projection of solid engineering108.com

8/10/2019 Projection of Solid Engineering108.Com

1/41


2/41

-The shape of the solid is described bydrawing its two orthographic views usuallyon the two principle planes i.e. H.P. & V.P.

PROJECTIONS OF SOLIDS

Definition of Solid:A solid is a three dimensional object havinglength, breadth and thickness. It iscompletely bounded by a surface or surfaceswhich may be curved or plane.

-For some complicated solids, in addition tothe above principle views, side view is also

required.

-A solid is an aggregate of points, lines andplanes and all problems on projections of

solids would resolve themselves intoprojections of points, lines and planes.


3/41


4/41


5/41

(1) Prism:

It is a polyhedra having twoequal and similar faces

called its ends or bases,parallel to each other and

joined by other faces which

are rectangles.

-The imaginaryline joining the

Centres of thebases or faces iscalled Axis of

Prism.

Axis

Faces

Edge


6/41

According to the shape of its base, prism can be sub classified into

following types:

a) Triangular Prism:

b) Square Prism:


7/41


8/41

2) Pyramid:

This is a polyhedra having plane

surface as a base and a numberof triangular faces meeting at apoint called theVertexorApex.

-The imaginaryline joining theApex with theCentre of thebase is called

Axisof pyramid.Axis

Edge

Base


9/41

According to the shape of its base, pyramid can be sub classified into following

types:

a) Triangular Pyramid:

b) Square Pyramid:


10/41

c) Pentagonal Pyramid:

d) Hexagonal Pyramid:


11/41

B) Solids of Revolutions:

When a solid is generated by revolutionsof a plane figure about a fixed line (Axis)

then such solids are named as solids ofrevolution.

Solids of revolutions may be of following

types;

(1) Cylinder

(2) Cone

(3) Sphere

(4) Ellipsoid

(5) Paraboloid

(6) Hyperboloid


12/41

1) Cylinder:

A right regular cylinder is a solidgenerated by the revolution of arectangle about its vertical sidewhich remains fixed.

Rectangle

Axis

Base


13/41

2) Cone:

A right circular cone is a solidgenerated by the revolution of a rightangle triangle about its vertical sidewhich remains fixed.

Right angle

triangle

Axis

Base

Generators


14/41

Important Terms Used in Projections of Solids:

1) Edge or generator:

For Pyramids & Prisms, edges are thelines separating the triangular faces orrectangular faces from each other.

For Cylinder, generators are thestraight lines joining different points

on the circumference of the bases witheach other


15/41


(2) Apex of solids:

For Cone andPyramids, Apexis the point

where all thegenerators orthe edges meet.

Apex

Apex

Edges

Generators

CONE

PYRAMID


16/41

Axis

Faces

Edge

PRISM

Rectangle

Axis

Base

Generators

CYLINDER


17/41


(3) Axis of Solid:

For Cone and Pyramids, Axis is animaginary line joining centre ofthe base to the Apex.

For Cylinder and Prism, Axis is animaginary line joining centres of

ends or bases.


18/41


(4) Right Solid:

A solid is said tobe a Right Solidif its axis isperpendicular toits base.

Axis

Base


19/41


20/41

Important Terms Used in Projections

of Solids:

(6) Regular Solid:

A solid is said to be a Regular Solid ifall the edges of the base or the end

faces of a solid are equal in length and

form regular plane figures


21/41


of Solids:

(7) Frustum of Solid:

When a Pyramid or a

Coneis cut by a Planeparallel to its base,

thus removing the top

portion, the remaininglower portion is called

its frustum. FRUSTUM OF A

PYRAMID

CUTTING PLANE

PARALLEL TOBASE


22/41


of Solids:

(8) Truncated Solid :

When a Pyramid or a

Cone is cut by a Planeinclined to its base,

thus removing the top

portion, the remaininglower portion is said to

be truncated.

Cl A(1) A i di l t H P d h


23/41

Class A(1):Axis perpendicular to H. P. and hence

parallel to both V.P. & P.P.

X Y

a

b

d

c

c,da,b

o

o

Axis

Cl A(2) A i di l t V P d h


24/41

c,3b,2

Class A(2):Axis perpendicular to V.P. and hence

parallel to both H.P. & P.P.

f,6

a

e,5

d,4a,1

b,f c,e d

43,52,61X Y

H

Cl A(3) A i di l t P P d h


25/41

b2

1

a112

Class A(3):Axis perpendicular to P.P. and hence

parallel to both H.P. & V.P.

X

Lc3

a,b

c

a

b

c 3

2

3

C ( ) A i ll l VP d i li d


26/41

Class B(1):Axis parallel to V.P. and inclined to

H.P. by & also inclined to P.P.

Exercise 1 :

A right regular pentagonal pr ism,

side of base 30 mm and height ofaxis as 75mm rests on HP on one

of its base corners such that its

long edge containing the corner is

incl ined to the HP at 60. Draw its

projections.

c


27/41

a

5

c1

X Y31

21

411

5141

2131

a1

d1

c1

b1

e1

d1 b1e1a1

c

be

11

5141

a

b

e

d

3

2

1

60

30

SCALE:-1:1

75

c

c


28/41

a

5

c1

X Y31

21

411

5141

2131

a1

d1

c1

b1

e1

d1 b1e1a1

c

be

11

5141

a

b

e

d

3

2

1

60

30

SCALE:-1:1

75

c


29/41


30/41

30

a

b

c

d

a

d

bc

b1c1

a1

d1

b

c1

a1d1

a2

d2

b2 c2X Y

40

45 c2

b2

a2

d2


31/41

30

a

b

c

d

a

d

bc

b1

c1

a1

d1

b1

c1

a1

d1

a2

d2

b2 c2

X Y

40

45 c2

b2

a2

d2


32/41

A cone, diameter of base 60mm andheight 70mm, is resting on HP onthe point of periphery of the base.Axis of the cone makes 60 with HPand 30 with the VP. Draw theprojections of the cone, when the

apex is nearer to the VP.

Exercise 3 :


33/41

O

70

60

ab,h d,fec,g e1

a1

O1

60

O2Locus of

O2

30

a e

fg

h

b dc

O2

a2

e2

c2g2

X

O1a1

c1

e1

g1

O

g2

a2

c2

e2

O


34/41


35/41


36/41

d1

e1a1

b1

c1

ba

c

d

e

1

23

4

5

dcba e

11

21

31

41

51

a1b

1

c1 d1

e1

42

1222

3252

d2

c2

b2 a2

e2

12

22

32 42

52

=45= 30

1

2 3

5

4

e2

d2c2

b2

a2

31 41

51

1121

X Y


37/41

Exercise 5 :

A regular hexagonal prism of30mm sides and axis 80mmlong is resting on HP on one

of its corners of the base. Theaxis makes 30 with HP andplan of the axis makes 45with the VP. Draw itsprojections.


38/41

a2

d2b2

f2

c2

e2

12

22 42

62

32

52

d1

b1a1

c1e1

f1

21

11

3141

51

61

a1 d1

c1b1

e1f1

42 31 56

df ecb

aX Y

5

1 42 3

6e

a d

cb

f

11

21 31

41

5161

b2

a2

c2 d2e2

f2

12

3222

42

52

62

45


39/41

A square pyramid, side of base50mm and height 64mm, is freely

suspended from one of thecorners of the base. Draw itsprojections when vertical plane

containing axis makes an angle of45 with the VP.

Exercise 6 :


40/41

A cube of 40 mm edges, is restingon the H.P. on one of the edges of

the base with face containing thatedge making 30 with the H.P.The edge on which the cube rests

on the H.P. is making 30 with theV.P. Draw the projections.

Exercise :


41/41

PROJECTIONS OF

SOLIDS

projection of solid engineering108.com

Documents