONOMETRIC  DRAWING

学习目标 learning target：

1.了解轴测图的分类，理解轴测图平行性、可量性的基本性质。

2.熟记正等测、斜二测图的轴间角和轴向伸缩系数，明确两者的不同点。

3.掌握基本体、叠加体、切割体轴测图的画法要点，能依据物体的三视图，准确绘制出它们的正等测或斜二测图。

Get to know the classification and have a good understanding of the parallel and measurement characteristics of axonometric drawing.

Memorize the parameters of isometric drawing and cabinet drawing and try to make sure to know about the differences between them.

Master the key points of axonometric drawing as to basic solids, superimpose solids and cutting solids. One is able to provide pictorial drawing based on three views.

       轴测图是一种能同时反映物体长、宽、高三个方向的单面投影图。轴测图具有立体感，可以弥补正投影的不足，是一种帮助读图、构思的辅助图样。

        Axonometric [aksə'nɒmetrɪk] projections are made on a single projection plane and show length, width and height of object. It plays an important role in understanding views and object. In fact, it is a useful auxiliary [ɔɡˈzɪljəri, -ˈzɪləri] drawing.

第一节 轴测投影的基本知识  SECTION  ONE  BASIC  KNOWLEDGE  OF  AXONOMETRIC  DRAWING

一、轴测图的概念 concept of axonometric drawing

       如图 7-1 所示，将物体连同参考直角坐标系，沿不平行于任一坐标平面的方向，用平行投影法将其投射在单一投影面上所得的具有立体感的图形称为轴测图。投影面 P 称为轴测投影面，参考直角坐标系（O1X1、O1Y1、O1Z1）在轴测投影面上的投影（OX、OY、OZ）称为轴测轴。

       When the object together with the reference Cartesian  coordinates projection on a single plane of projection using parallel projection, axonometric drawing can be produced . the single projection plane is called axonometric projection plane; the reference Cartesian coordinates （O1X1、O1Y1、O1Z1）in the axonometric projection plane (OX, OY, OZ) is called axonometric axis（OX、OY、OZ）.As shown in Figure 7-1.

       在轴测图中，相邻两轴测轴间的夹角称为轴间角。轴测轴上的投影长度与原长之比称为轴向伸缩系数，OX、OY、OZ 轴的伸缩系数分别用 p、q、r 表示。如图 7-1 所示：

      There are two parameters [pəˈræmɪtə(r)] of axonometric projection. They are angles between axonometric axis; and coefficient [ˌkəʊɪˈfɪʃnt] of axial  deformation. The coefficient of axial deformation p, q, and r are the ratios of the length of the axonometric projection of a line of the true length of the line in space along the directions of the coordinate axes OX、OY and OZ respectively.As shown in Figure 7-1.

                                      图7-1 轴测图的形成 formation of axonometric drawing

二、轴测图的分类 types of axonometric drawing

       根据所采用的投影方法，轴测图可分为如下两大类：

       According to the projection method, it can be classified into two types.

      (1)正轴测图。用正投影法所得到的轴测图称为正轴测图，如图 3-1(a)所示。由于物体相对于轴测投影面的相对位置及投射方向不同，轴向伸缩系数也不同，制图标准又将正轴测图具体分为三种：

       p＝q＝r，称为正等轴测图，可简称正等测。

       p＝q≠r 或 p≠q＝r 或 p＝r≠q，称为正二等轴测图，可简称正二测。

       p≠q≠r ，称为正三轴测图，可简称正三测。

       Orthogonal axonometric drawing is obtained by orthographic projection method as shown in Figure 3-1 (a). This kind of drawing includes three types depending on different parameters.

       If the coefficient of axial deformations are p＝q＝r, it is isometric drawing.

       If the coefficient of axial deformations are p＝q≠r ,p≠q＝r or p＝r≠q，it is dimetric drawing.

       If the coefficient of axial deformations are p≠q≠r, it is called trimetric drawing

       (2)斜轴测图。用斜投影法所得到的轴测图称为斜轴测图，如图 7-1(b)所示。制图标准同理也将斜轴测图具体分为斜等轴测图、斜二等轴测图和斜三轴测图三种，可简称为斜等测、斜二测和斜三测。

       Oblique axonometric drawing is obtained by oblique projection method.as shown in Figure 7-1 (b). cabinet drawing is often used in engineering drawing.

       本章介绍常用的正等测和斜二测的画法。

       Isometric and cabinet drawings will be introduced in the chapter.

三、轴测图的基本性质 principles of construction axonometric drawing

     （1）平行性。物体上互相平行的线段，在轴测图中仍然互相平行。物体上平行于坐标轴的线段，在轴测图中平行于相应的轴测轴。

       If lines are parallel in space, the lines must be parallel in axonometric projection. Meanwhile, if segments are parallel one coordinate axis ['æksɪs] , they must be parallel the corresponding axonometric axis in axonometric projection.

     （2）可量性。物体上互相平行的线段，在轴测图中伸缩系数相等。物体上平行于坐标轴的线段，在轴测图中与相应轴的伸缩系数相同。由于轴测图中只有轴测轴的伸缩系数是已知的，所以只有与轴测轴平行的线段，才能按相应轴测轴的轴向伸缩系数量取尺寸。这就是可量性，也是“轴测”二字的含义。

      Measurements can only be made on axonometric axis or on the lines parallel to axonometric axis.