DEVELOPMENT OF SURFACES
Part I
Prof.T.JEYAPOOVAN
Department of Mechanical Engineering
Hindustan Institute of Technology and Science
Chennai-603103, India
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Development of surfaces of a prism
• The surfaces (faces and
bases) of a solid which is
opened out and laid on a flat
plane is called as the
development of surfaces of
that object.
• In square prism, when the
faces are opened out, its faces
are seen as four rectangles of
same size and two square
bases as shown in figure.
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Parallel Line Method
• Parallel line method is used to
draw development of prisms
and cylinder.
• For example, in a square prism,
two stretch-out lines whose
length equal to perimeter of
base are drawn parallel to each
other with the gap between
them equal to the axis length
and rectangular faces are
marked on the development.
• The bases are opened out and
drawn in an arbitrary position.
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Example 1: A hexagonal prism of base side 30 mm and height 50 mm
rests vertically on HP with a side of base parallel to VP. Draw the
development of the surfaces of the prism.
• Draw the TV and project the
FV of the prism.
• Draw two stretch-out lines
whose length equal to
perimeter of base , parallel to
each other with the gap
between them equal to axis
length and six faces are
marked to complete the
development.
• Bases, hexagon, are drawn in
an arbitrary position.
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Example 2: A pentagonal prism of base side 30 mm and axis length 60
mm rests with its base on HP and an edge of the base to inclined at 40°
to VP. It is cut by a plane perpendicular to VP, inclined at 40° to HP and
passing through a point on the axis, at a distance of 30 mm from the
base. Develop the remaining surfaces of the truncated prism.
• Draw TV, project FV and the
cutting plane at 40º to XY. Mark
new corners on the longer edges.
• Draw two stretch-out lines,
length equal to perimeter of base,
parallel to each other, gap
between them equal to axis
length and faces are marked on it.
• Project and mark new corners on
the development.
• Since top base is removed,
bottom base, pentagon, is drawn.
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Example 3: Draw the development of the lower portion of a cylinder of
diameter 50 mm and axis 70 mm when sectioned by a plane inclined at
40º to HP and perpendicular to VP and bisecting the axis.
• Draw TV and divide it into 8 parts,
project FV and draw the cutting
plane at 40º to XY.
• Mark new corners on generators.
• Draw two stretch-out lines, length
equal to circumference of base,
parallel to each other, gap between
them equal to axis length and show
the 8 generators by dividing it into 8
equal parts.
• Project new corners to development.
• Since the top base is removed,
bottom base, circle, is drawn.
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Example 4: A vertical chimney of circular cross section of 400 mm diameter
joins the roof of a room sloping at 35º to the horizontal. The shortest length
of the chimney is 800 mm. Determine the shape of the sheet metal from
which the chimney can be made. Use 1:10 scale.
• Understand the shape of the
chimney from the figure. The
cutting plane is at 35º to XY as
shown.
• Use the same procedure as
discussed in the previous
problem to draw the
development.
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• Draw TV, project FV of the chimney. Draw trace of the
cutting plane at 35º to XY as shown. Mark the new
corners in FV.
• Draw the development as discussed earlier and project the
new corners to the development.
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Example 5: A cube of 40 mm edge stands on one of its faces on HP with a
vertical face making 45° to VP. A horizontal hole of 20 mm diameter is
drilled centrally through the cube, such that the hole passes through the
opposite vertical edge of the cube. Obtain the development of the lateral
surface of the cube with the hole.
• Draw TV, project FV of cube.
Draw the hole in FV as shown.
• Divide the circle in to 8 equal
parts and project the points to
the top view.
• Draw development of cube and
mark the position of the points
from TV to the development,
then project them as shown.
• Join all points to complete the
development of hole as an
ellipse.
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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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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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End of Lesson 9
Thank You
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