Development of Surfaces
SURFACE
DEVELOPMENT
Development of Surfaces
The development of
surface of an object
means the unrolling
and unfolding of all
surfaces of the object
on a plane
If the surface of a
solid is laid out on a
plain surface, the
shape thus obtained
is called the
development of that
solid
The development of a solid is the
shape of a plain sheet that by proper
folding could be converted into the
shape of the concerned solid.
Importance of Surface Development
Knowledge of
development is very
useful in sheet metal
work, construction of
storage vessels, chemical
vessels, boilers, chimneys
etc.
Such vessels are manufactured
from plates/sheets that are cut
according to these developments
and then properly bend into
desired shaped and the joints are
welded or riveted.
Principles of Surface Development
Every line on the development should show
the true length of the corresponding line on
the surface which is developed.
Methods of Development of Surface
Methods of Surface Development are:
1. Parallel line development
2. Radial line development
3. Triangulation development
4. Approximate development
Methods of Development of Surface
1. Parallel line development
uses parallel lines to construct the expanded pattern of each
three-dimensional shape. The method divides the surface into
a series of parallel lines to determine the shape of a pattern
Example: Prism, Cylinder.
Methods of Development of Surface
2. Radial line development
Radial line development uses lines radiating from a central
point to construct the expanded pattern of each threedimensional shape.
Example: Cone, Pyramid.
Methods of Development of Surface
3. Triangulation developments
Are made from polyhedrons, single-curved surfaces, and
wrapped surfaces.
It is used for developing transition pieces
This is done by assuming the surface to be made from a series
of triangular surfaces laid side-by-side to form the
development
Example: Tetrahedron and other polyhedrons.
Methods of Development of Surface
In approximate development,
the shape obtained is only approximate. After joining, the part
is stretched or distorted to obtain the final shape.
Example: Sphere
1. Parallel line development
Development of a Cylinder
Draw the plan & elevation of the cylinder
Divide the plan in to equal parts (i.e. 8, 12)
Draw horizontal lines A-A and A1-A1 from the side of the elevation
The length of these lines is D (circumference of the cylinder)
Divide the stretch-out line into the equal number of same parts as the
plan (i.e. 8, 12)
The rectangle (A- A; A1- A1), gives the development of the cylinder.
Side view
Development of a Truncated Cone
Draw the (truncated) cone elevation and plan
views as shown.
Divide the plan view into equal parts/segments
(i.e. 12)
Transfer these points to the elevation.
2. Radial line development
Development of a Pyramid
Draw the front and plan view of the
square pyramid
Find the true length of the slant edge
0 11
Take radius = length 0 - 11 with any
centre o, draw an arc of a circle.
Choose any point 1 on the arc and
join it to point o (centre of the arc).
On the plan view, use length 1-2, 2-3,
3-4, 4-1 to mark off four division
along the arc as 1, 2, 3, 4 etc. Join 1,
2, 3 and 4 along with 01. Join 1 to 2,
2 to 3, 3 to 4 and 4 to 1 with straight
lines.
Use radius = the base side of
the pyramid (i.e. 50 mm) mark
four divisions on the
The 4 isosceles triangles
represent the lateral
development of the pyramid.
2. Radial line development
Development of a Truncated Pyramid
Draw the front and plan view of the
Draw the front and top views of the
truncated pyramid
On the plan, draw the diagonal 1-3, 2-4 to
meet at 0. Numbered the plan and project to
the front as shown
Extend centre 0 horizontally. 0-1 as radius,
draw an arc to meet 11
Project 11 vertically to meet elevation at
11. Join 11 to 0 (equals the true length of
the slanting side)
Drop off the cutting points a b c d on the
elevation to meet the plan at d, c, b and a
respectively
2. Radial line development
..Truncated Pyramid cont.
0-11 as radius with centre 0, draw an arc.
Join any point 1 to centre 0 of the arc
From the plan use length 1-2, 2-3, 3-4 etc
to cut points along the arc and number the
points as 1, 2, 4, 1. Join these points to
centre 0.
0-a as radius, with centre 0, draw an inner
(smaller) arc.
Use length a-b, b-c, c-d and d-a, from the
plan, locate 5 points A, B, C, D and A on the
inner arc.
Join all the points on the big and smaller
arc to form the development of the
truncated pyramid
3. Triangulation developments
Transition pieces are the sheet metal used for connecting
pipes or openings either of different shapes of cross sections or
of same cross sections but not arranged in identical positions.
3. Triangulation developments
In this method, the lateral surfaces of the transition
pieces are divided in to a number of triangles
By finding the true lengths of the sides of each triangle
the development is drawn by laying each one of the
triangles in their true shapes adjoining each other.
Triangulation method
ELEVATION
PLAN
Triangulation method
Draw the elevation and the plan view
as shown
The semicircle in the plan view is
divided into eight equal parts 1,2,3,4,
etc.
Join pts 1,2,3,4 and 5 to pt. a. and 5, 6,
7, 8, 9 to pt b.
Triangulation method
The transition piece consists of 4 plane
triangles 1da, 5ab, 9bc, and 13cd and
4 curved triangles 1a5, 5b9, 9c13 and
13d1
Triangulation method
Project points 1,2,3,etc to the
front view to meet 1,2,3. etc.
Connect 1, 2, 3 etc to a and 5,
6, 7, 8 9 to b.
Triangulation method
Draw vertical line XY. The
first triangle to be drawn is
1pa (from plan)
The true length of sides 1p
and 1a are found from the
true length diagram.
Triangulation method
To get true length of sides 1p
& 1a
step off the distances 1p and
1a on the horizontal drawn
through X to get the point 1P
and 1A.
Connect these two points to
Y. The length Y-1P and Y-1A
are the true lengths of the
sides 1p and 1a respectively.
Triangulation method
DEVELOPMENT
Draw line 1P = Y-1P
Draw an arc with center 1
and radius Y-1A.
P as center & radius pa,
(from plan view) draw an arc
to cut the line 1-A at A.
Triangulation method
With A as center and radius equal to true
length of the line 2a (i.e. Y-2A), draw an arc.
With 1 as center & radius 1-2 (T.V),
draw another arc intersecting the
pervious arc at 2.
Triangulation method
Similarly determine the points 3, 4 and 5.
A -1 -2 -3 - 4 - 5 is the development of the
curved triangle 1-a-5.
AB is the true length of the plain triangle a-5-b.
Similar procedure is repeated for
the other three curved triangles
and plain triangles.
Triangulation method
A as center & radius = true length of the line 2a (i.e. Y-2A), draw an
arc.
With 11 as center & radius = 1-2 (T.V), draw another arc
intersecting the pervious arc at 2.
Triangulation method
In the same way, determine points 31, 41 and 51.
A -11-21-31- 41- 51 is the development of the curved triangle 1-a-5.
AB is the true length of the plain triangle a-5-b.
Similar procedure is repeated for the other three curved triangles
and plain triangles.
THANK YOU
