Engineering Drawing 26

Axonometric ProjectionAxonometric Projection

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Basic Knowledge of Axonometric Projection Isometric Projection Cabinet Axonometry Projection Exercises

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Basic Knowledge of Axonometric ProjectionBasic Knowledge of Axonometric Projection

Definiens :Definiens : An axonometric An axonometric projectionprojection is one in which the object is viewed in is one in which the object is viewed in such a position that such a position that several faces appear in a single view.. Trait :Trait : Axonometric drawings are Axonometric drawings are excellent for showing the third dimensionthe third dimension of objects, but it is difficult to drawing and of objects, but it is difficult to drawing and being transmutedbeing transmuted.. Purpose Purpose :: Axonometric drawings are often used to Axonometric drawings are often used to supplement drawings..

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(1)(1) FormForm of axonometric projection of axonometric projection1. 1. Form and characteristics of axonometric projectionForm and characteristics of axonometric projection

Place a P-plane (a new single Place a P-plane (a new single view) in the three-view system view) in the three-view system and select a proper direction of and select a proper direction of projection. Project both the projection. Project both the object and the coordinate object and the coordinate system of the three-view system system of the three-view system to the P-plane with parallel to the P-plane with parallel projection such that the new projection such that the new projected drawing projected drawing simultaneously reflects three simultaneously reflects three coordinate planes. Such a coordinate planes. Such a projection is called axonometric projection is called axonometric projection.projection.


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(2)(2) The Characteristics of Axonometric ProjectionThe Characteristics of Axonometric Projection

1) 1) Parallel line segments on the object are still parallel Parallel line segments on the object are still parallel with axonometric projection.with axonometric projection.

22)) If line segments on the object are parallel to coordinate, If line segments on the object are parallel to coordinate, they are parallel to coordinate on the axonometric they are parallel to coordinate on the axonometric projectionprojection..



Characteristics of parallelity

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The coefficient of axial deformation of the X-axis is p = O1A1 / OA.

The coefficient of axial deformation of the Y-axis is q = O1B1 / OB

The coefficient of axial deformation of the Z-axis is r = O1C1 / OC.

2. A2. Axes anglexes angle and and coefficient of axial deformationcoefficient of axial deformation


(1)(1)AAxes anglexes angle

(2)(2)CCoefficient of axial deformationoefficient of axial deformation

Angles between axonometric projection axis Angles between axonometric projection axis are called are called axes angleaxes angle..

The length ratio between line segments on axonometric axes andThe length ratio between line segments on axonometric axes andthat on the corresponding space coordinate axes is called that on the corresponding space coordinate axes is called ccoefficient of axial deformationoefficient of axial deformation . .


ZZ11

XX11 YY11

OO

∠∠XX11OO11YY11

∠∠XX11OO11ZZ11∠∠YY11OO11ZZ11

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Drawing Drawing method method 1)) Coordinate method

3.3. Drawing for Drawing for axonometric projectionaxonometric projection


2) Union method

3) Subtraction method

4) Synthetic method


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1. 1. Construction of isometric projectionConstruction of isometric projection


Isometric Projection Isometric Projection

2. A2. Axes anglexes angle and c and coefficient of axial deformationoefficient of axial deformation

To produce an To produce an isometric projection, it is necessary to view an , it is necessary to view an object such that its principal edges are equally inclined to the object such that its principal edges are equally inclined to the viewer and hence are foreshortened equally.viewer and hence are foreshortened equally.

120120 120 120

3030 0 0 3030

XX 120120 YY

ZZ (1)(1)AAxes anglexes angle

(2)(2)CCoefficient of axial deformationoefficient of axial deformation p = q = r p = q = r = 0.82 = 0.82 ≈≈ 1 1

∠∠XXOOY: Y: 120120 ∠∠XOZXOZ: : 120120 ∠∠YYOOZ: Z: 120120

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Isometric ProjectionIsometric Projection3. 3. Isometric drawing for polyhedral solidsIsometric drawing for polyhedral solidsCommon Common drawing stepsdrawing steps

(1)(1) Draw the isometric axes and position origins.Draw the isometric axes and position origins. (2)(2) Measure the size of lineMeasure the size of line segmentssegments on on XX , ,YY axesaxes andand draw draw parallel line to the parallel line to the XX,,YY ，， draw the lower base ofdraw the lower base of the solidthe solid.. (3)(3) From all end points draw lines parallel to the From all end points draw lines parallel to the Z Z axes, measure the axes, measure the

size of linesize of line segmentssegments equal to high equal to high, , construct top shape construct top shape of the solidof the solid. . ((4)4) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines. .


Example 1

Example 2

Example 3

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4. 4. Isometric drawing for Isometric drawing for curved solidscurved solids

Common Common drawing stepsdrawing steps(1)(1) Draw the isometric axes and position origins.Draw the isometric axes and position origins. (2)(2) Measure the size of Measure the size of DD ,construct diamond shape of the circle. ,construct diamond shape of the circle. (3)(3) Construct Construct approximate approximate ellipse ellipse with a compass from four centerswith a compass from four centers..

(4)(4) Draw Draw the tangent and profile lines.the tangent and profile lines. (5)(5) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines. .


Example4 Example5

Isometric ProjectionIsometric Projection

The long and short axis of the corresponding iso-circle

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1. Construction of 1. Construction of cabinet axonometry projection cabinet axonometry projection


Cabinet axonometry projectionCabinet axonometry projection

2. A2. Axes anglexes angle and c and coefficient of axial deformationoefficient of axial deformation

When the When the axonometry projection axonometry projection plane is parallel to a coordinate axis, plane is parallel to a coordinate axis, and the coefficientand the coefficient of axial deformationof axial deformation of two axes that parallel to the of two axes that parallel to the coordinate plane are equal, the coordinate plane are equal, the cabinet axonometry is produced.is produced.

(1)(1)AAxes anglexes angle

(2)(2)CCoefficient of axial deformationoefficient of axial deformation p = r = p = r = 11 q q = 0.5= 0.5

∠∠XXOZOZ: : 9090 ∠∠XOXOY: Y: 135135 ∠∠YYOOZ: Z: 135135

ZZ

9090XX OO

4545 135135

YY135135

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3.3.Cabinet axonometry projection Cabinet axonometry projection for polyhedral solids for polyhedral solids

Common Common drawing stepsdrawing steps

((1)1) Draw oblique axes and position origins Draw oblique axes and position origins OO.. (2) (2) Measure the size of lineMeasure the size of line segmentssegments onon XX axes and measure the axes and measure the size of linesize of line segmentssegments on on YY axesaxes withwith ½ ½ sizesize, and, and draw parallel draw parallel line to theline to the X X ,,YY ,, draw the lower base ofdraw the lower base of the solidthe solid.. (3)(3)From all end points draw lines parallel to the From all end points draw lines parallel to the Z Z axes, measure the axes, measure the size of linesize of line segmentssegments equal to high equal to high, , construct top shape construct top shape of the solidof the solid. .

。。(4)(4) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines. .

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4.4.Cabinet axonometry projectionCabinet axonometry projection for for curved solidscurved solids

(1) (1) Define the oblique coordinate frame and position origins Define the oblique coordinate frame and position origins OO.. (2)(2) Draw oblique axes and position origins Draw oblique axes and position origins OO, lay out the centerlines of the circles., lay out the centerlines of the circles. (3)(3) Draw all circles on the each plane Draw all circles on the each plane.. (4)(4) Complete the tangent and profile lines.Complete the tangent and profile lines. (5)(5) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines..

circles or arcs parallel to the projection plane


Common Common drawing stepsdrawing steps

Example 2 Example 3 Example 4

The long and short axis of the corresponding iso-circle


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Exercises

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1. Make an isometric drawing of the cylinder . .

2.2. Make an cabinet axonometry projection of the

composite solid.

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1.1. Make an isometric drawing of the right cylinder.Make an isometric drawing of the right cylinder.

==

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2.2.Make an cabinet axonometry projection of the composite solid.Make an cabinet axonometry projection of the composite solid.

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1/ 2 Y= 8

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z

0

X y

30 30

20 20

20

20

20

20

不可见的轮廓线一律不画不可见的轮廓线一律不画

1. Make an isometric drawing of the cube 1. Make an isometric drawing of the cube ((L=20L=20

cm)cm)..

StepsSteps::


1)1) Draw the isometric axes.Draw the isometric axes.

2)2) Draw the lower base ofDraw the lower base of the solid.the solid.

3)3)Construct top shape.Construct top shape.

4)4) Erase the unnecessary lines Erase the unnecessary lines andand deepen the visible linesdeepen the visible lines..

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2. Make an isometric drawing of the solid.2. Make an isometric drawing of the solid.

StageStage 11 StageStage 22

StageStage 3 3 StageStage 4 4

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3. Make an isometric drawing freehand.3. Make an isometric drawing freehand.

请请点点击击步步骤骤按按钮钮显显示示其其内内容容 Draw a box Construct basic shape Line in the view

StageStage 11

StageStage 22

StageStage 3 3

20

32

15

15

O1 9

9 4

15

9

9

1

2

3

1

2

3 4 O2 15

2. Make an isometric drawing of the truncated ordinary cone.2. Make an isometric drawing of the truncated ordinary cone.DD11=18=18mm,mm, DD22=30=30mm,mm, HH=32=32mmmm

不可见的轮廓线一律不画不可见的轮廓线一律不画请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容

oo11′′

oo22′′

Steps:

(4)(4)Draw Draw the tangent. the tangent.

(3)(3)Construct ellipse Construct ellipse with four centerswith four centers..

(5)(5)Erase the unnecessary lines andErase the unnecessary lines and deepen the deepen the visible linesvisible lines. .

Four centers Four centers ::①① FindFind 11 、、 2 2 、、 33 、、 44..

②② Draw arc. Draw arc.

③③ Draw tDraw the rest of he rest of arc. arc.

(2)(2) Construct diamond shape of the circleConstruct diamond shape of the circle..

(1)(1) Draw the isometric axes. Draw the isometric axes.

oo11(o(o22))

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12

R8

R8 12

12

24

48

R8 1 2

1 2

R8

不不可可见见的的轮轮廓廓线线一一律律不不画画

3. Make an isometric drawing of the3. Make an isometric drawing of the soleplatesoleplatea with round cornersa with round corners..


(2)(2)Construct top arc. Construct top arc.

(1)(1)Draw Draw thethe rectangle soleplaterectangle soleplatea.a.

StepsSteps:

R8

24

48

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(4)(4)Draw Draw the tangent. the tangent.

(3)(3)Construct Construct basebase arc. arc.

(5)(5)Erase the unnecessary lines andErase the unnecessary lines and deepen the visible deepen the visible lineslines. .

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90 0

z

X 20

y

20

20

45

1. Make an cabinet axonometry projection1. Make an cabinet axonometry projection of the cubeof the cube((L=20L=20

mm).mm). StepsSteps:


(1)(1) Draw the oblique axes.Draw the oblique axes.(2)(2) Draw the lower base ofDraw the lower base of the solid.the solid.

(4)(4) Erase the unnecessary lines andErase the unnecessary lines and

deepen the visible linesdeepen the visible lines..

(3)(3) Construct top shape.Construct top shape.

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2. Make an cabinet axonometry projection2. Make an cabinet axonometry projection of the cube with a hole. of the cube with a hole.


StepsSteps: (1)(1) Lay out the centre lines of the cube. Lay out the centre lines of the cube.

(2)(2) Draw circles on the cube.Draw circles on the cube.

(3)(3) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines..

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8

0116

02

3. Make an cabinet3. Make an cabinet axonometry projectionaxonometry projection of the component.of the component.

StepsSteps:

(2)(2)Draw circles and arc. Draw circles and arc.

(3)(3)Complete the tangent and profile lines.Complete the tangent and profile lines.

(4)(4)Erase the unnecessary lines andErase the unnecessary lines and deepen the visible deepen the visible lineslines. .

(1)(1)Draw the oblique axes.Draw the oblique axes.

O2" O1"


oo11(oo22)

16

R1515

282030

41 0

2 4

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4. Make an cabinet axonometry projection4. Make an cabinet axonometry projection of the lever.of the lever.

StageStage 11 StageStage 22

StageStage 3 3 StageStage 4 4

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P

P

S

Construction of isometric projectionConstruction of isometric projection

(1)(1) An projection planeAn projection plane PP is in front of a vertical plane. is in front of a vertical plane. (2)(2) Direction of projection Direction of projection SS is is vertical to the vertical to the projection plane.projection plane.

(3)(3) Change the relative position Change the relative position betweenbetween a solid and the a solid and the projection plane.projection plane.


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P

P

S

Construction of Construction of cabinet axonometry projectioncabinet axonometry projection


(1)(1) An projection planeAn projection plane PP is in front of a vertical plane. is in front of a vertical plane.

(2)(2) Direction of projection Direction of projection SS is is incline to the incline to the projection plane.projection plane.

(3)(3) Fixedness the relative position Fixedness the relative position betweenbetween a solid and the a solid and the projection plane.projection plane.

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Axonometric projectionAxonometric projection

Orthogonal projectionOrthogonal projection

Isometric projectionIsometric projection

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Circle toCircle toellipseellipse

Circle toCircle toellipseellipse

RectangleRectangle to to rhombusrhombus


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31


32


33

ZZ

XXYY


Characteristics of Characteristics of parallelityparallelity

XX

ZZ

YY

YY

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RightRight ErrorError

Positioning object relative to projection planePositioning object relative to projection plane

Place the face of the object Place the face of the object containing circles or arcs parallel to containing circles or arcs parallel to the projection plane.the projection plane.

Place the longest dimension of Place the longest dimension of the object containing circles or arcs the object containing circles or arcs parallel to the projection plane.parallel to the projection plane.

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The long and short axis of the corresponding iso-circle (the ellipse)

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The long and short axis of the corresponding iso-circle (the ellipse)

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