1.
DEVELOPMENT OF SURFACES
Part II
Prof.T.JEYAPOOVAN
Department of Mechanical Engineering
Hindustan Institute of Technology and Science
Chennai-603103, India
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2.
REFERENCE BOOKS
1. Jeyapoovan T, “Lesson Plans for Engineering
Graphics”, 2010, Vikas Publishing House Pvt
Ltd, New Delhi.
2. Jeyapoovan T, “Engineering Drawing and
Graphics”, 2011, Vikas Publishing House Pvt
Ltd, New Delhi.
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3.
Development of a pyramid
• Consider a square
pyramid, when the slant
triangular faces are
opened out, its faces are
seen as four triangles of
same size and shape, the
base is a square as shown
in fig.
• Radial line method is
used to draw development
of pyramids and cone.
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4.
Radial Line Method
• For example, consider a
square pyramid and its
development shown in fig.
• An arc with true length of
slant edge as radius and o
as center is drawn. The
base sides are marked
along the arc and the
triangular faces are drawn.
• The base is opened out and
drawn in an arbitrary
position as shown.
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5.
Example 1: A square pyramid of side of base 45 mm, altitude 70 mm
and resting with its base on HP with two sides of the base parallel to
VP. The pyramid is cut by a section plane which is perpendicular to VP
and inclined at 40° to the HP and bisects the axis of the pyramid. Draw
the development of lateral surface of the truncated pyramid.
• Draw TV, project FV of prism, the
draw cutting plane and mark new
corners.
• An arc with true length of slant edge
as radius and O as center is drawn.
The base sides are marked along the
arc and the triangular faces are
drawn.
• Measure true distance of new corners
from o’ and mark from O to complete
development of remaining portion of
lateral surfaces.
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6.
Example 2: A cone of base diameter 40 mm and axis length 50 mm is
resting on HP on its base cut by a plane inclined at 30° to HP and
perpendicular to VP and is passing through a point on the
circumference of the base. Draw the development of the remaining
upper portion of the cone.
• Draw TV and divide 8 parts, project FV and draw the
cutting plane at 30º to XY. Mark the new corners on the
generators. An arc with true length of generator as radius
and o as center is drawn for the subtended angle as given
below.
r
× 360°
R
where r = base circle radius in mm
Subtended angle θ =
R = true length of generator in mm (o′a ′ length)
θ=
30
× 360° 133°
54
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7.
• The chord length of each segment is marked along the
arc and draw the generators.
• Measure true distance of new corners from o’ and
mark from O to complete development of remaining
portion of lateral surfaces.
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8.
Example 3: A cone of base diameter 60 mm and height 70 mm is
resting on its base on HP. It is cut by a plane perpendicular to both the
HP and VP at a distance 15 mm to the left of the axis. Draw the
development of the lateral surface of the right remaining portion.
• Draw TV and divide 8 parts, project FV. Draw the cutting
plane perpendicular to both HP and VP at 15mm to the left of
axis. Mark the new corners on generators in FV and project
to TV.
• An arc with true length of generator as radius and o as center
is drawn for the subtended angle
r
o
θ = × 360
R
18
=
× 360o ; 146o
44.4
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9.
• The chord length of each segment is marked along the
arc and draw the generators.
• Measure true distance of new corners from o’ and
mark from O to complete development of remaining
portion of lateral surfaces.
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10.
Example 4: Draw the development of the lateral surface of a funnel
consisting of cylinder and a frustum of a cone. The diameter of the
cylinder is 20 mm and the top diameter of the funnel is 70 mm. The
height of frustum and cylinder are each equal to 40 mm.
• Draw FV of the funnel, note that the upper portion is a frustum of
a cone and lower portion is a cylinder.The frustum of the cone is
produced to get as a cone to draw the development.
• Draw the development of cylindrical portion as discussed earlier.
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11.
Tips to draw Development of Surfaces
• Draw the projections of the solid, then draw the
trace of the cutting plane. Carefully mark the new
corners on the edges/generators which are cut by the
cutting plane.
• First draw the development with 2H pencil. Then
project and mark new points on the development
and darken the remaining portion with HB pencil to
complete the development.
• To draw the development of the lateral surfaces,
bases need not be shown.
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12.
End of Lesson 10
Thank You
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