課件英文版大連理工2nd lecture-lines

1、2nd lectureLinesSection 3TL/TA of an oblique lineSection 1Projections of linesSection 2Lines -located on special positionSection 4Points on a straight lineDescriptive geometryLab of graphics study and communication, DUTSong HXSection 1 Projection of lines1. A straight lines projection still is a str

2、aight line, but in special cases, 2. How to construct a line (如何構(gòu)造直線)3. Lines position corresponding to projection planesit shows a point view（直線的投影仍為直線，特殊情況下積聚為一點(diǎn)）(直線相對投影面的位置)1. Projection of a straight line is a line, but in special cases, it shows a point view2. How to construct a lineA point and

3、 a given directionconstruct a line Two given points3. Lines position corresponding to projection planes (直線相對投影面的位置)Lines located at special positionOblique linePerpendicular to projection planeParallel with projection planeOblique to projection planeSection 2 Lines-located at special position1. Inc

4、lined lines: parallel with one of the principal planes of projection, and inclined to the other two projection planes.2. Principal lines/normal lines: perpendicular to one of the principal plane of projectionDiagram (inclined lines)Horizontal lines(水平線)Profile lines(側(cè)平線)Frontal lines(正平線)Horizontal

5、principal line/H-normal line (鉛垂線)Profile principal line/W(P) -normal line(側(cè)垂線)Frontal principal line/V-normal line(正垂線)Diagram (normal lines)3. Lines affiliate to projection planes or projection axesExercises（從屬于投影面和投影軸的直線)Horizontal lineCharacteristics ： 1 ab=AB2 ab OX ; ab OY13Reflect the true an

6、gles , Frontal linecharacteristics：(1) a b =AB(2) ab OX ; ab OZ (3)reflect the true angles of a, Profile lineCharacteristics：（1) ab=AB（2） ab OY ; a b OZ （3）reflect the true angles of a, bHorizontal principal line/H-normal lineCharacteristics ： 1. ab appears as a point2. a bOX ; a b OY1 or a b /OZ; a

7、 b /OZ 3. a b = a b = ABFrontal principal line/V-normal lineCharacteristics ： 1. ab shows a point2. a bOX ; a b OZ 3. a b = a b = ABW/P-normal lineCharacteristics: (1) a b appears as a point view(2) a bO ; ab OZ or a b /OX; a b /OX (3) a b = ab= ABLines in planes of projectionlines in VLines affilia

8、te to planes of projectionhorizontal principal lines in VLines on projection axesline on OX Section 3 TL/TA of an oblique line-Method of right triangleFind aFind bFind g Main points of the method: 1.Take one projection of the line (for example, horizontal projection) as a square edge of the right tr

9、iangle 2. Use the coordinate difference of the two end points as another square edge of the right triangle (the difference can be measured from the other projection)； 3.The hypotenuse(斜邊) of the right triangle is the true length of the oblique line； 4. In the right triangle, the angle between the hy

10、potenuse and the projection (as one of the square edge) is the angle between the spatial line and the corresponding projection plane.Oblique lineE.g. 1Oblique lineCharacteristics： (1) All projections are foreshortened (2) All projections are inclined to projection axes (3) True angles a, b , g cant

11、be obtained directlyAnimationFind the oblique lines TL and TA (a) between line AB and H planeTrue lengthTLTLHypotenuse AB: equal to ABs TL BC=bc =ZSquare edges : AC=abZAngle a: equal to a (TA between line AB and H plane)ZZZRT triangleIn RT ABC：TLYTLYYright triangleFind the oblique lines TL and TA (b

12、) between line AB and V planehypotenuse AB: equal to ABs TL DA=ad =Ysquare edge : BD=abangle b : equal to b TA (between line AB and V plane)In RT ABD：TLXXright triangleFind the oblique lines TL and TA (g) between line AB and W planehypotenuse AB: equal to ABs TL AE=ae =Xsquare edge : BE=abangle g :

13、equal to g TA (between line AB and W plane)In RT ABE：Section 4 A point on a linePrinciples: 1. If a point is known to be on a line, the projections of the point will appear on all the views/projections of the line;E.g. 2E.g.3E.g. 42. The proportion which a point divides a line is not changed after p

14、rojectionAB BC =abbc=abbc=a”b”b”c”EndTrue angle ,PositionAxonomatric drawingParallel with plane H（horizontal line）Projection drawingCharacteristicsParallel with plane W(Profile line)Parallel with plane V(Frontal line)表3-1True angle ,True angle ,PositionPictorial drawingPerpendicular to H（N-normal li

15、ne）-a point view -a point view-a point viewProjection drawingcharacteristicsPerpendicular to W（W/P-normal line）Perpendicular to V（V-normal line）表3-2判斷畫一般位置直線E.g.1 The projections of triangle ABC is given, find the true size for it.True shapeBC (TL)YYAC (TL)AB (TL)E.g. 2 Given the projections of line AB, divide AB in