Projections unit 3

PROJECTION

COURSE- Diploma SUB- BASICS OF ENGINEERING GRAPHICS UNIT-3

ORTHOGRAPHIC PROJECTIONS :

Horizontal Plane (HP), Vertical Frontal Plane ( VP )

Side Or Profile Plane ( PP)

Planes. Pattern of planes & Pattern of views Methods of drawing Orthographic Projections

Different Reference planes are

FV is a view projected on VP.TV is a view projected on HP.SV is a view projected on PP.

AndDifferent Views are Front View (FV), Top View (TV) and Side View (SV)

IMPORTANT TERMS OF ORTHOGRAPHIC PROJECTIONS:

Definition:Orthographic system of projections is a method of representing the exact shape of three dimensional object on a two dimensional drawing sheet in two or more views.

123

A.I.P.⊥ to Vp & ∠ to Hp

A.V.P.

⊥ to Hp & ∠ to Vp

PLANES

PRINCIPAL PLANESHP AND VP

AUXILIARY PLANES

Auxiliary Vertical Plane(A.V.P.)

Profile Plane ( P.P.)

Auxiliary Inclined Plane(A.I.P.)

1

THIS IS A PICTORIAL SET-UP OF ALL THREE PLANES.ARROW DIRECTION IS A NORMAL WAY OF OBSERVING THE OBJECT.BUT IN THIS DIRECTION ONLY VP AND A VIEW ON IT (FV) CAN BE SEEN.THE OTHER PLANES AND VIEWS ON THOSE CAN NOT BE SEEN.

X

Y

HP IS ROTATED DOWNWARD 900

AND BROUGHT IN THE PLANE OF VP.

PP IS ROTATED IN RIGHT SIDE 900

ANDBROUGHT IN THE PLANE OF VP.

X

Y

X Y

VP

HP

PP

FV

ACTUAL PATTERN OF PLANES & VIEWS OF ORTHOGRAPHIC PROJECTIONS

DRAWN IN FIRST ANGLE METHOD OF PROJECTIONS

LSV

TV

PROCEDURE TO SOLVE ABOVE PROBLEM:-

TO MAKE THOSE PLANES ALSO VISIBLE FROM THE ARROW DIRECTION, A) HP IS ROTATED 900 DOWNWARD B) PP, 900 IN RIGHT SIDE DIRECTION.THIS WAY BOTH PLANES ARE BROUGHT IN THE SAME PLANE CONTAINING VP.

PATTERN OF PLANES & VIEWS (First Angle Method)

2

Methods of Drawing Orthographic Projections

First Angle Projections MethodHere views are drawn

by placing object

in 1st Quadrant( Fv above X-y, Tv below X-y )

Third Angle Projections MethodHere views are drawn

by placing object

in 3rd Quadrant. ( Tv above X-y, Fv below X-y )

FV

TV

X Y X Y

G L

TV

FV

SYMBOLIC PRESENTATION

OF BOTH METHODSWITH AN OBJECT

STANDING ON HP ( GROUND) ON IT’S BASE.

3

NOTE:-HP term is used in 1st Angle method

&For the same

Ground term is used in 3rd Angle method of projections

FOR T.V.

FOR S.V. FOR F.V.

FIRST ANGLE PROJECTION

IN THIS METHOD, THE OBJECT IS ASSUMED TO BE

PLACED IN FIRST QUADRANT THAT MEANS

ABOVE HP & INFRONT OF VP.

OBJECT IS INBETWEENOBSERVER & PLANE.

ACTUAL PATTERN OF PLANES & VIEWS

IN FIRST ANGLE METHOD

OF PROJECTIONS

X Y

VP

HP

PP

FV LSV

TV

FOR T.V.

FOR S.V. FOR F.V.

IN THIS METHOD, THE OBJECT IS ASSUMED TO BE

PLACED IN THIRD QUADRANTTHAT MEANS

( BELOW HP & BEHIND OF VP. )PLANES BEING TRANSPERENT

AND INBETWEENOBSERVER & OBJECT.

ACTUAL PATTERN OF PLANES & VIEWS

OF THIRD ANGLE PROJECTIONS

X Y

TV

THIRD ANGLE PROJECTION

LSV FV

x y

FRONT VIEW

TOP VIEW

L.H.SIDE VIEWFOR F.V.

FOR S.V.

FOR T.V.

PICTORIAL PRESENTATION IS GIVENDRAW THREE VIEWS OF THIS OBJECT

BY USING FIRST ANGLE PROJECTION METHOD

ORTHOGRAPHIC PROJECTIONS

1

FOR F.V.FOR S.V.

FOR T.V.

X Y

FRONT VIEW

TOP VIEW

L.H.SIDE VIEW




2

FOR F.V.FOR S.V

.

FOR T.V.


X Y

FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

3



FOR T.V.

FOR S.V.


FOR F.V.

FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y

4



FOR T.V.

FOR F.V.

FOR S.V.


FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y

5



FOR T.V.

FOR F.V.FOR S.V.


FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y

6



FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y

FOR T.V.

FOR F.V.

FOR S.V.


7



ZSTUDY

ILLUSTRATIONS

X Y

50

20

25

25 20

FOR T.V.

FOR F.V.

8


FRONT VIEW

TOP VIEW



FOR T.V.

FOR F.V.FOR S.V

.

9


FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y



FOR T.V.

FOR S.V.

FOR

F.V.

10ORTHOGRAPHIC PROJECTIONS

FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y



FOR T.V.

FOR S.V.

FOR F.V.


FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y



FOR T.V.

FOR S.V. FOR F.V.

12


FRONT VIEW

TOP VIEW

L.H.SIDE VIEW

X Y



ZSTUDY

ILLUSTRATIONS

x y

FV35

35

10

TV

302010

40

70

O

FOR T.V.

FOR F.V.

13




ZSTUDY ILLUSTRATIONS

SV

TV

yx

FV

30

30

10

30 10 30

ALL VIEWS IDENTICAL

FOR T.V.

FOR S.V. FOR F.V.

14




x y

FV SV

ZSTUDY

ILLUSTRATIONS

TV

1040 60

60

40

ALL VIEWS IDENTICALFOR T.V.

FOR S.V. FOR F.V.

15




FOR T.V.

FOR S.V. FOR F.V.


x y

FV SV

ALL VIEWS IDENTICAL

40 60

60

40

10

TOP VIEW



40 20

30 SQUARE

20

50

60

30

10

F.V.S.V.

OFOR S.V

. FOR F.V.

17


FRONT VIEW L.H.SIDE VIEW

X Y



50

80

10

30 D

TV

O

FOR T.V.

FOR F.V.


40

10

45

FV

OX Y



X Y

FV

O

40

10

10

TV

25

25

30 R

100

103010

20 D

FOR F.V.O

19


FOR T.V.



O

20 D

30 D

60 D

TV

10

30

50

10

35

FV

X Y

RECT.SLOT

FOR T.V.

FOR F.V.


TOP VIEW

PICTORIAL PRESENTATION IS GIVENDRAW THREE VIEWS OF THIS OBJECTBY USING FIRST ANGLE PROJECTION

METHOD

O O

40

25

80

F.V.

10

15

25

25

25

25

10

S.V.

FOR S.V. FOR F.V.

21




450

X

FV

Y

30

40

TV

30 D

40

4015

O

FOR T.V.

FOR F.V.




O

O

20

2015

40

100

30

6030

20

20

50

HEX PART

FOR S.V.

FOR F.V.

23


FRONT VIEW L.H.SIDE VIEWPICTORIAL PRESENTATION IS GIVEN

DRAW THREE VIEWS OF THIS OBJECTBY USING FIRST ANGLE PROJECTION METHOD

O

10

30

10

80

30

T.V.

O

10

30

4020

F.V.

X Y

FOR T.V.

FOR F.V.


FRONT VIEW

TOP VIEWPICTORIAL PRESENTATION IS GIVENDRAW THREE VIEWS OF THIS OBJECT


LSV

Y

25

25

1050

FV

X

10 10 15

O

FOR S.V.

FOR F.V.

25




YX

F.V. LEFT S.V.

20 2010

15

15

1530

10

30

50

15

FOR S.V.

FOR F.V.

O

26




SECTIONS

Concept of auxiliary plane method for projections of the plane.

A.I.P.⊥ to Vp & ∠ to Hp

A.V.P.

⊥ to Hp & ∠ to Vp

PLANES

PRINCIPAL PLANESHP AND VP

AUXILIARY PLANES

Auxiliary Vertical Plane(A.V.P.)

Profile Plane ( P.P.)

Auxiliary Inclined Plane(A.I.P.)

-The shape of the solid is described by drawing its two orthographic views usually on the two principle planes i.e. H.P. & V.P.

PROJECTIONS OF SOLIDSDefinition of Solid:

A solid is a three dimensional object having length, breadth and thickness. It is completely bounded by a surface or surfaces which may be curved or plane.

-For some complicated solids, in addition to the above principle views, side view is also required.

-A solid is an aggregate of points, lines and planes and all problems on projections of solids would resolve themselves into projections of points, lines and planes.

TYPES OF SOLID

Classification of Solids:Solids may be divided into two main groups;

(A) Polyhedra

(B) Solids of revolution

(A) Polyhedra :

A Polyhedra is defined as a solid bounded by planes called faces which meet in straight lines called edges.

There are seven regular Polyhedra which may be defined as stated below;

(3) Tetrahedron

(4) Cube or Hexahedron: (5) Octahedron:

(6) Dodecahedron:

(7) Icosahedron:

(1) Prism

(2) Pyramid

(1) Prism:It is a polyhedra having two equal and similar faces called its ends or bases, parallel to each other and joined by other faces which are rectangles.

-The imaginary line joining the Centres of the bases or faces is called Axis of Prism.

Axis

Faces

Edge

According to the shape of its base, prism can be sub classified into following types:(a) Triangular

Prism:

(b) Square Prism:

(c) Pentagonal Prism:

(d) Hexagonal Prism:

(2) Pyramid:This is a polyhedra having plane surface as a base and a number of triangular faces meeting at a point called the Vertex or Apex.

-The imaginary line joining the Apex with the Centre of the base is called Axis of pyramid.

Axis

Edge

Base

According to the shape of its base, pyramid can be sub classified into following types:(a) Triangular

Pyramid:

(b) Square Pyramid:

(c) Pentagonal Pyramid:

(d) Hexagonal Pyramid:

(B) Solids of Revolutions:When a solid is generated by revolutions of a plane figure about a fixed line (Axis) then such solids are named as solids of revolution.

Solids of revolutions may be of following types;

(1) Cylinder(2) Cone(3) Sphere(4) Ellipsoid(5) Paraboloid(6) Hyperboloid

(1) Cylinder:

A right regular cylinder is a solid generated by the revolution of a rectangle about its vertical side which remains fixed.

RectangleAxis

Base

(2) Cone:

A right circular cone is a solid generated by the revolution of a right angle triangle about its vertical side which remains fixed.

Right angle triangle

Axis

Base

Generators

Important Terms Used in Projections of Solids:(1) Edge or

generator:For Pyramids & Prisms, edges are the lines separating the triangular faces or rectangular faces from each other.

For Cylinder, generators are the straight lines joining different points on the circumference of the bases with each other

Important Terms Used in Projections of Solids:(2) Apex of solids:

For Cone and Pyramids, Apex is the point where all the generators or the edges meet.

Apex

Apex

Edges

Generators

CONE

PYRAMID

Axis

Faces

Edge

PRISM

RectangleAxis

Base

Generators

CYLINDER

Important Terms Used in Projections of Solids:(3) Axis of Solid:

For Cone and Pyramids, Axis is an imaginary line joining centre of the base to the Apex.

For Cylinder and Prism, Axis is an imaginary line joining centres of ends or bases.

Important Terms Used in Projections of Solids:(4) Right Solid:

A solid is said to be a Right Solid if its axis is perpendicular to its base.

Axis

Base

Important Terms Used in Projections of Solids:(5) Oblique

Solid:A solid is said to be a Oblique Solid if its axis is inclined at an angle other than 90° to its base.

Axis

Base

Important Terms Used in Projections of Solids:

(6) Regular Solid:

A solid is said to be a Regular Solid if all the edges of the base or the end faces of a solid are equal in length and form regular plane figures

Important Terms Used in Projections of Solids:(7) Frustum of Solid:

When a Pyramid or a Cone is cut by a Plane parallel to its base, thus removing the top portion, the remaining lower portion is called its frustum. FRUSTUM OF A

PYRAMID

CUTTING PLANE PARALLEL TO BASE

Important Terms Used in Projections of Solids:(8) Truncated Solid :

When a Pyramid or a Cone is cut by a Plane inclined to its base, thus removing the top portion, the remaining lower portion is said to be truncated.

STEPS TO SOLVE PROBLEMS IN SOLIDS Problem is solved in three steps:STEP 1: ASSUME SOLID STANDING ON THE PLANE WITH WHICH IT IS MAKING INCLINATION. ( IF IT IS INCLINED TO HP, ASSUME IT STANDING ON HP) ( IF IT IS INCLINED TO VP, ASSUME IT STANDING ON VP)

IF STANDING ON HP - IT’S TV WILL BE TRUE SHAPE OF IT’S BASE OR TOP: IF STANDING ON VP - IT’S FV WILL BE TRUE SHAPE OF IT’S BASE OR TOP.

BEGIN WITH THIS VIEW: IT’S OTHER VIEW WILL BE A RECTANGLE ( IF SOLID IS CYLINDER OR ONE OF THE PRISMS): IT’S OTHER VIEW WILL BE A TRIANGLE ( IF SOLID IS CONE OR ONE OF THE PYRAMIDS):

DRAW FV & TV OF THAT SOLID IN STANDING POSITION:STEP 2: CONSIDERING SOLID’S INCLINATION ( AXIS POSITION ) DRAW IT’S FV & TV.STEP 3: IN LAST STEP, CONSIDERING REMAINING INCLINATION, DRAW IT’S FINAL FV & TV.

AXIS VERTICAL

AXIS INCLINED HP

AXIS INCLINED VP

AXIS VERTICAL

AXIS INCLINED HP

AXIS INCLINED VP

AXIS TO VPer

AXIS INCLINED

VP

AXIS INCLINED HP

AXIS TO VPer AXIS

INCLINED VP

AXIS INCLINED HP

GENERAL PATTERN ( THREE STEPS ) OF SOLUTION:

GROUP B SOLID.CONE

GROUP A SOLID.CYLINDER

GROUP B SOLID.CONE

GROUP A SOLID.CYLINDER

Three stepsIf solid is inclined to Hp

Three stepsIf solid is inclined to Hp

Three stepsIf solid is inclined to Vp

Three stepsIf solid is inclined to Vp

Class A(1): Axis perpendicular to H. P. and hence parallel to both V.P. & P.P.

X Y

a

b

d

c

c’,d’a’,b’

o’

o

Axis

c’,3’b’,2’

Class A(2): Axis perpendicular to V.P. and hence parallel to both H.P. & P.P.

f’,6’

a

e’,5’

d’,4’a’,1’

b,f c,e d

43,52,61X Y

H

b”2”

1

a”1”1’2’

Class A(3): Axis perpendicular to P.P. and hence parallel to both H.P. & V.P.

X Y

Lc”3”

a’,b’

c’

a

b

c 3

2

3’

PROJECTION OF SOLIDS WHEN ITS AXIS PARALLEL TO REFERENCE PLANE AND INCLINED TO THE OTHER Case (1) Axis inclined to H.P and Parallel to V.P

PROJECTION OF SOLIDS WHEN ITS AXIS PARALLEL TO REFERENCE PLANE AND INCLINED TO THE OTHER Case (2) Axis inclined to V.P and Parallel to H.P

SECTIONING A SOLID.SECTIONING A SOLID.An object ( here a solid ) is cut by An object ( here a solid ) is cut by

some imaginary cutting planesome imaginary cutting plane to understand internal details of that to understand internal details of that

object.object.

The action of cutting is calledThe action of cutting is called SECTIONINGSECTIONING a solid a solid

&&The plane of cutting is calledThe plane of cutting is called

SECTION PLANE.SECTION PLANE.

Two cutting actions means section planes are recommendedTwo cutting actions means section planes are recommended..

A) Section Plane perpendicular to Vp and inclined to Hp.A) Section Plane perpendicular to Vp and inclined to Hp. ( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)( This is a definition of an Aux. Inclined Plane i.e. A.I.P.) NOTE:- This section plane appears NOTE:- This section plane appears as a straight l ine in FV.as a straight l ine in FV. B) Section Plane perpendicular to Hp and inclined to Vp.B) Section Plane perpendicular to Hp and inclined to Vp. ( This is a definition of an Aux. Vertical Plane i.e. A.V.P.)( This is a definition of an Aux. Vertical Plane i.e. A.V.P.) NOTE:- This section plane appears NOTE:- This section plane appears as a straight l ine in TV.as a straight l ine in TV.Remember:-Remember:-1. After launching a section plane 1. After launching a section plane either in FV or TV, the part towards observereither in FV or TV, the part towards observer is assumed to be removed.is assumed to be removed.2. As far as possible the smaller part is 2. As far as possible the smaller part is assumed to be removed. assumed to be removed.

OBSERVEROBSERVER

ASSUME ASSUME UPPER PARTUPPER PARTREMOVED REMOVED SECTON PLANE

SECTON PLANE

IN FV.

IN FV.

OBSERVEROBSERVER

ASSUME ASSUME LOWER PARTLOWER PARTREMOVEDREMOVED

SECTON PLANE

SECTON PLANE IN TV.IN TV.

(A)(A)

(B)(B)

Section Plane Section Plane Through ApexThrough Apex

Section PlaneSection PlaneThrough GeneratorsThrough Generators

Section Plane Parallel Section Plane Parallel to end generator.to end generator.

Section Plane Section Plane Parallel to Axis.Parallel to Axis.

TriangleTriangle EllipseEllipse

Par

abol

a

Par

abol

a

HyperbolaHyperbola

EllipseEllipse

Cylinder throughCylinder through generators.generators.

Sq. Pyramid through Sq. Pyramid through all slant edgesall slant edges

TrapeziumTrapezium

Typical Section Planes Typical Section Planes &&

Typical Shapes Typical Shapes Of Of

SectionsSections..

CROSS SECTION OF SOLIDS

C.R.ENGINEERING COLLEGEAlagarkovil, Madurai - 625301

TERMS & CONVENTIONS

METHOD OF HATCHING

TYPES FOR SECTIONAL VIEWS – SECTIONAL FRONT VIEW

TYPES FOR SECTIONAL VIEWS – SECTIONAL TOP VIEW

SECTIONAL VIEW – PARALLEL TO H.P AND PERPENDICULAR TO V.PA cube of 40 mm side is cut by a horizontal section plane, parallel to H.P at a distance of 15 mm from the top end. Draw the sectional top view and front view

SECTIONAL VIEW – INCLINED TO H.P AND PERPENDICULAR TO V.P

A square prism of base side 50 mm and height of axis 80 mm has its base on H.P, it is cut by a section plane perpendicular to V.P and inclined to H.P such that it passes through the two opposite corners of the rectangular face in front. Draw the sectional Top View and Front View. Find the angle of inclination of the section plane

SECTIONAL VIEW – PERPENDICULAR TO H.P AND INCLINED TO V.PA square prism of base side 40 mm and height 70 mm is resting on its rectangular face on the ground such that its axis is parallel to H.P &V.P, it is cut by a section plane perpendicular to H.P & inclined to V.P at an angle of 45° and passing through a point 10 mm from one of its ends. Draw the sectional Front View and Top View

TRUE SHAPE OF A SECTION

PROCEDURE FOR TRUE SHAPE

EXAMPLE: TRUE SHAPE PROBLEMA square prism of base side 50 mm and height of axis 80 mm has its base on H.P, it is cut by a section plane perpendicular to V.P and inclined to H.P such that it passes through the two opposite corners of the rectangular face in front. Draw the sectional Top View and Front View and true shape of the section

References

• www.cs.unca.edu/~bruce/Spring11/180/isometricSketches.ppt

• www.tcd.ie/civileng/Staff/Bidisha.Ghosh/.../isometric.ppt

• www2.cslaval.qc.ca/cdp/UserFiles/File/.../isometric_drawings.ppt

• A text book of engineering graphics- Prof. P.J SHAH

• Engineering Drawing-N.D.Bhatt• Engineering Drawing-P.S.Gill

Education

Projections unit 3