工程制图第四章 立体的投影

1、1Chapter 4 Projection of Solids 立体的投影立体的投影4-1 Planar Solid Projection 平面立体的投影平面立体的投影 4-2 Reading Planar Solid Projection 平面立体的读图平面立体的读图4-3 Revolving Solid Projection 回转体的投影回转体的投影 2Look here, they are practical parts. This is a bolt, and this is a tailstock assembly of lathe.How to describe them on t

2、he paper? If you look them carefully, you will find that they are complex solids.Such as this bolt. This is hexagonal prism, cylinder and screw.And this is the more complicate solid. Here is a rectangular prism, a slot. And these are some cylinder holes and bolts, etc.Both of them are made up of bas

3、ic solids.Basic solids include prism, pyramid, cylinder, cone and sphere. All machines and parts are regarded that a group of basic solids are assembled together in a certain method.How to draw the projection of basic solids? That is what we will discuss today. Chapter 4- projection of solids.This c

4、hapter has three sections . One is planar solid projection , the second is reading planar solid projection,the last is revolving solid projection3Practical parts实用部件实用部件 How to describe it on the paper?如何在图纸上描述？如何在图纸上描述？4 All machines and objects are regarded that a group of basic solids are assembl

5、edtogether in a certain method, such as prisms, pyramids, cylinders, cones and spheres. 一般的机器零件或物体都可以看作是由若干基本形体，如棱柱、棱锥、一般的机器零件或物体都可以看作是由若干基本形体，如棱柱、棱锥、圆柱、圆锥和球等按某种方式组合而成。圆柱、圆锥和球等按某种方式组合而成。Conventional basic solids are classed in two groups：基本形体分为两类：基本形体分为两类：1. Planar solids are enclosed by planes, as

6、shown in Fig.5-1 a, b. 平面立体平面立体 是完全由平面围成的立体，如图是完全由平面围成的立体，如图5-1 a, b。2. Revolving solids are enclosed by curved surfaces and planes, as shown in Fig.5-1 c, d, e, f. 回转体回转体 是由回转面或回转面和平面围成的立体，如图是由回转面或回转面和平面围成的立体，如图5-1 c, d, e, f。Fig.5-1 Conventional basic solids常见的基本形体常见的基本形体(a)(b)(c)(d)(e)(f)51. Proj

7、ections of a prism and fixing points on the surface of a prism 棱柱的投影及其表面上取点和取线棱柱的投影及其表面上取点和取线2. Projections of a pyramid and fixing points on the surface of a pyramid 棱锥的投影及其表面上取点和取线棱锥的投影及其表面上取点和取线4-1 Planar Solid Projection 平面立体的投影平面立体的投影 3. Deformities of planar solids 带切口的平面立体的投影带切口的平面立体的投影6Demo

8、of projections of a hexaprism 六棱柱的投影六棱柱的投影7(1) Projections of a hexagonal prism 六六棱柱体的投影棱柱体的投影ABCD45abcda(d)b(c)b”a”c”d”1 Prisms 棱柱棱柱Three meanings in top view 俯视图的俯视图的3层含义层含义8(2)Fixing points of a hexagonal prism 六棱柱表面取点六棱柱表面取点9ABDCM45abcda(d)b(c)b”a”c”d”m”n(n”)m(N)Sss”sm(n)(2) Points on the surfac

9、e of a right hexaprism 六棱柱表面上的点六棱柱表面上的点10Demo of projections of a triangular pyramid 三棱锥的投影三棱锥的投影11(1) Projections of a triangular pyramid 棱锥体的投影棱锥体的投影SBAC(c”)sbbscaa”cs”ab”2 Pyramids 棱锥棱锥12ABCS(c”)saascba”cs”bb”1”11rrR(2) Points on the surface of a right triangular pyramid (一) 三棱锥表面上的点三棱锥表面上的点(一一)1

10、3ABCS(c”)saascba”cs”bb”22 2 (2) Points on the surface of a right triangular pyramid (二) 三棱锥表面上的点三棱锥表面上的点(二二)14ABCS(c”)saascba”cs”bb”3(3”)(2) Points on the surface of a right triangular pyramid (三) 三棱锥表面上的点三棱锥表面上的点(三）三）(3)15p25p25a ababc(c)b c m mk nn nmemne1.1.2.2.3.3.16 Correctly drawing the projec

11、tions of deformities of planar solids is not only applying the drawing methods of planar solids, but also using the methods of points and lines on the surface of planar solids. 若要完全正确地画出带切口平面立体的投影图，不仅要若要完全正确地画出带切口平面立体的投影图，不仅要运用绘制平面立体投影图的方法，还必须利用在平面立体表运用绘制平面立体投影图的方法，还必须利用在平面立体表面取点、取线的原理和作图方法来进行。面取点、取

12、线的原理和作图方法来进行。3. Deformities of planar solids 带切口的平面立体的投影带切口的平面立体的投影17 1. Make sure an original; 确定基形确定基形; 2. Find the piercing points of the edges which planes intersect solid; 找到找到截平面截平面与平面立体上各条棱线的交点；与平面立体上各条棱线的交点； 3. Join points in order by straight lines; 依次连接各点依次连接各点; 4. Make sure visibility; 判断

13、可见性判断可见性; 5. Block in all final lines. 整理轮廓线。整理轮廓线。Steps in drawing the deformities of planar solids:带带切口切口的平面立体的作图要求的平面立体的作图要求: :181234567864(3 )1(52)7 (8)12563478Example 1:19侧平面S正垂面R1. Shape analytical method 形体分析形体分析Deformable planar solid is considered that the simple planar solid is incised by

14、planes in special position. 带切口的平面立体可以看作是由一些基本的平面立体经过切割而形成。Example 2: Construct horizontal projection and profile projection of deformable pentagon. 试补全带缺口的正五棱柱的水平投影和侧面投影。试补全带缺口的正五棱柱的水平投影和侧面投影。 20gababf)(ce)(fdb) (gac)(fe)(dcgedyy2.Drawing procedure 作图步骤作图步骤8711121056943961（3）2（4）10571181112910431（2

15、）8（7）3（4）10（5）9（6）11黑板画图讲解Example222Example 3: Construct horizontal projection and profile projection of deformable right triangular pyramid 完成带切口的正三棱锥的水平投影和侧面投影。完成带切口的正三棱锥的水平投影和侧面投影。水平面水平面正垂面正垂面23Re-edit：整理后：整理后：4-2 Reading Planar Solid Projection 平面立体的读图平面立体的读图一、Reading the views together 要将几个视图联系

16、起来看要将几个视图联系起来看25Single enclosed frame a plane （either similar or collecting ）一个封闭的线框一个封闭的线框 一个平面一个平面 (对应投影非类似即积聚对应投影非类似即积聚) a solid 一个体一个体Two adjacent frames two intersecting planes 两个相邻的线框两个相邻的线框两个相交的面两个相交的面 two paralleling planes 两个错开的面两个错开的面Two frames which ring convex 、concave 、through两个套起来的线框两个

17、套起来的线框凸、凹、通凸、凹、通The projection of the plane which collects 具有积聚性的面的投影具有积聚性的面的投影Intersecting line of two planes两个面的交线两个面的交线Line直线直线Line frame线框线框二、Understand the meanings of lines and line frames 清楚视图中图线和线框的含义清楚视图中图线和线框的含义QcdqCDCorresponding relation of line直线的对应关系直线的对应关系The line on the views represe

18、nt a plane or the intersecting line of two planes. 视图上的直线在空间组合体上视图上的直线在空间组合体上表示表示一个平面一个平面，表示，表示两个面的两个面的交线交线。aABbcCdDCorresponding relation of line frame线框的对应关系线框的对应关系A enclosed frame represents a plane or a hole.一个封闭的线框表示一个封闭的线框表示一个一个平面平面，或，或一个孔一个孔 。Corresponding relation of two adjacent frames相邻两线框

19、的对应关系相邻两线框的对应关系aAbBcdCDe”f”EFTwo adjacent frames represent two intersecting planes or two paralleling planes.两个相邻的线框表示两个相邻的线框表示两个相两个相交的面交的面或者或者两个错开的面两个错开的面 。 Generally a enclosed frame represent the projection of plane, and the other views are either similar of collecting. 视图中一个视图中一个封闭线框封闭线框一般情况下表示一

20、个面的投影，一般情况下表示一个面的投影，非类似即积聚。非类似即积聚。Two frames which ring convex 、concave 、through套起来的线框套起来的线框凸、凹、通凸、凹、通Two adjacent frames represent two intersecting or paralleling plane.两个相邻的线框代表两个两个相邻的线框代表两个相交相交的面或两个的面或两个错开错开的面。的面。One of a plane view is an enclosed frame at least.一表面的三个投影中至少有一个是封闭线框；一表面的三个投影中至少有一个

21、是封闭线框；The other views according projecting relation are either similar or collecting. 该线框按投影关系对照其它投影，不类似，便积聚。该线框按投影关系对照其它投影，不类似，便积聚。Notice: Distinguish different figure according the change of hidden line and solid line. 注意图中虚实线变化，区分不同形体。注意图中虚实线变化，区分不同形体。 三、三、Corresponding relation of views and soli

22、ds 视图与空间形体的对应关系视图与空间形体的对应关系34PPQPQQRRRTTTExample: complete the third view according two given views. 由两视图补画第三视图由两视图补画第三视图3511221236Example: complete the third view according two given views. 由两视图补画第三视图由两视图补画第三视图Example: complete the third view according two given views. 由两视图补画第三视图由两视图补画第三视图立体构成模型394

23、04-3 Revolving Solid Projection 回转体的投影回转体的投影 一、The revolving surface and its characters 回转面及其性质回转面及其性质二、Projections of cylinders and points on the surface of a cylinder 圆柱体投影及面上取点圆柱体投影及面上取点三、Projections of cones and points on the surface of a cone 圆锥体投影及面上取点圆锥体投影及面上取点四、Projections of spheres and poi

24、nts on the surface of a sphere 圆球体圆球体投影及面上取点投影及面上取点41 The trace developed by which genertrix AB is evolving around axis OO is called revolving surface. The trace of any point on the genertrix AB is the circle which is perpendicular to the axis. Any position of genertrix is called element line. 母线母线A

25、B绕回转轴线绕回转轴线OO旋转的运动轨迹形成回转面旋转的运动轨迹形成回转面,母母线线AB上任一点的运动轨迹为一垂直于轴线上任一点的运动轨迹为一垂直于轴线OO的圆。母线的圆。母线的任一位置称为素线。的任一位置称为素线。一、一、The revolving surface and its characters 回转面及其性质回转面及其性质42Genertrix母线母线Axis轴线轴线Generatrix母线母线Axis轴线轴线Element line素线素线ACBGeneratrix43二、Projections of cylinders and points on the surface of a

26、 cylinder 圆柱体投影及面上取点圆柱体投影及面上取点2. Point and line on the surface of cylinders 圆柱体表面上取点、取线圆柱体表面上取点、取线1. Projections of cylinders 圆柱体的投影圆柱体的投影44Profile lines of a cylinder圆柱轮廓线圆柱轮廓线Profile lines of a cylinder圆柱轮廓线圆柱轮廓线aba bc dc”d”dca”b”1. Projections of cylinders 圆柱体的投影圆柱体的投影Three meanings in top view 俯

27、视图的俯视图的3层含义层含义4546A(D)CB2. Points and lines on the surface of a right cylinder 圆柱面上取点、取线圆柱面上取点、取线(d)(d”)472. Point and line on the surface of a cone 圆锥体表面上取点、取线圆锥体表面上取点、取线1. Projections of a cone 圆锥体的投影圆锥体的投影三、Projections of cones and points on the surface of a cone 圆锥体投影及面上取点圆锥体投影及面上取点481. Projecti

28、ons of a right cone 圆锥体投影圆锥体投影49aaa”bb(b”)d”(d)d2. Points and lines on the surface of a right cone（一） 圆锥体面上取点、取线圆锥体面上取点、取线 （一）（一）Abd50m”MElement line method素线法素线法2. Points and lines on the surface of a right cone（二） 圆锥体面上取点、取线圆锥体面上取点、取线 （二）（二）mm51(b)bb”BWeft circle method纬圆法纬圆法Aa”aa2. Points and lin

29、es on the surface of a right cone（三） 圆锥体面上取点、取线圆锥体面上取点、取线 （三）（三）52四、Projections of spheres and points on the surface of a sphere 圆球体圆球体投影及面上取点投影及面上取点1. Projections of spheres 圆球体的投影圆球体的投影2. Points on the surface of spheres 圆球体表面上取点圆球体表面上取点531. Projections of a sphere 圆球体的投影圆球体的投影54a2. Points on the

30、surface of a sphere (一)圆球表面上取点圆球表面上取点(一一)amm”n(n)(n”)s”s(s)a”m55Horizontal circle水平圆水平圆Profile circle侧平圆侧平圆2. Points on the surface of a sphere(二二) 圆球表面上圆球表面上取点取点(二二)Finding points on the surface of a sphere is applying auxiliary line (circle) which is parallel to the projecting plane.在球面上取点可以利用球面上在

31、球面上取点可以利用球面上平行于投影面的圆作为辅助线平行于投影面的圆作为辅助线来解决。来解决。56(2”)(2)(2)()Frontal circle正平圆正平圆2. Points on the surface of a sphere(三三)圆球表面上圆球表面上取点取点(三三)Horizontal circle水平圆水平圆57b b (b)caa c c a g d g e e d deY3YY2Y3Y1Y2YY1(h )(f )c fd dhf d Y2Y1Y1Y2ee (m) m（1）（4）（2）（3）zzg(h )p3258小结小结: :平面立体投影及其面上取点平面立体投影及其面上取点 棱柱棱柱 若棱线垂直投影面若棱线垂直投影面, ,各侧面具有积聚性各侧面具有积聚性; ; 棱锥棱锥 面上取点面上取点, ,将点落在已知投影的直线上。将点落在已知投影的直线上。回转体