Transcript proj of planes

UNIT – III
Syllabus
(a) Projection of planes: Introduction,
types of planes, projection of planes,
projection of planes perpendicular to
both the reference planes, perpendicular
to one plane and parallel to the other
plane, perpendicular to one plane and
inclined to the other plane.
.
(b) Projection of solids: Introduction,
types of solids, projection of solids in
simple position, projection of solids
with axes inclined to both H.P. and
V.P., section planes, types of
sections, true shape of section,
section of solids.
.
3.1 Classification of Planes
Planes can be broadly classified as :
1. Principal planes and
2. Secondary planes.
3.2 Types of Secondary Planes
1. Plane perpendicular to both the HP and
the VP.
2. Plane perpendicular to the HP and
parallel to the VP.
3. Plane perpendicular to the VP and
parallel to the HP
.
Auxiliary planes. Two views of an object can
be projected on two principal planes, H.P.
and V.P. Sometimes either of these two views
may not give the true shape of the surface of
the object, inclined to the principal planes.
Additional views called auxiliary views are
therefore obtained by projecting the object on
other planes known as auxiliary planes.
These planes are inclined to one of the
principal planes and perpendicular to the
other.
.
Types of Auxiliary Planes
1. Auxiliary vertical plane (A.V.P.)
It is perpendicular to the H.P but inclined
to the V.P.
1. Auxiliary inclined plane (A.I.P.)
It is perpendicular to the V.P. but inclined to
the H.P.
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Q. Explain profile plane.
A.
S 09
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Q. What are different types of auxiliary
planes?
(S10)
Q. Define auxiliary planes and classify.
(W07, W09)
Q. Show by means of traces, each of the
following planes:
(i) Perpendicular to HP and inclined at 30˚ to
VP.
(ii) Parallel to and 40 mm away from VP.
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Q. Why the projections of a plane are not
drawn in second and fourth quadrants?
(W09)
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3.1 A regular
pentagon of 30 mm
side is resting on one of its edges
on the HP which is inclined at 45˚
to the VP. Its surface is inclined at
30˚ to HP. Draw its projections.
(W06)
.
.
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3.2 A cube of 70 mm long edges has its
horizontal faces equally inclined to the
HP. It is cut by a sectional plane
perpendicular to HP so that true shape
of the section is a hexagon. Determine
the inclination of the cutting plane with
the VP and draw sectional front view
and true shape of the section.
(W06)
.
.
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3.3 A cone base 70 mm and axis length
80 mm is kept on HP on its base. It is cut
by an AIP in such a way that the true
shape of the section is a hyperbola of
base 50 mm and altitude 60 mm. Draw
front view, sectional top view and true
shape of the section.
(W07)
.
.
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3.4 A cone base diameter 70 mm and axis
length 80 mm is kept on the HP on its base.
It is cut by a section plane perpendicular to
both HP and VP in such a way that the true
shape of the section is hyperbola of altitude
50 mm. Draw front view, top view and true
shape of the section.
(W07)
.
.
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3.5 The base surface of a stand is a square of
90 cm sides and is on ground. The top surface
of it is a circle of 30 cm diameter and is 70 mm
above the ground. The lower ends of four legs
which are equal in length and equally spaced in
plan, and are connected to the corners of
square in base while the top ends are on the
circumference of the circle at top.
Draw the projections of the stand when the four
legs are equally inclined to front wall and find
the length of legs and their inclination with
ground.
.
.
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3.6 Draw the projections of a
regular pentagon of 40 mm side,
having its surface inclined at 30˚
to the HP and a side in the HP and
inclined at an angle of 60˚ to the
VP.
(W08)
.
.
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3.7 A hexagonal pyramid base 25
mm and axis 50 mm long has one
of its triangular faces in the VP and
edge of the base contained by that
face makes angle of 30˚ with the
HP. Draw its projections.
(W08)
.
.
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3.8 A cone diameter of base 50 mm
long is resting on its base on the
ground. It is cut by a section plane
perpendicular to the VP inclined at 75˚
to the HP and passing through the
apex. Draw its front view, sectional top
view and true shape of the section.
(W08)
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.
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3.9 Draw the projections of a regular
hexagon of 25 mm side, having one
of its sides in the HP and inclined at
60˚ to the VP and its surface making
an angle of 45˚ with the HP.
(09)
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3.10 Draw the projections of a
rhombus having diagonals 125 mm
and 50 mm long the smaller diagonal
of which is parallel to both the
principal planes, the other is inclined
at 30˚ to the HP.
(09)
.
.
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3.11 A triangular prism, base 30 mm
side and axis 50 mm long is lying on
the HP on one of its rectangular faces
with its axis inclined at 30˚ to the VP. It
is cut by a horizontal section plane at a
distance of 12 mm above ground. Draw
its front view and sectional top view.
(S09, S10)
.
.
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3.12 The top view of a plate, the
surface of which is perpendicular
to the VP and inclined at 60˚ to the
HP is a circle of 60 mm diameter.
Find the true shape of the plate.
(W09)
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3.13 A cube of 25 mm edges, is resting
on one of its faces on HP. It is cut by a
plane in such a way that the true
section available is a regular hexagon.
Find the apparent and true section of
the cube. Find the inclination of the
sectional top view with HP and VP.
(W09)
.
.
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3.14 A pentagonal pyramid of base
side 30 mm and height 50 mm is
resting on the ground on one of its
base side in such a way that one of
its triangular face is perpendicular
to both HP and VP. Draw the
projections.
(W09)
.
.
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3.15 An isosceles triangle PQR having the
sides of 75 mm long and altitude 75 mm
have its corners P, Q and R 25 mm, 50 mm
and 75 mm respectively above the ground.
Draw its projections.
(S10)
.
.
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3.16 Draw the projections of a hexagonal
pyramid base 30 mm side and axis 60 mm
long, having the base on the H.P. and one of
the edges of the base inclined at 45˚ to the
V.P.
(S10)
Solution:
.
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3.17 Draw the projections of a circle of 50
mm diameter resting in the horizontal plane
on a point A on the circumference, its plane
inclined at 45˚ to the H.P. and the top view of
the diameter AB making 30˚ angle with the
V.P.
(W02)
Solution:
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3.18 A tetrahedron 40 mm long edge parallel
to the H.P. and inclined at 45˚ to the V.P.
while a face containing that edge is vertical.
Draw its projections.
(W02)
Solution:
.
3.19 A circular disc 80 mm diameter and of
negligible thickness lies in a plane inclined
at 30˚ to the HP and perpendicular to the
VP. Its centre is 60 mm from horizontal trace
of the inclined plane. Draw its top view, front
view and side view. .
(S07)
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3.20 A cylinder of base diameter 45 mm and
height 65 mm rests on its base on HP. It is
cut by a plane perpendicular to VP and
inclined at 30˚ to HP and meets the axis at a
distance of 30 mm from base.
(S07)
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