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1、Axonometric Projection 轴 测 图,请点击相应标题显示其内容,Basic Knowledge of Axonometric Projection 轴测图的基本知识 Isometric Projection 正等轴测图 Cabinet Axonometry Projection 斜二轴测图 Exercises 练习题,Basic Knowledge of Axonometric Projection 轴测图的基本知识,Definiens 定义: An axonometric projection is one in which the object is viewed in
2、 such a position that several faces appear in a single view. 轴测图是一种能同时反映物体三维空间形状的单面投影图。,Trait 特点: Axonometric drawings are excellent for showing the third dimension of objects, but it is difficult to drawing and being transmuted. 轴侧图富有立体感，但它作图困难，且有变形。,Purpose 用途: Axonometric drawings are often used
3、to supplement drawings. 轴测图在工程应用中, 一般只作为辅助图样。,请点击鼠标左键显示后面内容,请点击鼠标左键显示后面内容,(1) Form of axonometric projection 轴测图的形成,1. Form and characteristics of axonometric projection 轴测图的形成和投影特性,Place a P-plane (a new single view) in the three-view system and select a proper direction of projection. Project both
4、 the object and the coordinate system of the three-view system to the P-plane with parallel projection such that the new projected drawing simultaneously reflects three coordinate planes. Such a projection is called axonometric projection. 在原三投影面体系中，在适 当位置设置一个投影面P，选取适 当的投射方向，将物体连同确定 其空间位置的直角坐标系用平行 投
5、影法投射到P平面上，使所得到 的投影图能反映出三个坐标面， 这样的投影图称为轴测图。,Basic Knowledge of Axonometric Projection 轴测图的基本知识,(2) The Characteristics of Axonometric Projection 轴测图的投影特性,1) Parallel line segments on the object are still parallel with axonometric projection. 物体上互相平行的线段，在轴测图上仍然互相平行。,2) If line segments on the object a
6、re parallel to coordinate, they are parallel to coordinate on the axonometric projection. 物体上与坐标轴平行的线段,在轴测图中仍平行于相应轴测轴。,请点击鼠标左键显示后面内容,Basic Knowledge of Axonometric Projection 轴测图的基本知识,Characteristics of parallelity 平行性特性,2. Axes angle and coefficient of axial deformation 轴测图的轴间角和轴向伸缩系数,Basic Knowled
7、ge of Axonometric Projection 轴测图的基本知识,(1)Axes angle 轴间角,(2)Coefficient of axial deformation 轴向伸缩系数,Angles between axonometric projection axis are called axes angle. 轴测投影轴之间的夹角称为轴间角。,The length ratio between line segments on axonometric axes and that on the corresponding space coordinate axes is call
8、ed coefficient of axial deformation . 轴测轴上的线段与空间坐标轴上对应线段的长度比称为轴向伸缩系数。,请点击鼠标左键显示后面内容,O,X1O1Y1,X1O1Z1,Y1O1Z1,Drawing method 基本作图方法: 1) Coordinate method 坐标法,3. Drawing for axonometric projection 轴测图的画法,请点击鼠标左键显示后面内容,2) Union method 堆积法,3) Subtraction method 切割法,4) Synthetic method 综合法,根据物体的形状特点确定作图方法，
9、以使作图最简便。,Basic Knowledge of Axonometric Projection 轴测图的基本知识,1. Construction of isometric projection 正等轴测图的形成,请点击鼠标左键显示后面内容,Isometric Projection 正等轴测图,2. Axes angle and coefficient of axial deformation 轴间角和轴向伸缩系数,To produce an isometric projection, it is necessary to view an object such that its prin
10、cipal edges are equally inclined to the viewer and hence are foreshortened equally. 当空间的直角坐标轴向轴测投影面倾斜的角度相同时，用正投影法得到的投影图称为正等轴测图。,(1)Axes angle 轴间角,(2)Coefficient of axial deformation 轴向伸缩系数 p = q = r = 0.82 1,Isometric Projection 正等轴测图,3. Isometric drawing for polyhedral solids 平面立体正等轴测图的画法,Common dr
11、awing steps 一般作图步骤,(1) Draw the isometric axes and position origins. 画出轴测轴和坐标原点； (2) Measure the size of line segments on X ,Y axes and draw parallel line to the X,Y，draw the lower base of the solid. 沿X轴量出其长,沿Y轴量出其宽,分别过X.Y轴上的点作X.Y轴的平行 线,即可求得立体的底面图形； (3) From all end points draw lines parallel to the
12、 Z axes, measure the size of line segments equal to high, construct top shape of the solid. 从求得的各端点作Z 轴平行线,量取其长度为高,即可求得立体顶面图形。 (4) Erase the unnecessary lines and deepen the visible lines. 擦去作图线及不可见轮廓线，加深可见轮廓线。,请点击鼠标左键显示后面内容,Example 1 正方体,Example 2 叠加体,Example 3 徒手画组合体,4. Isometric drawing for curve
13、d solids 曲面立体正等轴测图的画法,Common drawing steps 一般作图步骤,(1) Draw the isometric axes and position origins. 画出圆（弧）的轴测轴和坐标原点； (2) Measure the size of D ,construct diamond shape of the circle. 过圆心0分别沿X、Y轴量取直径D ,作各圆的外切方形的菱形投影； (3) Construct approximate ellipse with a compass from four centers. 采用四心圆弧法用圆规画圆形的椭圆
14、形投影； (4) Draw the tangent and profile lines. 画出公切线及其余的轮廓线； (5) Erase the unnecessary lines and deepen the visible lines. 擦去作图线及不可见轮廓线,加深其余图线。,请点击鼠标左键显示后面内容,Example4 圆台,Example5 圆角底板,Isometric Projection 正等轴测图,正等轴测图椭圆长短轴的方向,1. Construction of cabinet axonometry projection 斜二轴测图的形成,请点击鼠标左键显示后面内容,Cabin
15、et axonometry projection 斜二轴测图,2. Axes angle and coefficient of axial deformation 轴间角和轴向伸缩系数,When the axonometry projection plane is parallel to a coordinate axis, and the coefficient of axial deformation of two axes that parallel to the coordinate plane are equal, the cabinet axonometry is produced
16、. 轴测投影面平行于一个坐标轴,且平行于坐标平面的那两个轴的轴向伸缩系数相等的斜轴测投影称为斜二等轴测图(简称斜二轴测图)。,(1)Axes angle 轴间角,(2)Coefficient of axial deformation轴向伸缩系数 p = r = 1 q = 0.5,3.Cabinet axonometry projection for polyhedral solids 平面立体斜二轴测图的画法,Common drawing steps 一般作图步骤,(1) Draw oblique axes and position origins O. 画出轴测轴和坐标原点O; (2) M
17、easure the size of line segments on X axes and measure the size of line segments on Y axes with size, and draw parallel line to the X ,Y , draw the lower base of the solid. 沿X轴量出其长,沿Y轴量出其宽并取其1/2,分别过所得点作X.Y 轴的平 行线,即可求得立体的底面图形； (3)From all end points draw lines parallel to the Z axes, measure the size
18、 of line segments equal to high, construct top shape of the solid. 从求得的各端点作Z 轴平行线,量取其长度为高,即可求得立体顶面图形。 (4) Erase the unnecessary lines and deepen the visible lines. 擦去作图线及不可见轮廓线,加深可见轮廓线。,请点击鼠标左键显示后面内容,Example 1 正方体,Cabinet axonometry projection 斜二轴测图,4.Cabinet axonometry projection for curved solids
19、曲面立体斜二轴测图的画法,(1) Define the oblique coordinate frame and position origins O. 在视图上确定坐标轴和坐标原点O。 (2) Draw oblique axes and position origins O, lay out the centerlines of the circles. 画出轴测轴和坐标原点0，依次确定各圆孔(弧)的中心线; (注意:沿Y轴测量出前后表面的尺寸后应取其1/2。) (3) Draw all circles on the each plane. 分别画出各平面上的圆形(弧)。 (4) Compl
20、ete the tangent and profile lines. 画前后圆弧轮廓的公切线，再画其余轮廓线; (5) Erase the unnecessary lines and deepen the visible lines. 擦去作图线,加深可见轮廓线。,注意：斜二轴测图的观察方向应选有圆形的结构位于正面。,请点击鼠标左键显示后面内容,Commo drawing steps 一般作图步骤,Example 2 正方体穿圆孔,Example 3 组合体,Example 4 杠杆,斜二轴测图椭圆长短轴的方向,Cabinet axonometry projection 斜二轴测图,Exerc
21、ises 练习题,请点击题目显示其内容,Make an isometric drawing of the cylinder. 画出回转体的正等轴测图。,2. Make an cabinet axonometry projection of the composite solid. 画出组合体的斜二等轴测图。,本 章 结 束,谢谢您的认真学习！,退出,前一页,1. Make an isometric drawing of the right cylinder. 画出圆柱体的正等轴测图。,请点击解答显示其内容,2.Make an cabinet axonometry projection of t
22、he composite solid. 画出组合体的斜二等轴测图。,请点击解答显示其内容,1. Make an isometric drawing of the cube (L=20 mm). 求作正方体的正等轴测图(边长L=20mm)。,画出坐标原点和轴测轴；,沿X轴量出其长,沿Y轴量 出其宽,分别过X、Y轴上 的点作Y、X轴的平行线, 即求得立体的底面图形；,擦去作图线及被遮挡的 不可见轮廓线，加深可 见轮廓线。,Steps 作图步骤:,过底面各端点作Z轴的平 行线,其高度等于立体上 该线之高,连接各最高点 即为立体的顶面图形；,请点击鼠标左键显示后面内容,1) Draw the isom
23、etric axes.,2) Draw the lower base of the solid.,3)Construct top shape.,4) Erase the unnecessary lines and deepen the visible lines.,请点击步骤按钮显示其内容,2. Make an isometric drawing of the solid. 求作立体的正等轴测图。,作方箱,使物体置入其内。,作其基本形于轮廓内。,作中心块。,加深视图。,Stage 1,Stage 2,Stage 3,Stage 4,3. Make an isometric drawing fr
24、eehand. 徒手画立体的正等轴测图。,请 点 击 步 骤 按 钮 显 示 其 内 容,轴测图观察方向的比较（A最佳）,Draw a box 作方箱。,Construct basic shape 作基本形。,Line in the view 加深视图。,Stage 1,Stage 2,Stage 3,2. Make an isometric drawing of the truncated ordinary cone. 求作圆台的正等轴测图(顶圆直径D1=18mm,底圆直径D2=30mm,高H=32mm)。,请点击鼠标左键显示后面内容,Steps作图步骤:,(4)Draw the tange
25、nt. 作二椭圆的公切线;,(3)Construct ellipse with four centers. 用四心圆弧法画圆的投影(椭圆);,(5)Erase the unnecessary lines and deepen the visible lines. 擦去作图线及被遮挡的不可见轮廓线,加深可见轮廓线。,Four centers 四心圆弧法: Find 1、2 、3、4. 由菱形二钝角端点1、2分别向对边中点连线,求连线的交点即为3、4点;,Draw arc. 分别以1、2点为圆心,以1、2点到对边中点为半径画圆弧;,Draw the rest of arc. 再分别以3、4点为圆心
26、,以3、4点到中点为半径画剩余圆弧。,(2) Construct diamond shape of the circle. 过圆心01、02分别沿X、Y 轴量取直径D1、D2,作各圆的外切方形的菱形投影;,(1) Draw the isometric axes. 分别画出顶圆和底圆的圆心坐标01、02及其轴测轴;,o1(o2),不 可 见 的 轮 廓 线 一 律 不 画,3. Make an isometric drawing of the soleplatea with round corners. 求作带圆角底板的正等轴测图。,请点击鼠标左键显示后面内容,(2)Construct top
27、arc. 求顶面圆弧的投影;,(1)Draw the rectangle soleplatea.画矩形底板的轴测图;,Steps作图步骤:,在有圆弧的二角分别沿其二边 量取半径R之长求得1、2点,过 1、2点作该边的垂线 ,求得二 垂线的交点即为圆心 ,以R为 半径作圆弧即为顶面圆弧。,过所求的圆心作Z轴平行线,量 取底板高H即为底面圆心,以R 为半径作圆弧即为底面圆弧。,(4)Draw the tangent. 作顶面和底面圆弧的公切线;,(3)Construct base arc. 求底面圆弧的投影;,(5)Erase the unnecessary lines and deepen th
28、e visible lines. 擦去作图线及被遮挡的不可见轮廓线,加深可见轮廓线。,1. Make an cabinet axonometry projection of the cube(L=20 mm). 求作正方体的斜二轴测图(边长L=20 mm) 。,沿X轴量出其长,沿Y轴量出其宽后取其1/2,分别过量出点作X、Y轴的平行线,画立体的底面图形;,过底面各顶点作Z轴的平行线,其高度等于立体上该线之高,连接各最高点即为立体的顶面图形；,先画出轴测轴和原点；,Steps作图步骤:,擦去作图线及被遮挡的不可见轮廓线,加深可见轮廓线。,请点击鼠标左键显示后面内容,(1) Draw the ob
29、lique axes.,(2) Draw the lower base of the solid.,(4) Erase the unnecessary lines and deepen the visible lines.,(3) Construct top shape.,2. Make an cabinet axonometry projection of the cube with a hole. 求作中心穿半径为5 mm水平圆孔正方体的斜二轴测图。,请点击鼠标左键显示后面内容,以5 mm 为半径画圆形；,擦去作图线及被遮挡的不可见 轮廓线,加深可见的轮廓线。,先画出轴测轴和前后表面圆心；
30、,Steps 作图步骤:,(1) Lay out the centre lines of the cube.,(2) Draw circles on the cube.,(3) Erase the unnecessary lines and deepen the visible lines.,01,3. Make an cabinet axonometry projection of the component. 求组合体的斜二轴测图。,Steps作图步骤:,(2)Draw circles and arc. 分别过圆心01、02按其直径画圆形及圆弧;,(3)Complete the tange
31、nt and profile lines.画圆弧的切线,再画其余直线构成的轮廓;注意:沿Y轴量尺寸取其1/2,(4)Erase the unnecessary lines and deepen the visible lines. 擦去作图线及不可见轮廓线,加深图线。,(1)Draw the oblique axes.画出前后表面上圆孔(弧)的原点和轴测轴; 注意:沿Y轴量出前后表面的尺寸后取其1/2,请点击鼠标左键显示后面内容,o1(o2),请点击步骤按钮显示其内容,4. Make an cabinet axonometry projection of the lever. 求作杠杆的斜二等
32、轴测图。,作中心线,使圆平行投影面。,作圆及圆弧为杠杆轮廓。,作公切线完成外形。,作孔并加深视图。,Stage 1,Stage 2,Stage 3,Stage 4,Construction of isometric projection 正等轴测图的形成,An projection plane P is in front of a vertical plane. 以正(垂直)投影面作为轴测投影面P；,(2) Direction of projection S is vertical to the projection plane. 投射方向S垂直于轴测投影面P( S P )；,(3) Chan
33、ge the relative position between a solid and the projection plane. 改变物体与轴测投影面的相对位置。,(使其三方向的轴均倾斜于轴测投影面),请点击鼠标左键显示后面内容,Construction of cabinet axonometry projection 斜二轴测图的形成,(使其 X、Z 轴平行于轴测投影面),请点击鼠标左键显示后面内容,An projection plane P is in front of a vertical plane. 以正(垂直)投影面作为轴测投影面P；,(2) Direction of proj
34、ection S is incline to the projection plane. 投射方向S倾斜于轴测投影面P (S P )；,(3) Fixedness the relative position between a solid and the projection plane. 物体与投影轴测面的相对位置不变。,Axonometric projection 轴测图,Orthogonal projection 正投影图,Isometric projection 正等轴测图,轴承座零件的轴测图,Axonometric projection 轴测图,反映零件安装顺序的轴测分解图,Axon
35、ometric projection 轴测图,Axonometric projection 轴测图,滑动轴承的轴测分解图,活塞连杆副的轴测分解图,国外“连杆机构”安装顺序的轴测分解图,Axonometric projection 轴测图,物体上平行的直线轴测投影仍平行,与轴平行的直线仍与该轴测轴平行,请点击鼠标左键显示后面内容,Characteristics of parallelity 平行性特性,Right 正确,Error 错误,Positioning object relative to projection plane 物体对投影面的适当安置,斜二轴测图的观察方向: Place th
36、e face of the object containing circles or arcs parallel to the projection plane. 应使有圆形或圆弧的面与轴测投影面平行。 Place the longest dimension of the object containing circles or arcs parallel to the projection plane. 应使物体的最长尺寸结构与轴测投影面平行。,The long and short axis of the corresponding iso-circle (the ellipse) 正等轴测
37、图椭圆长短轴的方向,平行于H面的椭 圆长轴O1Z1轴， 短轴沿O1Z1轴。,平行于V面的椭圆 长轴 O1Y1轴， 短轴沿O1Y1轴。,平行于W面的椭圆 长轴 O1X1轴， 短轴沿O1X1轴。,The long and short axis of the corresponding iso-circle (the ellipse) 斜二轴测图椭圆长短轴的方向,在图片上点击鼠标左键可以“暂停”或再次“播放”,在图片上点击鼠标左键可以“暂停”或再次“播放”,在图片上点击鼠标左键可以“暂停”或再次“播放”,在图片上点击鼠标左键可以“暂停”或再次“播放”,在图片上点击鼠标左键可以“暂停”或再次“播放”,在图片上点击鼠标左键可以“暂停”或再次“播放”,