Mechanical Drafting Projection of solids

Mechanical Drafting
Projection of Solids.
Gaurav Mistry
AssistantProfessor
Diwaliba Polytechnic, UTU.

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 Introduction to Projections MechanicalDrafting
 “A projection is defined as an image or a drawing of an object made
on a plane”.
 All drawings used in the field of engineering are based on the
principles of projection.
 This is the reason engineering drawings are capable of precisely
conveying the external as well as internal features of objects in terms
of their shape and size.
 Projections can be classified on the basis of the lines of sight and the
positions of planes on which the drawing is made.
 The lines of sight are popularly called projectors and the planes on
which the drawings are made are called planes of projection.

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 “Figure shows the detailed classification of projections.”

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 “Figure shows the detailed classification of projections.”
Vertical Plane (VP)
HorizontalPlane (HP)
(VP)
(HP)

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 “Terminology”
1. Vertical plane: Vertical plane, also known as front reference plane, is assumed to be
placed vertically and is denotedby V.P.
2. Horizontal plane: Horizontal plane, also known as horizontal reference plane, is
assumed to be placed horizontallyand is denoted by H.P. It is perpendicularto V.P.
3. Profile plane: A plane perpendicular to both the above planes is known as a profile
plane. The plane on the right end of the planes is known is right profile plane while the
planeon the left end is known as left profile plane.
4. Reference plane: All the above mentioned mutually perpendicular planes are called
reference planes.
5. Principal plane:It is an alternative name of the reference plane.
6. Reference line: The line of intersection between the principal planes is known as a
reference line. It is also popularlycalled xy line.
7. Front view: The view of an object by observing it from the front and drawn on the
V.P. is called front view (F.V.) or elevation.
8. Top view: The view of an object by observing it from the top and drawn on the H.P.
is called top view (T.V.) or plan.
9. Side view: The view of an object by observing it from the left-hand side or right-
hand side and drawn on a profile planeis called side view or end view.

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 Introduction to Solids MechanicalDrafting
 “A three dimensional objects are called SOLIDS”

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Polyhedron: A polyhedron is a solid bounded by planes called faces, which meet in
straight lines called edges. A regular polyhedron has all the faces equal and regular.
a) Tetrahedron:It has four equal equilateraltriangular faces.
b) Cube: It has six equal square faces.
c) Octahedron:It has eight equal equilateral triangular faces.
d) Dodecahedron:It has 12 equal pentagonal faces.
e) Icosahedron:It has 20 equal equilateral triangular faces.

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Prism: A prism is a polyhedron with two n-sided polygonal bases which are parallel
and congruent, and lateral faces are rectangles.
• All cross-sections parallel to the bases are congruent with the bases. An imaginary
line that joins the centre of the bases is called an axis.
• A right and regular prism has regular polygonal bases, axis perpendicular to the
bases and all the faces are equal rectangles (which are parallel to principle planes), ,
as shown in Fig.
• Prisms are named according to the shape of their base, so a prism with a triangular
base is called a triangular prism; a square base is called a square prism and so on.

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Pyramid: A pyramid is a polyhedron with n-sided polygonal base and lateral faces
are triangles meeting at a point called the vertex or apex.
• An imaginary line that joins the apex with the centre of the base is known as the
axis. A right and regular pyramid has a regular polygon base, axis perpendicular to
the base and all the faces are equal isosceles triangles (which are not parallel to
principleplanes), as shown in Fig.
• Pyramids are named according to the shape of their base, so a pyramid with a
triangular base is called a triangular pyramid; a square base is called a square
pyramid and so on. The centre of gravity of pyramids lies on the axis at one-fourth
of its height from the base.

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Solid of Revolution: These solids are obtained by revolving a plane figure like
rectangle, triangle or a semi-circle about a fixed line.
(a). Cylinder: A cylinder is a solid of revolution obtained by revolving a rectangle
about one of its fixed side called an axis. It can be imagined as a prism of infinite
number of lateral faces. Any line on the surface of a cylinder is called its generator.
Thus, a cylinder has an infinite number of generators. A right cylinder has all the
generators and the axis perpendicular to the base, as shown in Fig (a).
(b). Cone: A cone is obtained by revolving a triangle about its fixed side called an axis.
A cone can be imagined as a pyramid with infinite number of lateral faces. Any line on
the surface of a cone is called its generator. Thus, a cone has an infinite number of
generators. A right cone has all generators of equal length and the axis perpendicular to
the base, as shown in Fig (b).
(c). Sphere: A sphere is obtained by revolving a semi-circle around its diameter, as
shown in Fig (c).

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Recommended method of labelling:

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 Projection of Solids MechanicalDrafting
Orientation of Solids:
The solid may be in one of the following positions:
1. Axis perpendicular to the H.P. (True shape of Base on H.P/T.V)
2. Axis perpendicular to the V.P. (True shape of Base on V.P/F.V)
3. Axis parallel to both the H.P. and the V.P. (i.e., perpendicular to the
profile plane) (True Shape of Base on P.P/Side View)
4. Axis inclined to the H.P. and parallel to the V.P. (True shape of Base
on H.P/T.V) (Two Stages)
5. Axis inclined to the V.P. and parallel to the H.P. (True shape of Base
on V.P/F.V) (Two Stages)
6. Axis inclined to both the H.P. and the V.P. (Final/Actual View)
(Three Stages)

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MechanicalDrafting
1. Axis perpendicular to the H.P. (True shape of Base on H.P/T.V)
• This is one of the basic positions of the solid. It is evident that if the axis of a right solid is
perpendicular to the H.P., its base will be parallel to the H.P.
• The true shape and size of the base can be viewed in the top view.
• Therefore, first obtain the top view of the solid and then project it to obtain the front view.
a. Side of the base parallel/perpendicular to V.P.
(Fig.a)
b. Side of base inclined at 30 deg to V.P (Fig. b)
c. All sides of base equally inclined at 45 deg to
V.P (Fig.c)
a. Face/side of the base parallel/perpendicular to V.P.
(Fig.a)
b. Face/side of base inclined at 30 deg to V.P (Fig. b)
c. All Faces/sides of base equally inclined at 45 deg
to V.P (Fig.c)
 Projection of Solids

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MechanicalDrafting
2. Axis perpendicular to the V.P. (True shape of Base on V.P/F.V)
• This is another basic position of the solid. It is evident that if the axis of a right solid is
perpendicular to V.P., its base will be parallel to the V.P.
• The true shape and size of the base can be viewed in the front view.
• Therefore, first obtain the front view of the solid and then project it to obtain the top view.
a. Face/side of the base parallel to
H.P. (Fig.a)
b. Face/side of base perpendicular
to H.P (Fig. b)
c. Face/side of base inclined at 45
deg to H.P (Fig.c)

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MechanicalDrafting
3. Axis parallel to both the H.P. and the V.P. (i.e., perpendicular to the profile plane)
(True Shape of Base on P.P/SideView)
As the axis is parallel to both the principle planes, the true shape and size of the base is
seen in the side view. Therefore, draw a pentagon on side view keeping one of its side
of base on XY.

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MechanicalDrafting
Axis inclined to one plane. (INITIAL POSITION OF THE SOLID)

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MechanicalDrafting
Axis inclined to one plane. (IDENTIFY VISIBLE AND HIDDEN LINES)
General rule adopted to identify and distinguish the visible and the hidden lines in
the orthographic views of the solid are as follows:
1. Outlines of an object are always visible, the outer edges of any view should be
shown with continuouslines (i.e., dashed narrow lines should never be used.)
2. The edges or faces in a view that are towards the observer (away from xy) are
visible. The corresponding edges or faces in the other view should be drawn using
continuouslines.
3. The edges or faces in a view that are away from the observer (towards xy) are not
visible. The corresponding edges or faces in the other view should be drawn using
dashed narrow lines.
4. Two continuous lines never cross each other inside. Similarly, two hidden lines
never cross each other.
5. When two lines representing the edges cross each other, one of them must be
dashed narrow line. These rules are applicable for only single solid. They do not
apply for the solids with a holeor combination of solids.

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MechanicalDrafting
4. Axis inclined to the H.P. and parallel to the V.P. (True shape of Base on H.P/T.V)
Pentagonal Prism having edge of its
base on HP
Pentagonal Prism having corner of its base on
HP

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MechanicalDrafting
Hexagonal Pyramid having its
triangular face on H.P (Ground).
Hexagonal Pyramid having its slant edge on
H.P (Ground).

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MechanicalDrafting
Cylinder having its generator in V.P and axis inclined at 45 deg to H.P

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MechanicalDrafting
5. Axis inclined to the V.P. and parallel to the H.P. (True shape of Base on V.P/F.V)
Pentagonal Pyramid having triangular face in
the V.P. and the base edge contained by that
triangular face is perpendicular to the H.P.
Pentagonal Prism having one of its rectangular
faces on the H.P. and the axis inclined at 60° to
the V.P.

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MechanicalDrafting
5. Axis inclined to the V.P. and parallel to the H.P. (True shape of Base on V.P/F.V)
A cone having a generator in the V.P. and the
axis parallel to the H.P.
Hexagonal Prism having edge of base on VP and
axis inclined at 45 deg to VP

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MechanicalDrafting
Orientation of Solids: (Most Important)
6. Axis inclined to both the H.P. and the V.P. (Final/ActualView) (Three Stages)
a. Element of solid in HP
A square prism of base edge 35 mm and axis 60 mm is resting on an edge of its base on the H.P. and the axis
inclined at 45° to the H.P. If the edge resting on the H.P. is inclined at 30° to the V.P., draw its projections.

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MechanicalDrafting
A pentagonal prism of base side 30 mm and height 60 mm rests on one of its base side on the H.P. inclined at
30° to the V.P. Its axis is inclined at 45° to the H.P. Draw its projections.

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MechanicalDrafting
A square pyramid of base side 40 mm and axis 55 mm is resting on one of its triangular faces on the H.P. A
vertical plane containing the axis is inclined at 45° to the V.P. Draw its projections.

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MechanicalDrafting
A hexagonal pyramid of base side 30 mm and axis 60 mm, has an edge of its base on the ground inclined at
45° to the V.P. and the axis is inclined at 30° to the H.P. Draw its projections.

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MechanicalDrafting
A hexagonal pyramid of base side 30 mm and axis 50 mm, rests on one of its base corners on the ground
with axis inclined at 45° to the H.P. Draw its projections when a vertical plane containing the axis and the
corner that lies in the H.P. is inclined at 30° to the V.P.

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MechanicalDrafting
A hexagonal pyramid of base side 30 mm and axis 60 mm has one of its slant edges on the H.P. and inclined
at 45° to the V.P. Draw its projections when the base is visible.

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MechanicalDrafting
A hexagonal pyramid of base side 30 mm and axis 60 mm rests on an edge of base on the H.P. with the
triangular face containing that edge perpendicular to the H.P. and parallel to the V.P. Draw its projections so
that the base is visible.

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MechanicalDrafting
A pentagonal pyramid of base side 30 mm and axis 60 mm rests on a corner of its base on the H.P. such that
its apex is 55 mm above the ground. A vertical plane containing the corner of the base that lies on the H.P.
and the axis is inclined at 30° to the V.P. Draw its projections.

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MechanicalDrafting
A pentagonal pyramid of base side 30 mm and axis 60 mm rests on an edge of its base on the ground so that
the highest point of the base is 20 mm above the ground. Draw its projections when a vertical plane
containing the axis is inclined at 30° to the V.P.

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MechanicalDrafting
A pentagonal pyramid of base side 30 mm and axis 60 mm is held on a corner of its base on the ground and
the triangular face opposite to it is horizontal. Draw the projections of the pyramid when the edge of the base
contained by this triangular face is inclined at 60° to the V.P. and the apex is towards the observer.

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MechanicalDrafting
A cylinder of base diameter 50 mm and axis 65 mm rests on a point of its base circle on the H.P. Draw its
projections when the axis is inclined at 30° to the H.P. and top view of the axis is perpendicular to the V.P.

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MechanicalDrafting
A cone of base diameter 50 mm and axis 60 mm is freely suspended from the midpoint of a generator. Draw
its projections when the top view of that generator is inclined at 45° to the reference line and apex is nearer
to the observer.

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MechanicalDrafting
Draw the projections of a cube of edge 40 mm resting on one of its corners on the H.P. with a solid diagonal
perpendicular to the V.P.

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MechanicalDrafting
A square pyramid of base diagonal 50 mm and axis 60 mm is titled until the top view of the base appears as a
rhombus having one of the diagonal twice of the other. Draw its projections when the axis as a vertical plane
is inclined at 45° to the V.P.

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MechanicalDrafting
b. Element of solid in VP
A pentagonal prism of base side 30 mm and axis 60 mm has an edge of its base in the V.P. and inclined at 45°
to the H.P. Its axis is inclined at 30° to the V.P. Draw its projections.

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MechanicalDrafting
A hexagonal prism of base edge 30 mm and axis 70 mm has an edge of its base in the V.P. and inclined at 60°
to the H.P. Draw its projections, when the edge of the other base farthest away from V.P. is at a distance of 85
mm from the V.P.

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MechanicalDrafting
A square pyramid of base side 40 mm and axis 60 mm has a corner of its base in the V.P. A slant edge
contained by that corner is inclined at 45° to the V.P. Draw its projections when a plane containing the slant
edge and the axis is inclined at 45° to the H.P.

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MechanicalDrafting
A cone of base diameter 50 mm and axis 60 mm has one of its generators in the V.P. and inclined at 30° to
the H.P. Draw its projections when the apex is 15 mm above the H.P.

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MechanicalDrafting Projection of Solids
A pentagonal prism rests on one of its edges of the base on HP with its axis is inclined at 45° to the HP. The
top view of the axis is inclined at 30° to the VP. Draw the projections of the prism assuming the edge of the
base to be 30 mm and the axis 70 mm long.
Solution:
Given Data:
1. Base Shape: Pentagon
2. Initial Stage:
 Resting on its base edge on HP. Element is on HP therefore True shape of base i.e. pentagon will be
drawn on HP (Top View).
 Since it is prism, the Front View will be Rectangular shape on VP.
3. Intermediate Stage:
 Axis inclined at 45 deg to HP (seen in Front view (VP)).
 Take projections from above and draw Top View on HP.
4. Final Stage (Real View):
 Axis is inclined at 30 deg to VP, so the Top View from Intermediate stage will be repeated (redrawn) but
at an angle of 30 deg to XY line.
 Now take projections from below and draw Front View on VP.
Orientation of Solids: (Problem 1)

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MechanicalDrafting
Orientation of Solids: (Solution 1)

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A Hexagonal Pyramid, Base 25 mm side and Axis 55 mm long, has one of its slant edges on the HP. A plane
containing that edge and axis is perpendicular to the HP and inclined at 45° to the VP. Draw its projections
when the Apex is nearer to VP then the Base.
Solution:
Given Data:
1. Base Shape: Hexagon
2. Initial Stage:
 Resting on its Slant edge on HP. Element is on HP therefore True shape of base i.e. hexagon will be
 Since it is pyramid, the Front View will be triangular shape on VP.
 Plane containing that edge and axis both is inclined at 90 deg (perpendicular) to HP (seen in Front view
(VP)).
 And that plane is inclined at 45 deg to VP, so the Top View from Intermediate stage will be repeated
(redrawn) but at an angle of 45 deg to XY line.

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A cone, base diameter 50 mm and axis length 60 mm is kept on the HP on a point of its base circle in such a
way that its axis makes an angle of 30° with HP. Draw the projections of the cone when plan of axis is
making 45° to the XY line.
Solution:
Given Data:
1. Base Shape: Circle
2. Initial Stage:
 Resting on a point of base circle on HP. Element is on HP therefore True shape of base i.e. circle will be
 Since it is cone, the Front View will be triangle shape on VP.
 Plan (top view) of Axis is inclined at 45 deg to XY line (VP), so the Top View from Intermediate stage
will be repeated (redrawn) but at an angle of 45 deg to XY line.

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A cylinder, base diameter 500 mm and axis length 70 mm is kept on the HP on the point of its base circle in
such a way that its axis makes an angle of 30° with HP. Draw the projections of the cylinder when plan of
axis is making 45° to the XY line.
Solution:
Given Data:
1. Base Shape: Circle
2. Initial Stage:
 Resting on a point of base circle on HP. Element is on HP therefore True shape of base i.e. circle will be
 Since it is cylinder, the Front View will be rectangular shape on VP.
 Plan (top view) of Axis is inclined at 45 deg to XY line (VP), so the Top View from Intermediate stage
will be repeated (redrawn) but at an angle of 45 deg to XY line.

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MechanicalDrafting Projection of Solids (For Self Study)
(a) Pentagonal Prism (b) Hexagonal Pyramid
(c) Cone (d) Cylinder

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REFERENCES:
1. Machine Drawing, K. L. Narayan, New Age Int. Pub.
2. Mechanical Drafting, S. V. Gosai, Atul prakashan.
3. Engineering Drawing, Basant Agrawal and C M Agrawal, McGraw Hill,
4. www.google.com
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Mechanical Drafting Projection of solids

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