developments surfaces

8/11/2019 Developments Surfaces

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8/12/2014 Engineering Drawing & Graphics 1


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DEVELOPMENT OF SURFACESOF SOLIDS

Engr. Nazeer Ahmed Anjum


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If a piece of paper is wrapped around a cylinder or on

all sides of a square prism and laid out or opened on a

flat surface. OR

INTRODUCTION

When the complete surface of a solid is opened out

and laid on a plane, the surface of the solid is said to

have been "developed" and the figure obtained is

called "development" of the surface.

Every line on the development must be the true length

of the corresponding line on the surface.


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INTRODUCTION

A developable surface is one which may be unfolded

or unrolled so is to coincide with a plane. Single

curved surfaces such as of cones and cylinders can be

accurately developed.Warped and double curved surfaces such as of sphere,

tours, ellipsoid and hyperboloid are undevelopable.

These can, however, be approximately developed by

dividing them into a number of parts.


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IMPORTANCE

In engineering practice an engineer is frequently

required to have a knowledge of development of

surfaces of an object in its design and manufacturing

processes. Practical applications of developmentsoccur in sheet-metal work, stone cutting, cartoons,

cigarette, Matches etc boxes and pattern making.


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DEVELOPMENT

PRISM CYLINDER


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DEVELOPMENT

PYRAMID CONE


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DEVELOPMENT OF A CYLINDER

This is a development of a cylinder. It is quite easily

formed by drawing a rectangle, adding a tab and

rolling it round to form the cylindrical shape. A

separate top and base can be added, these are circular.

Can you name any products that

have this type of package ?


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DEVELOPMENT OF A PRISM

This is a triangular prism. It is quite an unusual shape

although you may be able to think of a product that has

a package like this one.


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DEVELOPMENT OF A PYRAMIDThis is a net / development of a square pyramid. The

development gets its name from the square base. Tabsare positioned around the base and on the leading edge

so that when the development is folded it can be glued

in position.Can you name any

products that have this

type of products?


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DEVELOPMENT OF A CONE


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DEVELOPMENT OF A CUBOID


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PRINCIPLE DEVELOPMENT METHODS

There are four principle methods of development:

(i)Parallel-line development.

It is employed in cases of prisms and cylinders in

which stretch-out-line (SL) principle is used. A stretch-out-line is the development of the end of the prism or

the cylinder.

(ii) Radial line development

It is employed in cases of pyramids and cones inwhich the true length of the slant edge or the generator

is used as radius.


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PRINCIPLE DEVELOPMENT METHODS

(iii) Triangular developmentIt is employed where the connecting surface is neither prismatic

nor pyramidal. In this method the various plane surfaces are

divided into several triangular areas, and each triangle is laid

out in the development after the termination of its true from.

This method is used where the connecting surface is a

combination of prismatic, pyramidal, cylindrical types or a

combination of any two of these.

(iv) Approximate Development

It is employed where the surface of a solid is theoreticallyundevelopable like wrapped & double-curved surfaces. These

can be approximately developed by dividing them up into a

number of parts.


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DEVELOPMENT OF A TRUNCATEDCYLINDER

Draw the TOP & FRONT views of the cylinder.

Divide the TOP view into 12 equal parts

Project the divisions to the front view.

Number the divisions on both the views.

Draw the stretch out line (SL) equal to D

Divide the SL into 12 equal divisions & number

each division.Draw lines at each division & project the heightof each line from the front view.


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DEVELOPMENT OF A TRUNCATEDCYLINDER


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DEVELOPMENT OF THE LATERAL SURFACE OFA TRUNCATED PYRAMID

TOP VIEW

Develop the lateral

surface of a truncated

hexagonal pyramid of

base edge 25 mm &

height 60 mm.


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DEVELOPMENT OF THE LATERAL SURFACE OFA TRUNCATED PYRAMID

TOP VIEW

Draw the

development of the

lateral surface of a

truncated pentagonal

pyramid of base edge20 mm & height 60

mm. it is truncated at

20mm from the apex.


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DEVELOPMENT OF LATERAL SURFACES OFTRUNCATED CONE

The development of the cone will be a sector of acircle & the angle subtended by the arc at the center iscalculated by the formula:

)(

)(360

lconetheofheightSlant

rcirculebasetheofRadiuso

The radius of the base circle is 10mm & slant height is30mm, then = 360(10/30)

= 120o


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DEVELOPMENT OF LATERAL SURFACES OFTRUNCATED CONE

Draw the development of the lateral surface of a truncated cone

of base 50 mm & height 80 mm.

Draw the true length diagram. The lines 0-1 and 0-7 are the

true length because they are ||e

to the front plane. Since all theother lines are foreshortened, hence true lengths are needed.

Draw the stretch out line SL. Measure distance from 1 to 2 on the

top view. Using this distance, step off 12 spaces on SL.


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DEVELOPMENT OF A TRANSITION PIECE

A transition piece is a specially formed pipe that is used to join

two other pipes of different shapes, such as a square pipe & around pipe. The word transition means change.

In a transition piece there are four

large triangular-shaped pieces and

four parts that are made o smalljoined triangles.

The development of a transition

piece is done by the principal of

triangulation. Triangulation is the

processes of dividing a curved

surface into small triangles which

can be bent into shape instead of

stretched.

eve opmen o


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eve opmen oFour Piece Elbow

O

15

1530

30

d1d2

O

15

1530

30


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A

B

C

D E

F

G

H

I J

O

Draw tangents to the arcs from each point to bring the piece

in the required shape.


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1

2

35

6

4

Draw a semicircle at the bottom & divide it into 6 equal

parts i.e at an angle of 30.

7


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Draw the projections from the point of intersections of

circles up to section A.From A draw parallel lines to the

tangent of section B.

1

2

34

5

6

7

A

B

C

D

A & D


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11 2 3 4 5 67 56 34 2

D

C

B

A

1

23

45

6

7

A & D

Draw a line having length equal to circumference of circle. Divide circumference

into 12 equal parts. Draw the projections of part A of Elbow. Join the points

with hand sketch. Part A & D are same in shape.

B & C


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5

BB

B & C

1

2

34

56

7 1 2 3 4 5 6 7 6 5 4 3 2 1

Draw part B of Elbow above the semicircle. Draw projections of B to

circumference of circle. Join points obtained with hand sketch. Part B & C are

same in shape.


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A

B

C

D

Final Four pieces of Elbow obtained will be in this form.


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Step # 1:draw the separate view ofeach part and make the

development of each one by one

Development of T-Joint


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Piece no. 1 of tee joint


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Piece no. 2 of tee joint


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Step # 1

12

3

5

4

67

8

9

10

12

1

11

1;

2;12


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Step # 2:

1: Draw the front view of piece no. 1 which is double

truncated cylinder

2: Draw the top view of the cylinder and divide it into

twelve divisions.

3: Draw the projection of each point on front view and

extended them which intersect the unfolded

development of cylinder join the points and complete

the development of piece no. 1.


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Step # 2


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Step # 3Same procedure is adopted for development of

piece no. 2.


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6

1

2

345

6789

101112

13

.

Step # 3


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Step # 4 Remove the extra material to get finished piece

and join them to form the required tee joint.


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FINAL DEVELOPED SHAPE OF PIECE NO. 1


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2

.


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PROCEDURE FOR T-JOINT First of all draw a circle and divide it into twelve

equal parts.

Now draw the vertical projections of the circle.

Draw the horizontal projections of the circle.Now draw a triangle making an angle of 30 degree

with the horizontal.


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PROCEDURE

Now draw a segment representing the upper part of the

T-joint..

Draw another segment representing the lower part ofthe T-joint.

On the vertical projections of the circle cut a distance

pi()*diameter, and divide it into twelve equal

segments.


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PROCEDURE

From these segments draw horizontal lines.

Now draw the projections of the figures drawn

(triangle & lines), these vertical projections willcut the equally spaced horizontal lines.

Mark the point of intersection of vertical and

horizontal projections.


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PROCEDURE

Join these points and you will obtain different curves.

Cut those curves and join them and T-JOINT is

obtained.


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CUTTING SECTIONS


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FINAL SHAPE


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ASSIGNMENT

1. A cone has a base diameter 40 mm & slant height 60 mm. develop theslant surface of the cone.

2. A hexagonal prism standing on H.P with one of its base edge ||eto theV.P is cut by an oblique plane. Develop the lateral surfaces of the prismwhen its upper portion is removed.

3. A pipe elbow is formed by joining three cylindrical pipe pieces. Develop

the lateral surfaces of the elbow.4. Development of Y-Joint5. Development of T-Joint6. Development of 90oElbow with flanges7. Development of 45oElbow with flanges

8. Development of Truncated Cone9. Development of Truncated Pyramid10. Development of Truncated Hexagonal Pyramid

Submission Date: 1405 - 2008


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PROCEDURE OF Y-JOINT

First of all draw a circle and divide it intotwelve equal parts.

Now draw the vertical projections of the

circle.

Draw the horizontal projections of thecircle.

Now draw a triangle making angle of30(degree)with the horizontal.


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PROCEDURE

Now draw a line making an angle of30(degree) with the horizontal.

Draw another triangle and line three timesadopting the same procedure.

On the vertical projections of the circle cut

a distance pi*diameter ,and divide it intotwelve equal segments.


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PROCEDURE

From these segments draw horizontallines.

Now draw the projections of the figuresdrawn (triangle & lines), these verticalprojections will cut the equally spaced

horizontal lines.Mark the point of intersection of vertical

and horizontal projections.


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PROCEDURE

Join these points and you will obtaindifferent curves.

Cut those curves and join them andY-JOINTis obtained.


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CUTTING SECTIONS


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This type of two sections will beformed.


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This type of two sections will beformed.


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FINAL SHAPE

developments surfaces

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