工程制圖第四章立體的投影

1Chapter4ProjectionofSolids

立體的投影§4-1PlanarSolidProjection

平面立體的投影

§4-2

ReadingPlanarSolidProjection

平面立體的讀圖§4-3

RevolvingSolidProjection

回轉(zhuǎn)體的投影

2Lookhere,theyarepracticalparts.Thisisabolt,andthisisatailstockassemblyoflathe.

Howtodescribethemonthepaper?Ifyoulookthemcarefully,youwillfindthattheyarecomplexsolids.Suchasthisbolt.Thisishexagonalprism,cylinderandscrew.Andthisisthemorecomplicatesolid.Hereisarectangularprism,aslot.Andthesearesomecylinderholesandbolts,etc.Bothofthemaremadeupofbasicsolids.Basicsolidsincludeprism,pyramid,cylinder,coneandsphere.Allmachinesandpartsareregardedthatagroupofbasicsolidsareassembledtogetherinacertainmethod.Howtodrawtheprojectionofbasicsolids?Thatiswhatwewilldiscusstoday.Chapter4----projectionofsolids.Thischapterhasthreesections.Oneisplanarsolidprojection,thesecondisreadingplanarsolidprojection,thelastisrevolvingsolidprojection3Practicalparts

實用部件

Howtodescribeitonthepaper?

如何在圖紙上描述？4Allmachinesandobjectsareregardedthatagroupofbasicsolidsareassembledtogetherinacertainmethod,suchasprisms,pyramids,cylinders,conesandspheres.

一般的機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。Conventionalbasicsolidsareclassedintwogroups：基本形體分為兩類：Planarsolidsareenclosedbyplanes,asshowninFig.5-1a,b.

平面立體是完全由平面圍成的立體，如圖5-1a,b。Revolvingsolidsareenclosedbycurvedsurfacesandplanes,asshowninFig.5-1c,d,e,f.

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5-1c,d,e,f。Fig.5-1Conventionalbasicsolids常見的基本形體(a)(b)(c)(d)(e)(f)51.Projectionsofaprismandfixingpointsonthesurfaceofaprism

棱柱的投影及其表面上取點和取線2.Projectionsofapyramidandfixingpointsonthesurfaceofapyramid

棱錐的投影及其表面上取點和取線§4-1PlanarSolidProjection

平面立體的投影

3.Deformitiesofplanarsolids

帶切口的平面立體的投影6Demoofprojectionsofahexaprism

六棱柱的投影7(1)Projectionsofahexagonalprism

六棱柱體的投影ABCD45°a’b’c’d’a(d)b(c)b”a”c”d”1Prisms

棱柱Threemeaningsintopview俯視圖的3層含義8(2)Fixingpointsofahexagonalprism

六棱柱表面取點9ABDCM45°a’b’c’d’a(d)b(c)b”a”c”d”m”n(n”)m(N)Ss’s”sm’(n’)(2)Pointsonthesurfaceofarighthexaprism

六棱柱表面上的點10Demoofprojectionsofatriangularpyramid

三棱錐的投影11(1)Projectionsofatriangularpyramid

棱錐體的投影SBAC(c”)s’b’bsc’a’a”cs”ab”2Pyramids

棱錐12ABCS(c”)s’a’asc’b’a”cs”bb”1”11’r'rⅠR(2)Pointsonthesurfaceofarighttriangularpyramid(一)

三棱錐表面上的點(一)13ABCS(c”)s’a’asc’b’a”cs”bb”2"2'2'

Ⅱ(2)Pointsonthesurfaceofarighttriangularpyramid(二)

三棱錐表面上的點(二)14ABCS(c”)s’a’asc’b’a”cs”bb”Ⅲ3(3”)(2)Pointsonthesurfaceofarighttriangularpyramid(三)

三棱錐表面上的點(三）(3’)15p25aab"a"bc(c")bcmmknnn'm'e'mne6

Correctlydrawingtheprojectionsofdeformitiesofplanarsolidsisnotonlyapplyingthedrawingmethodsofplanarsolids,butalsousingthemethodsofpointsandlinesonthesurfaceofplanarsolids.

若要完全正確地畫出帶切口平面立體的投影圖，不僅要運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、取線的原理和作圖方法來進行。3.Deformitiesofplanarsolids

帶切口的平面立體的投影171.Makesureanoriginal;

確定基形;2.Findthepiercingpointsoftheedgeswhichplanesintersectsolid;

找到截平面與平面立體上各條棱線的交點；3.Joinpointsinorderbystraightlines;

依次連接各點;4.Makesurevisibility;

判斷可見性;5.Blockinallfinallines.

整理輪廓線。Stepsindrawingthedeformitiesofplanarsolids:

帶切口的平面立體的作圖要求:181〞2〞3〞4〞5〞6〞7〞8〞6ˊ4ˊ(3ˊ)1ˊ(5ˊ2ˊ)7ˊ(8ˊ)12563478Example1:19側平面S正垂面R1.Shapeanalyticalmethod

形體分析Deformableplanarsolidisconsideredthatthesimpleplanarsolidisincisedbyplanesinspecialposition.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)過切割而形成。Example2:Constructhorizontalprojectionandprofileprojectionofdeformablepentagon.試補全帶缺口的正五棱柱的水平投影和側面投影。

20gaba〞b〞f〞)(ce)(fdb′)(g′a′c′)(f′e′)(d′c〞g〞e〞d〞yy2.Drawingprocedure作圖步驟87111"2"10"5"6"9"4"3"961（3）2（4）1057"11"8"1112910431'（2'）8'（7'）3'（4'）10'（5'）9'（6'）11'黑板畫圖講解Example222Example3:Constructhorizontalprojectionandprofileprojectionofdeformablerighttriangularpyramid

完成帶切口的正三棱錐的水平投影和側面投影。水平面正垂面23Re-edit：整理后：§4-2

ReadingPlanarSolidProjection

平面立體的讀圖一、Readingtheviewstogether

要將幾個視圖聯(lián)系起來看25Singleenclosedframe—aplane（eithersimilarorcollecting）一個封閉的線框—一個平面(對應投影非類似即積聚)

asolid

一個體Twoadjacentframes—twointersectingplanes兩個相鄰的線框—兩個相交的面

twoparallelingplanes

兩個錯開的面Twoframeswhichring

—convex、concave、through兩個套起來的線框—凸、凹、通Theprojectionoftheplanewhichcollects具有積聚性的面的投影Intersectinglineoftwoplanes兩個面的交線Line直線Lineframe線框二、Understandthemeaningsoflinesandlineframes

清楚視圖中圖線和線框的含義Qc’d’qCDCorrespondingrelationofline直線的對應關系Thelineontheviewsrepresentaplaneortheintersectinglineoftwoplanes.視圖上的直線在空間組合體上表示一個平面，表示兩個面的交線。a’ABbcCdDCorrespondingrelationoflineframe線框的對應關系Aenclosedframerepresentsaplaneorahole.一個封閉的線框表示一個平面，或一個孔。Correspondingrelationoftwoadjacentframes相鄰兩線框的對應關系a’Ab’BcdCDe”f”EFTwoadjacentframesrepresenttwointersectingplanesortwoparallelingplanes.兩個相鄰的線框表示兩個相交的面或者兩個錯開的面。Generallyaenclosedframerepresenttheprojectionofplane,andtheotherviewsareeithersimilarofcollecting.視圖中一個封閉線框一般情況下表示一個面的投影，非類似即積聚。Twoframeswhichring—convex、concave、through套起來的線框—凸、凹、通Twoadjacentframesrepresenttwointersectingorparallelingplane.兩個相鄰的線框代表兩個相交的面或兩個錯開的面。Oneofaplaneviewisanenclosedframeatleast.一表面的三個投影中至少有一個是封閉線框；Theotherviewsaccordingprojectingrelationareeithersimilarorcollecting.該線框按投影關系對照其它投影，不類似，便積聚。Notice:Distinguishdifferentfigureaccordingthechangeofhiddenlineandsolidline.注意圖中虛實線變化，區(qū)分不同形體。

三、Correspondingrelationofviewsandsolids

視圖與空間形體的對應關系上上下下左左右右后后前前34PPQPQQRRRTTTExample:completethethirdviewaccordingtwogivenviews.由兩視圖補畫第三視圖351'12'21"2"36Example:completethethirdviewaccordingtwogivenviews.由兩視圖補畫第三視圖Example:completethethirdviewaccordingtwogivenviews.由兩視圖補畫第三視圖

立體構成模型3940§4-3

RevolvingSolidProjection

回轉(zhuǎn)體的投影

一、Therevolvingsurfaceanditscharacters

回轉(zhuǎn)面及其性質(zhì)

二、Projectionsofcylindersandpointsonthesurfaceofacylinder

圓柱體投影及面上取點

三、Projectionsofconesandpointsonthesurfaceofacone

圓錐體投影及面上取點

四、Projectionsofspheresandpointsonthesurfaceofasphere

圓球體投影及面上取點41ThetracedevelopedbywhichgenertrixABisevolvingaroundaxisOOiscalledrevolvingsurface.ThetraceofanypointonthegenertrixABisthecirclewhichisperpendiculartotheaxis.Anypositionofgenertrixiscalledelementline.

母線AB繞回轉(zhuǎn)軸線OO旋轉(zhuǎn)的運動軌跡形成回轉(zhuǎn)面,母線AB上任一點的運動軌跡為一垂直于軸線OO的圓。母線的任一位置稱為素線。一、Therevolvingsurfaceanditscharacters

回轉(zhuǎn)面及其性質(zhì)

42Genertrix母線Axis軸線Generatrix母線Axis軸線Elementline素線ACBGeneratrix43二、Projectionsofcylindersandpointsonthesurfaceofacylinder

圓柱體投影及面上取點

2.Pointandlineonthesurfaceofcylinders

圓柱體表面上取點、取線1.Projectionsofcylinders

圓柱體的投影44Profilelinesofacylinder圓柱輪廓線Profilelinesofacylinder圓柱輪廓線a’b’abcdc”d”d’c’a”b”1.Projectionsofcylinders

圓柱體的投影Threemeaningsintopview俯視圖的3層含義4546A(D)CB2.Pointsandlinesonthesurfaceofarightcylinder

圓柱面上取點、取線(d’)(d”)472.Pointandlineonthesurfaceofacone

圓錐體表面上取點、取線1.Projectionsofacone

圓錐體的投影三、Projectionsofconesandpointsonthesurfaceofacone

圓錐體投影及面上取點

481.Projectionsofarightcone

圓錐體投影49a’aa”bb’(b”)d”(d’)d2.Pointsandlinesonthesurfaceofarightcone（一）

圓錐體面上取點、取線（一）Ab’d50m”MElementlinemethod素線法2.Pointsandlinesonthesurfaceofarightcone（二）

圓錐體面上取點、取線（二）m’m51(b’)bb”BWeftcirclemethod緯圓法Aa”aa’2.Pointsandlinesonthesurfaceofarightcone（三）

圓錐體面上取點、取線（三）52四、Projectionsofspheresandpointsonthesurfaceofasphere

圓球體投影及面上取點1.Projectionsofspheres

圓球體的投影2.Pointsonthesurfaceofspheres

圓球體表面上取點531.Projectionsofasphere

圓球體的投影54a’2.Pointsonthesurfaceofasphere(一)

圓球表面上取點(一)am’m”n(n’)(n”)s”s’(s)a”m55Horizontalcircle水平圓Profilecircle側平圓2.Pointsonthesurfaceofasphere(二)

圓球表面上取點(二)Findingpointsonthesurfaceofasphereisapplyingauxiliaryline(circle)whichisparalleltotheprojectingplane.在球面上取點可以利用球面上平行于投影面的圓作為輔助線來解決。56(2”)(2)(2’)(Ⅱ)Frontalcircle正平圓2.Pointsonthesurfaceofasphere

(三)

圓球表面上取點(三)Horizontalcircle水平圓57bb(b)caaccagdgeeddeY3YY2Y3Y1Y2YY1(h)(f)cfddhfdY2Y1Y1Y2ee(m)m（1）（4）（2）（3）zzg(h