The document discusses the projection of planes, including: 1. A plane is a two-dimensional object defined by length and breadth. Projection of planes involves extending the plane shape to reference planes (horizontal and vertical planes). 2. The intersection of the plane with the reference planes forms traces (lines) called the horizontal trace and vertical trace. 3. Planes can have various orientations relative to the reference planes, such as parallel, perpendicular, or inclined. 4. Projection of planes involves drawing the top, front, and side views of objects placed in different plane orientations.

1. What is Projection of Planes
A plane is a two dimensional object having length and
breadth only .Its thickness is always neglected .Various
shapes of plane figures are considered such as square,
rectangle, circle, pentagon, hexagon, etc.
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Dr.RGM, Professor/ Mechanical

2. Projection of Planes
Meaning of Trace of a Plane
It is defined as the extension of a given plane shape to
the reference plane (HP or VP) to which it is
perpendicular or inclined.
The plane meets the HP or VP as a line. This line is
called trace of a plane.
Horizontal Trace(HT) &Vertical Trace (VT) a plane.
The line in which the plane shape meets the HP is
called HT.
The line in which the plane shape meets the VP is
called as VT.
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Dr.RGM, Professor/ Mechanical

3. Orientation of Planes in Space
The following position of Planes in space
❖ Planes Parallel to VP and Perpendicular to HP
❖ Planes Perpendicular to VP and Parallel to HP
❖ Planes Parallel to both VP and HP or
both Perpendicular VP and HP
❖ Planes Perpendicular to VP and Inclined to HP
❖ Planes Inclined to VP and Perpendicular to HP
❖ Planes Inclined to both VP and HP
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Dr.RGM, Professor/ Mechanical

4. Notations of object in Planes
Following notations should be followed while
naming different views projections of planes.
Object Point
It’s top view a , b, c ,…
It’s front view a’ , b’, c’,…
It’s side view a’’, b’’, c’’,…
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Dr.RGM, Professor/ Mechanical

5. Position in Projection of Planes
1.A plane perpendicular to HP and parallel to VP
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Dr.RGM, Professor/ Mechanical

6. Position in Projection of Planes
2.A plane perpendicular to VP and parallel to HP
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Dr.RGM, Professor/ Mechanical

7. Position in Projection of Planes
3.A plane perpendicular to both VP and HP
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Dr.RGM, Professor/ Mechanical

8. Position in Projection of Planes
4. A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

9. Position in Projection of Planes
5. A plane inclined to VP and perpendicular HP
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Dr.RGM, Professor/ Mechanical

10. Position in Projection of Planes
6. A plane inclined to both VP and HP
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Dr.RGM, Professor/ Mechanical

11. Position in Projection of Planes
6. A plane inclined to both VP and HP
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Dr.RGM, Professor/ Mechanical

12. Position in Projection of Planes
A plane resting on one of its base side on HP
A plane resting on one of its base side on VP
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Dr.RGM, Professor/ Mechanical

13. Position in Projection of Planes
A plane resting on one of its corner on HP
A plane resting on one of its corner on VP
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Dr.RGM, Professor/ Mechanical

14. Problems in Projection of Planes
1.A square lamina ABCD of side 40mm is perpendicular
to HP and parallel to VP. Draw its projections
Plane is perpendicular to HP and parallel to VP
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Dr.RGM, Professor/ Mechanical

15. Problems in Projection of Planes
2. An equilateral triangle ABC of 50 mm side is parallel to VP
and 15 mm in front of V.P, its base AB is parallel and 75 mm
above H.P.Draw the projections of the triangle when the
corner is near the H.P
Plane is perpendicular to HP and parallel to VP
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Dr.RGM, Professor/ Mechanical

16. Problems in Projection of Planes
3.A square lamina ABCD of side 40mm is perpendicular
to VP and parallel to HP. Draw its projections
Plane is perpendicular to VP and parallel to HP
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Dr.RGM, Professor/ Mechanical

17. Problems in Projection of Planes
4. An equilateral triangle ABC of 50 mm side has its plane
parallel to H.P and side AB parallel to V.P Draw its
projections when the corner C is 15 mm from H.P and 45mm
from the V.P
Plane is perpendicular to VP and parallel to HP
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Dr.RGM, Professor/ Mechanical

18. Problems in Projection of Planes
5. A rectangle ABCD of size 40x25 has the corner A, 10mm
above HP and 15 mm in front of VP. All the sides of the rectangle
are inclined at 450 to HP and parallel to VP. Draw the projection
of lamina.
A plane inclined to HP and parallel to VP
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Dr.RGM, Professor/ Mechanical

19. Problems in Projection of Planes
6. A pentagonal plate of side 30mm is placed with one side on
the HP and the surface inclined at 500 to HP and perpendicular
to VP. Draw the projection of lamina.
A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

20. Problems in Projection of Planes
7. A circular plate of diameter 50mm is resting non the HP on a
point on the circumference with its surface inclined at 450 to HP
and perpendicular to VP. Draw the projection of lamina.
A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

21. Problems in Projection of Planes
8. A circle of diameter 50 mm inclined at 300 to HP and
perpendicular to VP. Has its centre 30 mm in front of VP. Draw
the projection of lamina and side view.
A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

22. Problems in Projection of Planes
9.A regular hexagon of 25mm side and Has its a lamina is
perpendicular to VP and inclined at 400 HP. Draw the three
views.
A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

23. Problems in Projection of Planes
10. A pentagonal plate of side 30mm is placed with one side on
the HP and the surface inclined at 500 to HP and perpendicular
to VP. Draw the projection of lamina.
A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

24. Problems in Projection of Planes
11. A hexagonal plate of side 30mm side has a corner at 20mm
from VP and 50 mm from HP. Its surface is inclined at 500 to VP
and perpendicular to HP. Draw the projection of lamina.
A plane inclined to VP and perpendicular HP
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Dr.RGM, Professor/ Mechanical

25. Problems in Projection of Planes
12.Draw the projections of a circular lamina of 30 mm diameter.
The lamina is inclined a an angle of 45° to V.P and 25mm above
HP in centre of circular lamina and 15 mm in front of VP
A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

26. Problems in Projection of Planes
13.A rectangle ABCD 30 x 60 is perpendicular to VP and inclined
at 450 HP Draw the projection of lamina.
A plane inclined to HP and perpendicular VP
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Dr.RGM, Professor/ Mechanical

27. Problems in Projection of Planes
14.Draw the projections of a circular lamina of 50 mm diameter.
The lamina is inclined a an angle of 40° to V.P and lies in a
plane.
A plane inclined to VP and perpendicular HP
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Dr.RGM, Professor/ Mechanical

28. Problems in Projection of Planes
14.Draw the projections of a hexagonal lamina of 30 mm side
has a corner at 20mm from the VP and 50mm from the HP. Its
surface is inclined at 45° to V.P and perpendicular HP.
A plane inclined to VP and perpendicular HP
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Dr.RGM, Professor/ Mechanical

29. Problems in Projection of Planes
15.A square lamina PQRS of side 40mm is perpendicular to
VP and HP. Draw its projections
A plane perpendicular both VP and HP
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Dr.RGM, Professor/ Mechanical

30. Problems in Projection of Planes
16 . A semicircle of diameter, CD = 50 is kept in the 1st quadrant
such that its diameter is perpendicular to V.P and H.P, Draw its
projections, when the diameter is near V.P, distance of diameter
from H.P is 15 mm and from V.P is 20mm
A plane perpendicular to both VP and HP
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Dr.RGM, Professor/ Mechanical

31. Problems in Projection of Planes
A plane inclined to both VP and HP
17.Rectangle 30mm and 50mm sides is resting on HP on one
small side which is at 30° inclined to VP. while the surface of the
plane makes at 45° inclination with HP. Draw it’s projections.
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Dr.RGM, Professor/ Mechanical

32. Problems in Projection of Planes
A plane inclined to both VP and HP
18. A regular pentagon of 30 mm sides is resting on HP on one
of it’s sides with it’s surface 45° inclined to HP. Draw it’s
projections when the side in HP makes 30° angle with VP.
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Dr.RGM, Professor/ Mechanical

33. Problems in Projection of Planes
A plane inclined to both VP and HP
19. A regular pentagon of 30 mm sides is resting on HP on one
of it’s sides while it’s opposite vertex (corner) is 30 mm above
HP. Draw projections when side in HP is 30° inclined to VP.
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Dr.RGM, Professor/ Mechanical

34. Problems in Projection of Planes
A plane inclined to both VP and HP
20. A rectangular plate of 60x40 mm has one of its shorter edge
in the VP and inclined 40° to the HP. Draw its top view is a
square of side 40 mm.
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Dr.RGM, Professor/ Mechanical

35. Problems in Projection of Planes
A plane inclined to both VP and HP
21. A square plate ABCD of 50mm side has one of its corner A
on the ground, its diagonal AC inclined at 30° to the HP and the
diagonal BD inclined at 45° to the VP and parallel to the HP.
Draw its projection.
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Dr.RGM, Professor/ Mechanical

36. Problems in Projection of Planes
A plane inclined to both VP and HP
22. A square plate ABCD of 40mm side has one of its corner A
on the ground, its diagonal AC inclined at 45° to the HP and
apparently inclined at 30° to the VP. Draw its projection.
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Dr.RGM, Professor/ Mechanical

37. Problems in Projection of Planes
A plane inclined to both VP and HP
23. A pentagonal lamina of 30mm side has one edge in HP and
inclined at 30° to the VP. Draw its projection when its surface is
inclined at 45° to the HP.
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Dr.RGM, Professor/ Mechanical

38. Problems in Projection of Planes
A plane inclined to both VP and HP
24.Draw the projections of a hexagon of side 30mm having one
of its sides in HP and top view inclined at 65° to the VP and the
surfaces inclined at 35° to the HP.
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Dr.RGM, Professor/ Mechanical

39. Problems in Projection of Planes
A plane inclined to both VP and HP
25.A circular plate of diameter 60 mm has the end A of the
diameter AB in the HP and the plate is inclined at 45° to the HP.
Draw its projections when the diameter AB appears to be inclined
at 60° to the VP in the top view.
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Dr.RGM, Professor/ Mechanical

40. Problems in Projection of Planes
A plane inclined to both VP and HP
26. An isosceles triangle of 40 mm long base side, 60 mm long
altitude is freely suspended from one corner of Base side .It’s
plane is 45° inclined to VP. Draw it’s projections.
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Dr.RGM, Professor/ Mechanical

41. Problems in Projection of Planes
A plane inclined to both VP and HP
27. A thin circular plate with 60 mm diameter appears in the front
view as an ellipse of major and minor axes 60 mm and 40 mm
length respectively . Draw the projection of circular plate when
one of the diameters is parallel to both the reference planes.
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Dr.RGM, Professor/ Mechanical

42. Problems in Projection of Planes
A plane inclined to both VP and HP
28. A regular hexagonal lamina of 25 mm side has a central
square hole of 20 mm size. Draw the front and top views when
the surface of the lamina is inclined at 450 to the HP. A side of
lamina is inclined at 350 to VP.
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Dr.RGM, Professor/ Mechanical

43. Problems in Projection of Planes
A plane inclined to both VP and HP
29. A circular lamina of diameter 60 mm has the end A of the
diameter AB in the HP and the end B on the VP. Draw its
projections when the surface inclined at 400 to the HP and 500 to
VP.
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Dr.RGM, Professor/ Mechanical

44. Problems in Projection of Planes
A plane inclined to both VP and HP
30. Draw the projections of a pentagonal sheet of 25 mm side
resting on VP having its surface inclined at 300 to VP. its one side
is parallel to VP and inclined at 450 to HP
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Dr.RGM, Professor/ Mechanical