development of solids

7/30/2019 Development of Solids

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Assume solid object as hollow and made-up of thin sheet. Onopening it from one side completely, the shape of that unfoldedsheet is called Development of Lateral Surface (surface excluding

solid top and bottom). Application: In engineering so many products are difficult to

manufacture by conventional manufacturing methods.Development of solids assists under such situation in variety ofapplications.

Thus, development of solid is basically essential for designing andmanufacturing of products.

Important Points: Its simply showing area (2-D plain drawing),hence, all dimensions should be true dimensions.

After development no edge remains invisible. Therefore, nodimensions should be dotted in development of solid.

Development of solid, when folded or rolled, gives the generatingsolid

WHAT IS

OUR OBJECTIVE

IN THIS TOPIC ?

To learn methods of development of surfaces of

different solids, their sections and frustums.


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D

H

D

SS

H

=R

L 3600

R=Base circle radius.L=Slant height.

L= Slant edge.

S = Edge of base

H= Height S = Edge of base

H= Height D= base diameter

Development of lateral surfaces of different solids.

(Lateral surface is the surface excluding top & base)

Prisms: No.of Rectangles

Cylinder: A RectangleCone: (Sector of circle) Pyramids: (No.of

triangles)

Tetrahedron: Four Equilateral Triangles

All sides

equal in length

Cube: Six Squares.


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Parallel line development : Used for prisms (full and truncated) andcylinder (full and truncated). Two Parallel lines are drawn from thetwo ends of the solid and the lateral surfaces are located betweenthese two lines.

50m

m

50 mm

1 2 3 4

6

5


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50 mm

80mm

1 2 3 4

9

5


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a' b'd'c'

e'

h'

g'

f'

1

34

2

A B

E G

B

C D

F H

H

D

F

C

E

A

1

3

4

1

3

4

2

4

1A B

E G

C D

F H


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A B

E F

D C

G

b

c

a

d

f

g

e

h

H

b' a' c' d'

f' e' g' h'

1

2

34

5

B

F

C

G

D

H

A

E

B

F

1

2

5

1

3

4

AB

e h

34

4


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X Y

a

e

d

b

c

A B C D E A

DEVELOPMENT

Problem 1: A pentagonal prism , 30 mm base side & 50 mm axis

is standing on Hp on its base whose one side is perpendicular to Vp.

It is cut by a section plane 450 inclined to Hp, through mid point of axis.

Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and

Development of surface of remaining solid.

For Development:Draw development of entire solid. Name from

cut-open edge I.e. A. in sequence as shown.

Mark the cut points on respective edges.

Join them in sequence in st. lines.

Make existing parts dev.dark.


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Development of Cylinder & Truncated Cylinder

1

2

1

21 1

2

2

22


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Radial line development: Used for development of pyramids andcones. Assuming O as the center and radius equal to the true lengthof the slant edge of the pyramid draw the arc of the circle. Now cutthis complete arc in required no of parts by the information

regarding the side of the base. In case of cone, divide the base ofthe cone in suitable parts and carry out same exercise.

Example: Develop the full size pattern of the right regular pentagonalpyramid, base 24 mm and height 50 mm.


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Development of pyramids

1

3

2

o

1

c

2

o

a'

b'

o

O

12

3

1

oa=OA

b

C

A

ob=OB=OC

B

A

3

a b

d c

O

B

1

2

3

a b'

d c'4

o

a1

a1'1

2

4

3

O

A

B C

D

A

1 2 3 4

1

oa1=OA


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Problem: A pentagonal pyramid with base edges measuring 25 mmand axis measuring 50 mm, is resting on its base with an edge of itsbase parallel to the VP and nearit. It is cut by a plane perpendicularto the VP, inclined at 60o to the H.P, and passing through a point onthe axis, 15 mm above the base. Draw the development of the

surface of the pyramid.

P bl A 50 b di t d 70 i i


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Y

h

a

b

c

d

e

g

f

a b decg fh

o

A

B

C

D

E

F

A

G

H

SECTIONAL T.V

DEVELOPMENT

Problem: A cone, 50 mm base diameter and 70 mm axis is

standing on its base on Hp. It cut by a section plane 450 inclined

to Hp through base end of end generator. Draw projections,

sectional views, true shape of section and development of surfaces

of remaining solid.

o

= RL 3600

R=Base circle radius.L=Slant height.

development of solids

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