工程制圖第四章立體的投影

1、1Chapter 4 Projection of Solids 立體的投影立體的投影4-1 Planar Solid Projection 平面立體的投影平面立體的投影 4-2 Reading Planar Solid Projection 平面立體的讀圖平面立體的讀圖4-3 Revolving Solid Projection 回轉(zhuǎn)體的投影回轉(zhuǎn)體的投影 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實(shí)用部件實(shí)用部件 How to describe it on the paper?如何在圖紙上描述？如何在圖紙上描述？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. 一般的機(jī)器零件或物體都可以看作是由若干基本形體，如棱柱、棱錐、一般的機(jī)器零件或物體都可以看作是由若干基本形體，如棱柱、棱錐、圓柱、圓錐和球等按某種方式組合而成。圓柱、圓錐和球等按某種方式組合而成。Conventional basic solids are classed in two groups：基本形體分為兩類：基本形體分為兩類：Planar solids are enclosed by planes, as sho

6、wn in Fig.5-1 a, b. 平面立體平面立體 是完全由平面圍成的立體，如圖是完全由平面圍成的立體，如圖5-1 a, b。Revolving solids are enclosed by curved surfaces and planes, as shown in Fig.5-1 c, d, e, f. 回轉(zhuǎn)體回轉(zhuǎn)體 是由回轉(zhuǎn)面或回轉(zhuǎn)面和平面圍成的立體，如圖是由回轉(zhuǎn)面或回轉(zhuǎn)面和平面圍成的立體，如圖5-1 c, d, e, f。Fig.5-1 Conventional basic solids常見(jiàn)的基本形體常見(jiàn)的基本形體(a)(b)(c)(d)(e)(f)51. Projection

7、s of a prism and fixing points on the surface of a prism 棱柱的投影及其表面上取點(diǎn)和取線棱柱的投影及其表面上取點(diǎn)和取線2. Projections of a pyramid and fixing points on the surface of a pyramid 棱錐的投影及其表面上取點(diǎn)和取線棱錐的投影及其表面上取點(diǎn)和取線4-1 Planar Solid Projection 平面立體的投影平面立體的投影 3. Deformities of planar solids 帶切口的平面立體的投影帶切口的平面立體的投影6Demo of pro

8、jections of a hexaprism 六棱柱的投影六棱柱的投影7(1) Projections of a hexagonal prism 六六棱柱體的投影棱柱體的投影ABCD45abcda(d)b(c)b”a”c”d”1 Prisms 棱柱棱柱Three meanings in top view 俯視圖的俯視圖的3層含義層含義8(2)Fixing points of a hexagonal prism 六棱柱表面取點(diǎn)六棱柱表面取點(diǎn)9ABDCM45abcda(d)b(c)b”a”c”d”m”n(n”)m(N)Sss”sm(n)(2) Points on the surface of a

9、 right hexaprism 六棱柱表面上的點(diǎn)六棱柱表面上的點(diǎn)10Demo of projections of a triangular pyramid 三棱錐的投影三棱錐的投影11(1) Projections of a triangular pyramid 棱錐體的投影棱錐體的投影SBAC(c”)sbbscaa”cs”ab”2 Pyramids 棱錐棱錐12ABCS(c”)saascba”cs”bb”1”11rrR(2) Points on the surface of a right triangular pyramid (一) 三棱錐表面上的點(diǎn)三棱錐表面上的點(diǎn)(一一)13ABCS(

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

11、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. 若要完全正確地畫(huà)出帶切口平面立體的投影圖，不僅要若要完全正確地畫(huà)出帶切口平面立體的投影圖，不僅要運(yùn)用繪制平面立體投影圖的方法，還必須利用在平面立體表運(yùn)用繪制平面立體投影圖的方法，還必須利用在平面立體表面取點(diǎn)、取線的原理和作圖方法來(lái)進(jìn)行。面取點(diǎn)、取線的原理和作

12、圖方法來(lái)進(jìn)行。3. Deformities of planar solids 帶切口的平面立體的投影帶切口的平面立體的投影17 1. Make sure an original; 確定基形確定基形; 2. Find the piercing points of the edges which planes intersect solid; 找到找到截平面截平面與平面立體上各條棱線的交點(diǎn)；與平面立體上各條棱線的交點(diǎn)； 3. Join points in order by straight lines; 依次連接各點(diǎn)依次連接各點(diǎn); 4. Make sure visibility; 判斷可見(jiàn)性判斷可

13、見(jiàn)性; 5. Block in all final lines. 整理輪廓線。整理輪廓線。Steps in drawing the deformities of planar solids:帶帶切口切口的平面立體的作圖要求的平面立體的作圖要求: :181234567864(3 )1(52)7 (8)12563478Example 1:19側(cè)平面S正垂面R1. Shape analytical method 形體分析形體分析Deformable planar solid is considered that the simple planar solid is incised by planes

14、 in special position. 帶切口的平面立體可以看作是由一些基本的平面立體經(jīng)過(guò)切割而形成。Example 2: Construct horizontal projection and profile projection of deformable pentagon. 試補(bǔ)全帶缺口的正五棱柱的水平投影和側(cè)面投影。試補(bǔ)全帶缺口的正五棱柱的水平投影和側(cè)面投影。 20gababf)(ce)(fdb) (gac)(fe)(dcgedyy2.Drawing procedure 作圖步驟作圖步驟8711121056943961（3）2（4）10571181112910431（2）8（7）3

15、（4）10（5）9（6）11黑板畫(huà)圖講解Example222Example 3: Construct horizontal projection and profile projection of deformable right triangular pyramid 完成帶切口的正三棱錐的水平投影和側(cè)面投影。完成帶切口的正三棱錐的水平投影和側(cè)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 平面立體的讀圖平面立體的讀圖25Single enclosed frame a plane （either sim

16、ilar or collecting ）一個(gè)封閉的線框一個(gè)封閉的線框 一個(gè)平面一個(gè)平面 (對(duì)應(yīng)投影非類似即積聚對(duì)應(yīng)投影非類似即積聚) a solid 一個(gè)體一個(gè)體Two adjacent frames two intersecting planes 兩個(gè)相鄰的線框兩個(gè)相鄰的線框兩個(gè)相交的面兩個(gè)相交的面 two paralleling planes 兩個(gè)錯(cuò)開(kāi)的面兩個(gè)錯(cuò)開(kāi)的面Two frames which ring convex 、concave 、through兩個(gè)套起來(lái)的線框兩個(gè)套起來(lái)的線框凸、凹、通凸、凹、通The projection of the plane which collect

17、s 具有積聚性的面的投影具有積聚性的面的投影Intersecting line of two planes兩個(gè)面的交線兩個(gè)面的交線Line直線直線Line frame線框線框二、Understand the meanings of lines and line frames 清楚視圖中圖線和線框的含義清楚視圖中圖線和線框的含義QcdqCDCorresponding relation of line直線的對(duì)應(yīng)關(guān)系直線的對(duì)應(yīng)關(guān)系The line on the views represent a plane or the intersecting line of two planes. 視圖上的直線

18、在空間組合體上視圖上的直線在空間組合體上表示表示一個(gè)平面一個(gè)平面，表示，表示兩個(gè)面的兩個(gè)面的交線交線。aABbcCdDCorresponding relation of line frame線框的對(duì)應(yīng)關(guān)系線框的對(duì)應(yīng)關(guān)系A(chǔ) enclosed frame represents a plane or a hole.一個(gè)封閉的線框表示一個(gè)封閉的線框表示一個(gè)一個(gè)平面平面，或，或一個(gè)孔一個(gè)孔 。Corresponding relation of two adjacent frames相鄰兩線框的對(duì)應(yīng)關(guān)系相鄰兩線框的對(duì)應(yīng)關(guān)系aAbBcdCDe”f”EFTwo adjacent frames represen

19、t two intersecting planes or two paralleling planes.兩個(gè)相鄰的線框表示兩個(gè)相鄰的線框表示兩個(gè)相兩個(gè)相交的面交的面或者或者兩個(gè)錯(cuò)開(kāi)的面兩個(gè)錯(cuò)開(kāi)的面 。 Generally a enclosed frame represent the projection of plane, and the other views are either similar of collecting. 視圖中一個(gè)視圖中一個(gè)封閉線框封閉線框一般情況下表示一個(gè)面的投影，一般情況下表示一個(gè)面的投影，非類似即積聚。非類似即積聚。Two frames which ring c

20、onvex 、concave 、through套起來(lái)的線框套起來(lái)的線框凸、凹、通凸、凹、通Two adjacent frames represent two intersecting or paralleling plane.兩個(gè)相鄰的線框代表兩個(gè)兩個(gè)相鄰的線框代表兩個(gè)相交相交的面或兩個(gè)的面或兩個(gè)錯(cuò)開(kāi)錯(cuò)開(kāi)的面。的面。One of a plane view is an enclosed frame at least.一表面的三個(gè)投影中至少有一個(gè)是封閉線框；一表面的三個(gè)投影中至少有一個(gè)是封閉線框；The other views according projecting relation are e

21、ither similar or collecting. 該線框按投影關(guān)系對(duì)照其它投影，不類似，便積聚。該線框按投影關(guān)系對(duì)照其它投影，不類似，便積聚。Notice: Distinguish different figure according the change of hidden line and solid line. 注意圖中虛實(shí)線變化，區(qū)分不同形體。注意圖中虛實(shí)線變化，區(qū)分不同形體。 三、三、Corresponding relation of views and solids 視圖與空間形體的對(duì)應(yīng)關(guān)系視圖與空間形體的對(duì)應(yīng)關(guān)系34PPQPQQRRRTTTExample: complet

22、e the third view according two given views. 由兩視圖補(bǔ)畫(huà)第三視圖由兩視圖補(bǔ)畫(huà)第三視圖3511221236Example: complete the third view according two given views. 由兩視圖補(bǔ)畫(huà)第三視圖由兩視圖補(bǔ)畫(huà)第三視圖Example: complete the third view according two given views. 由兩視圖補(bǔ)畫(huà)第三視圖由兩視圖補(bǔ)畫(huà)第三視圖立體構(gòu)成模型39404-3 Revolving Solid Projection 回轉(zhuǎn)體的投影回轉(zhuǎn)體的投影 一、The revolv

23、ing surface and its characters 回轉(zhuǎn)面及其性質(zhì)回轉(zhuǎn)面及其性質(zhì)二、Projections of cylinders and points on the surface of a cylinder 圓柱體投影及面上取點(diǎn)圓柱體投影及面上取點(diǎn)三、Projections of cones and points on the surface of a cone 圓錐體投影及面上取點(diǎn)圓錐體投影及面上取點(diǎn)四、Projections of spheres and points on the surface of a sphere 圓球體圓球體投影及面上取點(diǎn)投影及面上取點(diǎn)41 The

24、 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. 母線母線AB繞回轉(zhuǎn)軸線繞回轉(zhuǎn)軸線OO旋轉(zhuǎn)的運(yùn)動(dòng)軌跡形成回轉(zhuǎn)面旋轉(zhuǎn)的運(yùn)動(dòng)軌跡形成回轉(zhuǎn)面,母母線線AB上任一點(diǎn)的運(yùn)動(dòng)軌跡為一垂直

25、于軸線上任一點(diǎn)的運(yùn)動(dòng)軌跡為一垂直于軸線OO的圓。母線的圓。母線的任一位置稱為素線。的任一位置稱為素線。一、一、The revolving surface and its characters 回轉(zhuǎn)面及其性質(zhì)回轉(zhuǎn)面及其性質(zhì)42Genertrix母線母線Axis軸線軸線Generatrix母線母線Axis軸線軸線Element line素線素線ACBGeneratrix43二、Projections of cylinders and points on the surface of a cylinder 圓柱體投影及面上取點(diǎn)圓柱體投影及面上取點(diǎn)44Profile lines of a cylind

26、er圓柱輪廓線圓柱輪廓線Profile lines of a cylinder圓柱輪廓線圓柱輪廓線aba bc dc”d”dca”b”1. Projections of cylinders 圓柱體的投影圓柱體的投影Three meanings in top view 俯視圖的俯視圖的3層含義層含義4546A(D)CB2. Points and lines on the surface of a right cylinder 圓柱面上取點(diǎn)、取線圓柱面上取點(diǎn)、取線(d)(d”)47三、Projections of cones and points on the surface of a cone

27、圓錐體投影及面上取點(diǎn)圓錐體投影及面上取點(diǎn)481. Projections of a right cone 圓錐體投影圓錐體投影49aaa”bb(b”)d”(d)d2. Points and lines on the surface of a right cone（一） 圓錐體面上取點(diǎn)、取線圓錐體面上取點(diǎn)、取線 （一）（一）Abd50m”MElement line method素線法素線法2. Points and lines on the surface of a right cone（二） 圓錐體面上取點(diǎn)、取線圓錐體面上取點(diǎn)、取線 （二）（二）mm51(b)bb”BWeft circle m

28、ethod緯圓法緯圓法Aa”aa2. Points and lines on the surface of a right cone（三） 圓錐體面上取點(diǎn)、取線圓錐體面上取點(diǎn)、取線 （三）（三）52四、Projections of spheres and points on the surface of a sphere 圓球體圓球體投影及面上取點(diǎn)投影及面上取點(diǎn)531. Projections of a sphere 圓球體的投影圓球體的投影54a2. Points on the surface of a sphere (一)圓球表面上取點(diǎn)圓球表面上取點(diǎn)(一一)amm”n(n)(n”)s”s(

29、s)a”m55Horizontal circle水平圓水平圓Profile circle側(cè)平圓側(cè)平圓2. Points on the surface of a sphere(二二) 圓球表面上圓球表面上取點(diǎn)取點(diǎn)(二二)Finding points on the surface of a sphere is applying auxiliary line (circle) which is parallel to the projecting plane.在球面上取點(diǎn)可以利用球面上在球面上取點(diǎn)可以利用球面上平行于投影面的圓作為輔助線平行于投影面的圓作為輔助線來(lái)解決。來(lái)解決。56(2”)(2)(2

30、)()Frontal circle正平圓正平圓2. Points on the surface of a sphere(三三)圓球表面上圓球表面上取點(diǎn)取點(diǎn)(三三)Horizontal circle水平圓水平圓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小結(jié)小結(jié): :平面立體投影及其面上取點(diǎn)平面立體投影及其面上取點(diǎn) 棱柱棱柱 若棱線垂直投影面若棱線垂直投影面, ,各側(cè)面具有積聚性各側(cè)面具有積聚性; ; 棱錐棱錐 面上取點(diǎn)面上取點(diǎn), ,將點(diǎn)落在已知投影的直線上。將點(diǎn)落在已知投影的直線上。回轉(zhuǎn)體回轉(zhuǎn)體( (曲面體曲面體) )投影及其面上取點(diǎn)投影及其面上取點(diǎn) 圓柱圓柱