Descriptive Geometry and Descriptive Geometry and Mechanical Drawing (1)Mechanical Drawing (1)

王霞

AssemblyAssemblydrawingdrawing

1. Introduction of the course1. Introduction of the courseTask: How to represent a 3D object Task: How to represent a 3D object with a 2D drawing with a 2D drawing

2. Form of Projection2. Form of Projection

Projection method : Projection method : When the lines of projection pass through the object and the pre - When the lines of projection pass through the object and the pre - established plane, there will be graphics produced on the plane. established plane, there will be graphics produced on the plane. This method is called projection. This method is called projection.

Center of projectionCenter of projection

Plane of projectionPlane of projection

ObjectObject

Lines of projectionLines of projection

ProjectionProjection

Types of ProjectionTypes of Projection

Projection methodProjection method

Central projection method (( The central projection is mainly used for the pictorial The central projection is mainly used for the pictorial drawings of buildings.drawings of buildings.))

Parallel projection method

(( It is used in most engineering drawings.It is used in most engineering drawings.))

a b c

SS（（ Sight or centerSight or center of projectionof projection ））

A

B

C

Central projectionCentral projection ： ： When the lines of projection meet at a point, When the lines of projection meet at a point, it is called central projection.it is called central projection.

Central projection methodCentral projection method

Projection linesProjection lines

ObjectObject

PP Projection planeProjection plane

ProjectionProjection

Lines of projection will be parallelLines of projection will be parallel

a b c

A

B

C

Parallel projection: When the lines of projection are parallel withParallel projection: When the lines of projection are parallel with each other, it is called parallel projection.each other, it is called parallel projection.

Parallel projection methodParallel projection method

ObjectObject

PP Projection planeProjection plane

ProjectionProjection

SS

Parallel Projection methodParallel Projection method

((SSPP))

Oblique projection methodOblique projection method

Orthographic projection methodOrthographic projection method

((SSPP))

SS

PP

SS

PP

3. Similarity: When planar features or lines are inclined to the3. Similarity: When planar features or lines are inclined to the projection plane , the projection produces projection plane , the projection produces similar shapes of the original feature. The length of similar shapes of the original feature. The length of projected lines will be shorter than the real length.projected lines will be shorter than the real length.

2.2. Accumulation: When planar features or lines are orthogonal to theAccumulation: When planar features or lines are orthogonal to the projection plane, the projection accumulates to a projection plane, the projection accumulates to a line or a point.line or a point.

1. 1. Authenticity: When planar features or lines are in parallel with the Authenticity: When planar features or lines are in parallel with the projection plane, the projection shows the real shape projection plane, the projection shows the real shape or true length of the features being projected.or true length of the features being projected.

Features of Orthographic ProjectionFeatures of Orthographic Projection

These axes meet at a point These axes meet at a point which is called the origin.which is called the origin.Y-axis

0X

Y

Z V

H

W

Three-Planes Projection SystemThree-Planes Projection System

1) Set up three-planes projection system

The three projection planes are orthogonal from The three projection planes are orthogonal from each other.each other. Make up of one projection system.Make up of one projection system.

V-plane → Vertical (Frontal) plane

H-plane → Horizontal plane

W-plane→Profile (Wall) plane

The intersection lines of the The intersection lines of the three projection planes are three projection planes are called the axes of projection.called the axes of projection.

X-axis

Z-axis

To draw three-view drawings on a drawing sheetTo draw three-view drawings on a drawing sheet

The V-Plane is first fixed. The The HH-Plane turns down 90-Plane turns down 90..

The The WW-Plane turns right 90-Plane turns right 90..

X

Y

Z

V

H

W

Three-Three-PlanesPlanes Projection System Projection System

Projection of a point Relative position of two pointsRelative position of two points

Identification and labeling of coincident point Identification and labeling of coincident point

Exercises Exercises

3. Projection of Points3. Projection of Points

W

Y

V

H

x

Z

O

A

Projection of a pointProjection of a point

1. Projection of the point 1. Projection of the point AA

aa ———— The horizontal projection of the point The horizontal projection of the point AA

aa'' ———— The frontal projection of the pointThe frontal projection of the point AA

aa""—— —— The profile projection of the pointThe profile projection of the point AA

aa'' aa""

aa

Z = a''ax = aa""aYw→ The distance of A to H.

aa''aa""OZOZ The height alignment, The height alignment, Z Z equal equal. .

H

X 0 Yw

YH

Z

V W

X YY

Z

2. The 2. The principleprinciple of points of points

3. Relation of points projection & coordinate3. Relation of points projection & coordinate

Projection of a pointProjection of a point

aaaa'' OXOX The length alignment, The length alignment, XX equal equal. .

aaaa"" OYOY The width equality , The width equality , YY equal. equal.

X = a''az = aaYH → The distance of A to W. Y = aax = aa""az → The distance of A to V.

aa''

aa

aa""

ax

aZ

aYH aYW

15

10

5

aa'

aa

aa"

45 x

z

YH

Yw 0

StepsSteps（ 1 ） Drawing coordinate origin and axis. （ 2 ） According to coordinate of point A, construct projection aa'',,aa;;

（ 3 ） According to rules projections of point, draw projection aa"".

Example1. The point Example1. The point AA ( (5, 10, 155, 10, 15) . construct three projections of ) . construct three projections of AA..

AA

Y

Z

WV

H

W V

H

Z Z

Y

Y

X

X

Relative position of two pointsRelative position of two points

Relative positions of point Relative positions of point AA BB

Up and down Up and down ZZ

Front and back Front and back YY

Left and right Left and right XX

b

aa' aa"

aa

B bb"

bb'

A

X

x 0 YW

YH

z

a' a"

a

Bel ow10

Left10

Af ter

5

b

StepsSteps

（（ 22 ）） Construct projection bb""..

Example2. Point Example2. Point BB below below A10A10, after , after A5A5,left ,left A10A10.construct projections of .construct projections of BB..

AA

BB

（（ 11 ）） Construct projection bb'',b,b. .

b' b"

IdentificationIdentification When projected to the H-Plane, up covering down.

Identification and labeling of coincident point Identification and labeling of coincident point

LabelingLabeling

DefiningDefining when two points are on the same vertical line of a projection plane, the two projected points will be the same point and the two points are called the coincident point of the projection.

When projected to the V-Plane, front covering back.

When projected to the W-Plane, left covering right.

All invisible projections of points are written in brackets.

b' AA

BB

5

10 1015

105

d StepsSteps

2. Construct projections DD, dd, dd '',dd "";

1. Construct projections CC , cc,, c' c',,c"c";

CC

DD

(c)

Example3. Point Example3. Point CC from from WW 5mm, from 5mm, from V V10mm, from10mm, fromHH10mm. point10mm. point D D from from WW15mm, from 15mm, from VV 10mm, from 10mm, from HH 5mm.construct three projections of point 5mm.construct three projections of point C.DC.D and distinguish its and distinguish its visibility.visibility.

a' a"

x 0 Yw

YH

z

b"

a

b

c' c" d" ( )d'

1.Draw the third-view from its two other views shown1.Draw the third-view from its two other views shown..

ExercisesExercises

2.2.Construct the three projections of points Construct the three projections of points A, B, C, DA, B, C, D. from. from its coordinate and distance.its coordinate and distance.

3.3.Draw three projections of points Draw three projections of points A, B, C, DA, B, C, D, from its coordinate., from its coordinate.

b"(c")

a"

a b c

a"b"

c"

a'b'

c'

1. Draw the third view from its two other views shown.1. Draw the third view from its two other views shown.

(1)(1) (2)(2)

b a c

a'

b' c'

( )

2. Construct the three projections of points 2. Construct the three projections of points A,B,C,DA,B,C,D. . from its coordinate and distance.from its coordinate and distance.

PointPoint

distancedistance HH

distance distance VV

distance distance WW

X Y Z

A 15 10 20

B 10 0 10

C 15 10 0

D 0 20 20

3.3. Draw three projections of points Draw three projections of points A,B,C,DA,B,C,D, from its coordinate., from its coordinate.

AA ( (2020 、、 1515 、、 1010))；；

BB ( (2020 、、 1515 、、 2525))；；

CC ( (1010 、、 1515 、、 1010))；；

DD ( (1010 、、 2525 、、 1010))。。

d

d"d'

c'

c

c"

b"

b

b'

2. Construct the three projections of points 2. Construct the three projections of points A,B,C,D.A,B,C,D. from its from its coordinate and distance. coordinate and distance.

a'

45

0 x

z

YH

Yw

a

a"

poi nt Di stanc

e H Di stance V

Di stance W

X Y Z

A 15 10 20 B 10 0 10 C 15 15 0 D 0 20 20

1. Draw projection of point Draw projection of point AA

2. Draw projection of point Draw projection of point BB

3. Draw projection of point Draw projection of point CC

4. Draw projection of point Draw projection of point DD

StepsSteps

b( )

d'( )

a

b'

4. Draw three projections of points4. Draw three projections of points A,B,C,D A,B,C,D, from its coordinate. , from its coordinate.

AA ( (2020 、、 1515 、、 1010))；；B B ((2020 、、 1515 、、 2525))；；C C ((1010 、、 1515 、、 1010))；；D D ((1010 、、 2525 、、 1010))。。

c'

c

0 x

z

YH

Yw 1. Draw projection of point Draw projection of point AA

2. Draw projection of point Draw projection of point BB

3. Draw projection of point Draw projection of point CC

a'a"

b"

(c")

45

d"

d

4. Draw projection of point Draw projection of point DD

StepsSteps