工程制图第四章立体的投影

1Chapter4ProjectionofSolids

立体的投影§4-1PlanarSolidProjection

平面立体的投影

§4-2

ReadingPlanarSolidProjection

平面立体的读图§4-3

RevolvingSolidProjection

回转体的投影

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

实用部件

Howtodescribeitonthepaper?

如何在图纸上描述？4Allmachinesandobjectsareregardedthatagroupofbasicsolidsareassembledtogetherinacertainmethod,suchasprisms,pyramids,cylinders,conesandspheres.

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。Conventionalbasicsolidsareclassedintwogroups：基本形体分为两类：Planarsolidsareenclosedbyplanes,asshowninFig.5-1a,b.

平面立体是完全由平面围成的立体，如图5-1a,b。Revolvingsolidsareenclosedbycurvedsurfacesandplanes,asshowninFig.5-1c,d,e,f.

回转体是由回转面或回转面和平面围成的立体，如图5-1c,d,e,f。Fig.5-1Conventionalbasicsolids常见的基本形体(a)(b)(c)(d)(e)(f)51.Projectionsofaprismandfixingpointsonthesurfaceofaprism

棱柱的投影及其表面上取点和取线2.Projectionsofapyramidandfixingpointsonthesurfaceofapyramid

棱锥的投影及其表面上取点和取线§4-1PlanarSolidProjection

平面立体的投影

3.Deformitiesofplanarsolids

带切口的平面立体的投影6Demoofprojectionsofahexaprism

六棱柱的投影7(1)Projectionsofahexagonalprism

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

棱柱Threemeaningsintopview俯视图的3层含义8(2)Fixingpointsofahexagonalprism

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

六棱柱表面上的点10Demoofprojectionsofatriangularpyramid

三棱锥的投影11(1)Projectionsofatriangularpyramid

棱锥体的投影SBAC(c”)s’b’bsc’a’a”cs”ab”2Pyramids

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

三棱锥表面上的点(一)13ABCS(c”)s’a’asc’b’a”cs”bb”2"2'2'

Ⅱ(2)Pointsonthesurfaceofarighttriangularpyramid(二)

三棱锥表面上的点(二)14ABCS(c”)s’a’asc’b’a”cs”bb”Ⅲ3(3”)(2)Pointsonthesurfaceofarighttriangularpyramid(三)

三棱锥表面上的点(三）(3’)15p25aab"a"bc(c")bcmmknnn'm'e'mne6

Correctlydrawingtheprojectionsofdeformitiesofplanarsolidsisnotonlyapplyingthedrawingmethodsofplanarsolids,butalsousingthemethodsofpointsandlinesonthesurfaceofplanarsolids.

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面取点、取线的原理和作图方法来进行。3.Deformitiesofplanarsolids

带切口的平面立体的投影171.Makesureanoriginal;

确定基形;2.Findthepiercingpointsoftheedgeswhichplanesintersectsolid;

找到截平面与平面立体上各条棱线的交点；3.Joinpointsinorderbystraightlines;

依次连接各点;4.Makesurevisibility;

判断可见性;5.Blockinallfinallines.

整理轮廓线。Stepsindrawingthedeformitiesofplanarsolids:

带切口的平面立体的作图要求:181〞2〞3〞4〞5〞6〞7〞8〞6ˊ4ˊ(3ˊ)1ˊ(5ˊ2ˊ)7ˊ(8ˊ)12563478Example1:19侧平面S正垂面R1.Shapeanalyticalmethod

形体分析Deformableplanarsolidisconsideredthatthesimpleplanarsolidisincisedbyplanesinspecialposition.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。Example2:Constructhorizontalprojectionandprofileprojectionofdeformablepentagon.试补全带缺口的正五棱柱的水平投影和侧面投影。

20gaba〞b〞f〞)(ce)(fdb′)(g′a′c′)(f′e′)(d′c〞g〞e〞d〞yy2.Drawingprocedure作图步骤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'黑板画图讲解Example222Example3:Constructhorizontalprojectionandprofileprojectionofdeformablerighttriangularpyramid

完成带切口的正三棱锥的水平投影和侧面投影。水平面正垂面23Re-edit：整理后：§4-2

ReadingPlanarSolidProjection

平面立体的读图一、Readingtheviewstogether

要将几个视图联系起来看25Singleenclosedframe—aplane（eithersimilarorcollecting）一个封闭的线框—一个平面(对应投影非类似即积聚)

asolid

一个体Twoadjacentframes—twointersectingplanes两个相邻的线框—两个相交的面

twoparallelingplanes

两个错开的面Twoframeswhichring

—convex、concave、through两个套起来的线框—凸、凹、通Theprojectionoftheplanewhichcollects具有积聚性的面的投影Intersectinglineoftwoplanes两个面的交线Line直线Lineframe线框二、Understandthemeaningsoflinesandlineframes

清楚视图中图线和线框的含义Qc’d’qCDCorrespondingrelationofline直线的对应关系Thelineontheviewsrepresentaplaneortheintersectinglineoftwoplanes.视图上的直线在空间组合体上表示一个平面，表示两个面的交线。a’ABbcCdDCorrespondingrelationoflineframe线框的对应关系Aenclosedframerepresentsaplaneorahole.一个封闭的线框表示一个平面，或一个孔。Correspondingrelationoftwoadjacentframes相邻两线框的对应关系a’Ab’BcdCDe”f”EFTwoadjacentframesrepresenttwointersectingplanesortwoparallelingplanes.两个相邻的线框表示两个相交的面或者两个错开的面。Generallyaenclosedframerepresenttheprojectionofplane,andtheotherviewsareeithersimilarofcollecting.视图中一个封闭线框一般情况下表示一个面的投影，非类似即积聚。Twoframeswhichring—convex、concave、through套起来的线框—凸、凹、通Twoadjacentframesrepresenttwointersectingorparallelingplane.两个相邻的线框代表两个相交的面或两个错开的面。Oneofaplaneviewisanenclosedframeatleast.一表面的三个投影中至少有一个是封闭线框；Theotherviewsaccordingprojectingrelationareeithersimilarorcollecting.该线框按投影关系对照其它投影，不类似，便积聚。Notice:Distinguishdifferentfigureaccordingthechangeofhiddenlineandsolidline.注意图中虚实线变化，区分不同形体。

三、Correspondingrelationofviewsandsolids

视图与空间形体的对应关系上上下下左左右右后后前前34PPQPQQRRRTTTExample:completethethirdviewaccordingtwogivenviews.由两视图补画第三视图351'12'21"2"36Example:completethethirdviewaccordingtwogivenviews.由两视图补画第三视图Example:completethethirdviewaccordingtwogivenviews.由两视图补画第三视图

立体构成模型3940§4-3

RevolvingSolidProjection

回转体的投影

一、Therevolvingsurfaceanditscharacters

回转面及其性质

二、Projectionsofcylindersandpointsonthesurfaceofacylinder

圆柱体投影及面上取点

三、Projectionsofconesandpointsonthesurfaceofacone

圆锥体投影及面上取点

四、Projectionsofspheresandpointsonthesurfaceofasphere

圆球体投影及面上取点41ThetracedevelopedbywhichgenertrixABisevolvingaroundaxisOOiscalledrevolvingsurface.ThetraceofanypointonthegenertrixABisthecirclewhichisperpendiculartotheaxis.Anypositionofgenertrixiscalledelementline.

母线AB绕回转轴线OO旋转的运动轨迹形成回转面,母线AB上任一点的运动轨迹为一垂直于轴线OO的圆。母线的任一位置称为素线。一、Therevolvingsurfaceanditscharacters

回转面及其性质

42Genertrix母线Axis轴线Generatrix母线Axis轴线Elementline素线ACBGeneratrix43二、Projectionsofcylindersandpointsonthesurfaceofacylinder

圆柱体投影及面上取点

2.Pointandlineonthesurfaceofcylinders

圆柱体表面上取点、取线1.Projectionsofcylinders

圆柱体的投影44Profilelinesofacylinder圆柱轮廓线Profilelinesofacylinder圆柱轮廓线a’b’abcdc”d”d’c’a”b”1.Projectionsofcylinders

圆柱体的投影Threemeaningsintopview俯视图的3层含义4546A(D)CB2.Pointsandlinesonthesurfaceofarightcylinder

圆柱面上取点、取线(d’)(d”)472.Pointandlineonthesurfaceofacone

圆锥体表面上取点、取线1.Projectionsofacone

圆锥体的投影三、Projectionsofconesandpointsonthesurfaceofacone

圆锥体投影及面上取点

481.Projectionsofarightcone

圆锥体投影49a’aa”bb’(b”)d”(d’)d2.Pointsandlinesonthesurfaceofarightcone（一）

圆锥体面上取点、取线（一）Ab’d50m”MElementlinemethod素线法2.Pointsandlinesonthesurfaceofarightcone（二）

圆锥体面上取点、取线（二）m’m51(b’)bb”BWeftcirclemethod纬圆法Aa”aa’2.Pointsandlinesonthesurfaceofarightcone（三）

圆锥体面上取点、取线（三）52四、Projectionsofspheresandpointsonthesurfaceofasphere

圆球体投影及面上取点1.Projectionsofspheres

圆球体的投影2.Pointsonthesurfaceofspheres

圆球体表面上取点531.Projectionsofasphere

圆球体的投影54a’2.Pointsonthesurfaceofasphere(一)

圆球表面上取点(一)am’m”n(n’)(n”)s”s’(s)a”m55Horizontalcircle水平圆Profilecircle侧平圆2.Pointsonthesurfaceofasphere(二)

圆球表面上取点(二)Findingpointsonthesurfaceofasphereisapplyingauxiliaryline(circle)whichisparalleltotheprojectingplane.在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来解决。56(2”)(2)(2’)(Ⅱ)Frontalcircle正平圆2.Pointsonthesurfaceofasphere

(三)

圆球表面上取点(三)Horizontalcircle水平圆57bb(b)caaccagdgeeddeY3YY2Y3Y1Y2YY1(h)(f)cfddhfdY2Y1Y1Y2ee(m)m（1）（4）（2）（3）zzg(h