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TERM PAPER

ENGINEERING DRAWING (103)

TOPIC :- DEVELOPMENT OF SURFACE

SUBMITTED BY:-

SHAILESH SINGH

ROLL NO:D4901A59

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ACKNOWLEDGEMENTI take this opportunity to present my votes of thanks to all those guidepost who really

acted as lightening pillars to enlighten our way throughout this project that has led to

successful and satisfactory completion of this study.

We are really grateful to our HOD for providing us with an opportunity to undertake

this project. We are highly thankful to PARDEEP SIR for her active support,

valuable time and advice, whole-hearted guidance, sincere cooperation and pains-

taking involvement during the study and in completing the assignment of preparing the

said project within the time stipulated.

Lastly, We are thankful to all those, particularly the various friends , who have beeninstrumental in creating proper, healthy and conductive environment and including new

and fresh innovative ideas for us during the project, their help, it would have been

extremely difficult for us to prepare the project in a time bound framework.

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INTRODUCTION:-

Development is a graphical method of obtaining the area of the surface of a solid. When a solid

is opened out and its complete surface is laid on a plane, the surface of the solid is said to be

development. The figure thus obtained is called a development of the surface of the solid .It

should be noted that every line on the development represents the true length of the

corresponding line on the surface of the solid. Development of the solid , when folded or rolled

,gives the solid .For Ex- when a piece of a paper having the shape of a sector is rolled so the the

extreme edges meet.

The knowledge of development of surface of solid is required in designing and manufacturing of the

object. Practical application of development occur in sheet metal work.

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layot development

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Development of Curved Surfaces

Note: I have not been able to find any handy resources regarding development; the books on

Amazon.com seem to be either out of print or expensive as hell, and the Web has, for once, failed

to provide many answers. The methods I demonstrate here are my own, and may or may not becorrect. However, I have used them, and they do indeed seem to work.

Development is the graphical process of producing a flat pattern from drawings of a curved

surface. Not all surfaces lend themselves to development; any surface with a compound curve

cannot be developed. I have used development in designing a boat and in sheet metal work, butI'm sure it is useful in other fields as well.

There are three methods of development; parallel line development, radial line development, and

triangulation.

I. Parallel Line Development

Parallel Line Development uses geometry to measure a series of heights above a base line, and

marks these heights off on a series of parallel lines. Often applied to pipe, it can be applied to

any object with a constant cross section, as long as a view perpendicular to the cross section isavailable.

Basically it is nothing more than a series

of lengthsalong the surface of a cylinder.

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This is the plan

we'll start with.

No, I don't knowwhat it is. We'll

develop the

surface of the

small branch.

1. Divide the

plan view of the

branch of the teewith a

convenientnumber ofequally spaced

radii. I've used 9

radii because itproduces

eighths. Because

this part is

symetrical, I'veonly marked off

half of it - I

could actuallyonly mark aquarter, since it'ssymetrical about

two axes.

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2. Extendperpendicular

lines from the

ends of eachradii to the

curved edge of

the profile viewof the branch.

3. From thepoints where the

lines in step 2

meet the curved

edge of theprofile view,

drop verticallines down. Addan extra line

where the lines

cross the baseline.

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4. Measure thedistance between

the points where

the radii meedthe edge of theplan view, and

mark off this

distance on thevertical lines

drawn in step 3.

Draw horizontal

lines through themarks.

5. Connect thedots where the

correspondinglines cross.

II. Radial Line Development

Radial Line Development basically just Parallel Line Development for tapered objects -. cones,

pyramids etc. Alternately, Parallel Line Development is just Radial Line Development for aninfinitely small taper.

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This is the plan

we'll start with; atruncated conewith angle cut out.

This is actually a

design underconsideration for

the turret of my

tank.

1. Divide the plan

view into equally

spaced radii. The

more the better. Asthis object is

symetrical, weonly need to dothis to half the

plan - the other

half will be amirror image.

http://www.gizmology.net/tanks.htmhttp://www.gizmology.net/tanks.htm

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2. Extend vertical

lines from the

points where theseradii meet the

circumference of

the plan viewupward to the base

line of the

profile...

3. ...and then to theapex of the cone.

This cone has a

very shallow taper,so the apex is way

up there.

4. This particulardesign has one

more point that has

to be marked - theupper edge of the

angled surface.

Run a line from

the apex throughthe edge of the

angled surface to

the base line of the

profile, thenvertical down to

the circumference

of the plan. It isn't

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necessary to

continue the line tothe center of the

plan, but it looks

nice.

5. Draw horixontallines from the

points along the

angled surface to

the outermost radiion the profile

view...

6. ... and continuethem as arcs

around the apex.

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7. Measure the

distance betweenthe points where

the radii meet the

circumference inthe plan view, and

mark these

distances off onthe arc drawn in

step 6 that

cooresponds to the

base line in theprofile view.

8. Connect the

dots where the

radii cross theircooresponding

arcs. Remember

that you've only

got half a patternhere; the other side

is a mirror image

of this one.

III. Triangulation

Triangulation is used for irregular surfaces. A good example is a boat hull. However, not all hulls

can be developed - only those that do not have compound curves.

A little simple geometry is first required. The length of a line can be derived from the (X,Y,Z)

coordinates of it's endpoints, using the following formula:

L = ((X1 - X2)2

+ (Y1 - Y2)2

+ (Z1 - Z2)2)

If the distance LXY in the XY plane between the endpoints is known, this formula can be

simplified to:

L = (Lxy2

+ (Z1 - Z2)2)

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Assuming one point to be the origin simplifies this even further, and allows the Z dimension tobe measured directly:

L = (Lxy2

+ Z2)

This last formula is used to calculate the distance between two points on a surface from thedistance between them on the plan drawing and the height difference on the profile drawing.

Triangulation can be VERY tedious.

This is the plan we'll start with; a

simple boat.

1. The first step is to draw vertical

lines through the plan. I drew nine

lines; the more lines, the moreaccurate the developed surface. It

is not necessary for the lines to

coincide with the extreme front andback of the plan.

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2. On the plan view, measure the

distance between two points on the

plan, and the heightof the two

same points on the profile.

3. Calculate the true length of lineAB using the formula L = (Lxy

2+

Z2). Elsewhere, draw a circle of

this radius. Point A will be at the

center, and point B somewhere on

the circumference of this circle.

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4. Repeat step 2 with two more

points, one of which was used in

step 2. In this case, I am usingpoint B to point C.

5. Calculate the true length of line

BC as in step 3, and draw a circle

of this radius at an arbitrary point

on the radius of the circle drawn instep 3. As point B is at the center

of this circle, connect the centers ofthe two circles with line AB.

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6. Now we complete the triangle

by measuring the distance between

points A and C.

7. Calculate the true length and

draw a circle of this radius around

point A. Point C lies where thecircles around points A and B

intersect.

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8. Now measure one of the sides of

an adjacent triangle. One of the

ends of this triangle must be a

point on the first triangle. points A,B or C.H Here I am measuring

between points C and the new D.

9. Calculate the true length, draw a

circle around point C. Point D will

be on the circumference of this

circle... but where?

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10. Measure the other side of the

adjacent triangle.

11. Calculate the true length, and

draw a circle around point B. The

intersection of this circle and theone around point C is the location

of point D.

12. Repeat steps 8 through 11 until you've layed out the entire surface.

.

Development of Hollow Rectangular Prism.

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Cone If a cone be placed on its side on a plane surface, one element will rest on the

surface. If now the cone be rolled on the plane, the vertex remaining stationary until the

same element is in contact again, the space rolled over will represent the development

of the convex surface of the cone. Is a cone cut by a plane paralle to the base. let the

vertex of the cone be placed at V, and one element of the cone coincide with V F 1. Thelength of this element is taken from the elevation, Fig of either contour element. All of

the elements of the cone are of the same length, so that when the cone is rolled, each

point of the base as it touches the plane will be at the same distance from the vertex.

From this it follows that in the development of the base, the circumference will become

the arc of a circle of radius equal to the length of an element, and of a length equal to

the distance around the base. To find this length divide the circumference of the base in

the plan into any number of equal parts, say twelve, and lay off twelve such spaces, 1. .

.13 along an arc drawn with radius equal to VI; join 1 and 13 with V, and the resulting

sector is the development of the cone from vertex to base. In order to represent on the

development the circle cut by the section plane D F, draw, from the vertex V as a center

and with V F as a radius, the arc F C. The development of the frustum of the cone will

be a portion of a circular .This of course does not include the development of the bases,

which would be simply two circles the same sizes as shown in plan.

Plan and

Elevation of Cone.

. Development of Cone.

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Regular Triangular Pyramid represents the plan and elevation of a regular triangular

pyramid, and Fig. 135, its development. If face C is placed on the plane its true size will

be shown in the development. The true length of the base of triangle C is shown in the

plan. As the slanting edges, however, are not parallel to the vertical, their true length is

not shown in elevation but must be obtained by the method given on Page 64, asindicated in Fig. 134. The triangle may now be drawn in its full size at C in the

development, and as the pyramid is regular, two other equal triangles, D and E, may be

drawn to represent the other

sides.

Plan and Elevation of Triangular Pyramid.

Development of Triangular Pyramid.

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Truncated Circular Cylinder. If a truncated circular cylinder is to be developed, or rolled

upon a plane, the elements, being parallel, will appear as parallel lines, and the base

line being perpendicular to the elements, will appear as a straight line of length equal to

the circumference of the base. The base of the cylinder in Fig. 136 is divided into twelve

equal parts, 1, 2, 3, etc., and commencing at point 1 on the development, these twelve

equal s