Lesson 2-lines-ii

PROJECTIONS OF STRAIGHT LINES
Part II

Prof.T.JEYAPOOVAN
Department of Mechanical Engineering
Hindustan Institute of Technology and Science
Chennai-603103, India
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Projections of a Line kept inclined to
both HP and VP
• In this position both the top view (TV) and front
view (FV) are smaller than true length (TL), so
one of the following methods is used to draw the
projections.
– Rotating Line Method
– Rotating Trapezoidal Plane Method
– Auxiliary Plane Method

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Rotating Line Method
• This method has 4 steps
• STEP 1: Assume the line is
kept inclined to HP and
parallel to VP, Draw the FV
and project the TV as shown
in fig.
– Note: Normally any two values
of TL, θ or TV will be given,
draw either the FV or TV and get
the other view projected.
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• STEP 2: Assume the line is
kept inclined to VP and
parallel to HP, Draw the TV
and project the FV as shown
in fig.
– Note: Normally any two values
of TL, Φ or FV size will be
given, draw either the TV or FV
and get the other view
projected.

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• STEP 3: Draw the locus of
other end of the line in FV
and TV as shown in fig.
– Note: The figures of STEP 1 and
STEP 2 are shown together with
the locus drawn parallel to XY
line.

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• STEP 4: Rotate TV and FV to the
required position with the centre
as shown in fig. Complete the TV
and FV by drawing dark lines.
– Also show the projector of the other
end of the line which is at 90º to the
XY line for correct answer.

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Example 1: A line AB 80mm long has its end A 20mm above HP
and 25mm in front of VP. The line is inclined at 45º to HP and 35º
to VP. Draw its projections.

• Draw the XY line and mark the
projections of end A of the line.
• Step 1: Draw FV using TL and
θ. Project the TV.
• Step 2: Draw TV using TL and
Φ . Project the FV.
• Step 3: Draw locus of b’ and b.
• Step 4: Rotate the TV and FV to
the required position on locus.
– Note: These 4 steps are used to
solve a given problem in any
sequence as per the given data.
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Rotating Trapezoidal Plane Method
• This method assumes
trapezoidal planes to
draw the projections of
the straight line.
• Consider a trapezoidal
plane which contains the
straight line in space and
top view of the line as
shown in Fig.

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• Rotate this trapezoidal plane
and put it on HP.
• Note that the true shape of
this plane is seen in top view
which can be constructed by
using measurements from
the front view of the ends of
the line from XY line as
shown in fig.

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• Consider another
trapezoidal plane which
contains the straight line
in space and front view
of the line as shown in
Fig.

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• Rotate this trapezoidal
plane and put it on VP.
• Note that the true shape of
this plane is seen in front
view which can be
constructed by using
measurements from the top
view of the ends of the line
from XY line as shown in
fig.

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Example 2: A line AB has its end A 20mm above HP and 25mm in
front of VP. The other end B is 45mm above HP and 40mm in front
of VP. The distance between end projectors is 60mm. Draw its
projections. Also find the true length, true inclinations of the line
with HP and VP and mark the traces.

• Draw the XY line and mark the projections of the
end A of the line. Also draw the projections of
the other end B of the line.
• Construct the trapezoidal plane in top view using
measurements from the front view of the ends of
the line from XY line as shown in fig.
• Extend the TL and TV to get HT and θ.
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• Construct another trapezoidal plane in front view using
measurements from the top view of the ends of the line from
XY line as shown in fig.
• Extend the TL and FV to get VT and Φ.

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Important special Case Problems
• The straight line is placed
such a way that the sum of
its inclinations with HP
and VP is equal to 90º (i.e.
θ + Φ = 90º)
• Note: Use the 4 steps of
rotating line method.
• Also note that the final
projections (TV & FV) are
obtained perpendicular to
HP and VP.
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Important special Case Problems
• The straight line is placed
such a way that one end of
the line is in HP and another
end in VP.
• Note: Use the 4 steps of
rotating line method but
drawn separately.
• Also note that the final
projections are obtained
using the top and front view
sizes from step 1 and step 2.

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Tips to solve problems
• Use your notebook in
open position as VP and
HP and pencil as straight
line to understand the
given position and its
projections.

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Tips to solve problems
• Have thorough knowledge of problems when a
line is kept inclined to one plane and parallel to
other plane.
• Familiarize with the 4 steps of Rotating line
method.
• Steps (1) to (4) can be done in any order to draw
projections of the line.

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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 2
Thank You

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Lesson 2-lines-ii

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