This document discusses different methods for developing the surfaces of 3D objects onto 2D planes. It introduces parallel line development, which is used for objects with parallel edges like prisms and cylinders. Radial line development is used for forms with radiating lines like pyramids and cones. Triangulation development divides warped surfaces into triangles. Approximate development approximates double curved surfaces like spheres by developing zones cut from the surface. The key methods are parallel line, radial line, triangulation, and approximate development.

1. ME 101
Engineering Drawing

2. M o d u l e # 0 8
DEVELOPMENT OF SURFACES

3. LEARNING
OBJECTIVES
Students should be able to learn
1. Introduction to development of surfaces
2. Methods of development
a. Parallel line development
b. Radial line development
c. Triangulation development
d. Approximate development
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4. Introduction
• In industrial world, an engineer is frequently confronted with problems where the development
of surfaces of an object has to be made to help him to go ahead with the design and
manufacturing processes.
• For example, in sheet metal work, it plays a vital role, thus enabling a mechanic to cut proper
size of the plate from the development and then to fold at proper places to form the desired
objects, namely, boilers, boxes, buckets, packing boxes, chimneys, hoppers, air-conditioning
ducts etc.
• “The development of surface of an object means the unrolling and unfolding of all surfaces of
the object on a plane.”
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5. Introduction
• “If the surface of a solid is laid out on a plain surface, the shape thus obtained is called the
development of that solid.”
• Development is a graphical method of obtaining the area of the surfaces of a solid.
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Knowledge of development is very useful in sheet metal work, construction of storage
vessels, chemical vessels, boilers, and chimneys. Such vessels are manufactured from plates
that are cut according to these developments and then properly bend into desired shaped. The
joints are then welded or riveted.

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7. Introduction
• It should be noted that every line on the development represents the true length of the
corresponding line on the surface of the solid.
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TRUE LENGTHS

8. Introduction
• For example:
• When a piece of paper having the shape of a sector is rolled so that the extreme edges meet, we
get a cone.
• In the same way, when a rectangular sheet is rolled so that extreme edges meet, we get a
cylinder.
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9. Development – Examples
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Many products are manufactured from pattern developments

10. Development – Important Points
1. Development is different drawing than PROJECTIONS.
2. It is a shape showing AREA, means it’s a 2-D plain drawing.
3. Hence all dimensions of it must be TRUE dimensions.
4. As it is representing shape of an un-folded sheet, no edges can remain hidden, and hence
DOTTED LINES are never shown on development.
LATERLAL SURFACE is the surface excluding solid’s top & base.
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1. Parallel lines are extended from the top and bottom of the front view, which represents
the true height of the pattern. These lines are called “stretch-out lines” because they
represent the pattern’s stretched out form.
2. Tabs are necessary for making edges and joints.
3. The fold lines are extended upward using construction lines, and the height of each
corner is projected from the front view to the stretch-out lines.

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D
H
D
S
S
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 Rectangle
Cone: (Sector of circle) Pyramids: (No.of triangles)
Tetrahedron: Four Equilateral Triangles
All sides
equal in length
Cube: Six Squares.

14. Methods of Development
• The following methods are mainly employed to obtain the development of surfaces of solids.
1. Parallel-line development
2. Radial-line development
3. Triangulation development
4. Approximate development
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15. 1. Parallel-line Development
• This method is used for developing prisms and single curved surfaces like cylinders, in which
all the edges/generation of lateral surfaces are parallel in each other.
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Steps for parallel line development of a rectangular prism

16. 1. Parallel-line Development
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Steps for parallel line development of a cylinder
A1
A
A
A1
A A

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1. Draw a plan and elevation of a cylinder with the given dimensions.
2. Divide a circle (of the plan) in a number of equal parts (say 8) by drawing diameters. Project these
divisions in the elevation. Each line in the elevation represents a generator.
3. Draw horizontal lines on the side of the elevation. These lines are called stretch-out lines (A A and A1,
A1). The length of these lines is equal to the circumference of the cylinder pi × D, where D is the
diameter of the cylinder.
4. Divide the stretch-out line into the same number of equal parts in which the plan circle has been divided
(here, eight parts).
5. The rectangle (A A A1 A1), so obtained, is the development of the lateral surface of the cylinder.

18. 1. Parallel-line Development
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Steps for parallel line development of a truncated cylinder

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1. Draw the front and top views of a truncated cylinder.
2. Divide the base circle into a number of equal parts and project the generator on the front view.
3. Mark the points of intersection 1, 2, 3, etc, between the generators and the truncated zone of the
cylinder.
4. Draw the stretch-out line equal to the circumference of the base of the cylinder.
5. Divide the stretch-out line into the same number of equal parts as that of the base and draw the
generators through them.
6. Locate the points 1, 2, and 3, etc. by a smooth curve.
Development of the Surface of a Truncated Cylinder

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Develop the lateral surface of the truncated cylinder shown in fig. 2-7(i).

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Draw the projections of a cylinder, base 30mm diameter and axis 40mm long, resting with
a point of its base circle on HP. Draw projections of cylinder and development of surface.

22. 2. Radial-line Development
• Geometric forms, such as pyramids and cones, do not contain parallel lines.
• These forms contain lines that radiate to a common apex and are developed through the use of
radial lines.
• Since the inclined vertical edges of cones and pyramids are not parallel, stretch-out lines are
not parallel.
• In radial line developments, stretch-out lines are arcs, and element lines become triangles
that radiate from an apex to the stretch-out arc.
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23. 2. Radial-line Development
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Steps for radial line development of a rectangular pyramid

24. 2. Radial-line Development
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Steps for radial line development of a cone

25. 2. Radial-line Development
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Computing the stretch-out angle for the development of a cone’s pattern

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The development of the lateral surface of a cone is a sector of a circle. The radius and length of the arc are equal
to the slant height and circumference of the base of the cone respectively. The included angle of the sector is
given by (r / s) x 360°, where r is the radius of the base of the cone and s is the true length.

27. 3. Triangulation Development
• Parallel line and radial line developments are used to develop patterns for objects that contain flat or
single-curved surfaces.
• These methods cannot be used to develop patterns for warped surfaces, such as spheres,
paraboloids, or hyperboloids, including oblique pyramids, oblique cones, and square-to-round
intersections.
• Since warped surfaces are curved in two directions, the even distribution of elements used in
parallel and radial line development is not possible.
• The process of triangulation is used to develop patterns for warped surfaces.
• Triangulation development is a method of dividing a warped surface into a series of triangles and
transferring the true size of each triangle to a flat pattern. When flat triangulated patterns are bent
or folded into a three-dimensional form, the desired warped form is created.
• It is used for developing transit ion pieces.
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28. 3. Triangulation
Development
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Steps for triangulation development of an
oblique pyramid

29. 4. Approximate Development
• It is employed for double curved surfaces like spheres, as they are theoretically not possible to
develop. The surface of the sphere is developed by approximate method. When the surface is
cut by a series of cutting planes, the cut surfaces is called a zone.
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30. Key Take Away
1. Introduction to development of surfaces
2. Methods of development
a. Parallel line development
b. Radial line development
c. Triangulation development
d. Approximate development
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31. THANKS!