Construction of conical curves by Eccentricity
method.
i.Ellipse
1.
Construct an ellipse when the distance between the focus and the directix is 30
mm and the eccentricity is 3/4. Draw
tangent and normal at any point on the curve using directrix.
2.
A fixed point F is 7.5 cm from a fixed straight line. Draw the locus of a point
P moving in such a way that its distance from the fixed straight line is 2/3
times its distance from focus F. Name the curve. Draw normal and tangent at a
point 6cm from focus F.
ii. Parabola
1. Construct a parabola when the distance
between focus and the directrix is 40 mm. draw tangent and normal at any point
P(locus) on the curve.
2.
A fixed point F is 6.5 cm from a fixed straight line. Draw the locus of a point
P moving in such a way that its distance from the fixed straight line is equal
to its distance from F. Name the curve. Draw normal and tangent at a point 6 cm
from focus F.
iii.Hyperbola
1.
Construct a curve when the distance between the focus and directix is 40 mm.
The eccentricity is 4/3. Draw a tangent and normal at 5cm from focus on the
curve.
2. . A fixed point F is 5.5 cm from a fixed
straight line. Draw the locus of a point P moving in such a way that its
distance from the fixed straight line is 3/2 times its distance from focus F.
Name the curve. Draw normal and tangent at a point 5.5 cm from focus F.
Cycloids
1.
A coin of 40 mm diameter rolls over a horizontal table without slipping. A
point on the circumference of the coin is in contact with the table surface in
the beginning and after one complete revolution. Draw the path traced by the
point. Draw a tangent and normal at any point on the curve.
2.
A roller of 40mm diameter rolls on a straight line without slip. In the initial
position the diameter AB of the circle is parallel to the line on which it
rolls. Draw the locus of the point A and B for one complete revolution of the
roller. Name the curve. Draw a tangent and normal at any point on the curve.
3.
A circle of 40mm diameter rolls on a horizontal line. Draw the curve traced out
by a point R on the circumference for one half revolution of the circle. For
the remaining half revolution the circle rolls on the vertical line. The point
R is vertically above the center of the circle in the starting position.
Involute of square and circle
1.
Draw the involute of a square of side 25 mm. Draw a tangent and normal at any
point M.
2.
A string( thread or coir) is unwound from a drum of 30 mm diameter. Draw the
locus of the free end of the coir for unwinding through an angle of 3600.
Draw also normal and tangent at any point on the curve.
3.
An inelastic string of length 100 mm is wound around a circle of 26 mm
diameter. Draw the path traced by the end of the string.
4.
An inelastic string is wound around the circumference of a semi-circular
cylinder of diameter 66 mm. The string is wound completely by holding its free
end such that it is always tightly stretched. Draw the path of the free end of
the string.
Orthographic projection
Draw
an orthographic projection (Front and Top view, Left side view and Right side
view) for a given perspective projection using first angle projection.
Note:-
(Front
view or Elevation)
(Top
view or Plan)
Unit-2
Projection of points
1.
Point A is 30mm above HP and 45mm in front of VP. Draw its Front view
(Elevation) and Top view (Plan).
2.
Draw the projections of a point A lying on HP and 50mm in front of VP.
3.
Draw the projection of a point A lying on VP and 55 mm above HP.
4.
Mark the projection of the following points on a common reference line keeping
the projectors 15 mm apart
A-25mm above HP and 35mm
in front of VP, B-25mm above HP and 40mm behind VP,C-30mm below HP and 45mm behind VP, D-30mm below HP and 40mm in front of VP, E- 25mm above HP and VP, F-35mm
below HP and VP, G- 25mm in front of
VP and on HP, H- 20mm behind VP and
on HP.
5.
Draw the projections of the following points on a common reference ine.
I - 23mm above HP
and 28mm in front of VP, J- 40mm
below HP and 15mm behind VP, K- 50mm
above HP and 25mm behind VP, L- 45mm
below HP and 17mm behind VP, M-30mm
behind VP and HP
Projection of straight lines
Line
parallel to both HP and VP.
1.
A line CD 30mm long is parallel to both the planes. The line is 40mm above HP
and 25mm in front of VP. Draw its orthographic projections (Front and Top view)
2.
A line RS 60mm long lies in HP and 45mm infront of VP. Draw its orthographic
projections.
3.
A line PQ 55mm long is lying in VP and 45mm above HP. Draw its projections.
4.
A line AB 55mm long is lying on both HP and VP. Draw its projections.
Line
perpendicular to one plane and parallel to the other plane.
1.
A line AB 25mm long is parallel to VP and perpendicular to HP. Point A is 35mm
above HP and 20mm in front of VP. Point B is 10mm above HP. Draw the projection
of the line AB.
2.
A line AB 25mm long is perpendicular to VP and parallel to HP. Its end A is
10mm in front of VP and the line is 20mm above HP. Draw the projections of the
line.
Line
parallel to one plane and inclined to other plane.
1.
A line PQ 40mm long is parallel to VP and inclined at an angle of 300
to HP. The lower end P is 15mm above HP and 20mm in front of VP. Draw the
projections of the line.
2.
Draw the projections of a line EF 40mm long parallel to HP and inclined at 350
VP. E is 20 mm above HP and 15mm in front of VP.
3.
A line AB 50mm long is in VP and inclined at 350 to HP. End A is
10mm above HP. Draw the projections.
4.
A line RS measuring 52mm is in HP and inclined at an angle of 450 to
VP. The end R is 10mm in front of VP. Draw the projections.
Line
inclined to both HP and VP
(Rotating
line method)
1.
A line CD measuring 80mm (True length of line) is inclined at an angle of 300
to HP and 450 to VP. The point C is 20mm above HP and 30mm in front
of VP. Draw its orthographic projection of the straight line. Find the length
of Front view (Elevation), Top view (Plan) and Apparent angles.
2.
A line PQ 75mm long has its end P in both HP and VP. It is inclined at an angle
of 300 to HP and 450 to VP. Draw its projections.
3.
A line AB is 75mm long. A is 50mm in front of VP and 15mm above HP. B is 15mm
in front of VP and is above HP. Top view of AB is 50mm long. Find the front
view length and the true inclinations.
4.
A line measuring 80mm long has one of its ends 60mm above HP and 20mm in front
VP. End B is 40mm above HP and 65mm in front of VP. Draw the projections of AB.
Find its inclination with HP and VP.
5.
The distance between the projectors of two points A and B is 70mm. A is 10mm
above HP and 15mm in front of VP. B is 50mm above HP and 40mm in front of VP.
Find the shortest distance between A and B by rotating line method. Find true
inclinations of AB with VP and HP.
(Midpoint method)
1.
The midpoint M of a straight line AB is 60mm above HP and 50mm in front of VP.
The line measures 80mm long and inclined at an angle of 300 to HP
and 450 to VP. Draw its projections.
2.
The projections of a line measures 80mm in the top view and 70mm in the front
view. The mid point of the line is 45mm in front of VP and 35mm above HP. One
end is 10mm in front of VP and nearer to it. Draw the projections. Find true
length and true inclinations with reference planes.
3.
A line AB 120mm long is inclined at 450 to HP and 300 to
VP. Its mid point C is in VP and 20mm above HP. The end A is in third quadrant
and B is in first quadrant. Draw the projection of the line.
Projection of plane or plane surfaces or lamina or
plate
Plane surface perpendicular to one plane
and parallel to the other plane
1.
A square lamina ABCD of side 40mm is perpendicular to HP and parallel to VP.
Draw its orthographic projection (front and top view).
2.
Square lamina of side 40mm is perpendicular to VP and parallel to HP. Draw its
projections.
Plane
surface perpendicular to one plane and inclined to other plane
1.
A regular pentagonal plate of side 28mm is place with one side on HP such that
the surface is inclined at 450 to HP and perpendicular to VP. Draw
its projections.
2.
A regular hexagonal plate of side 25mm is place with one side 15mm in front VP
such that the surface is inclined at 300 to VP and perpendicular to
VP. Draw its projections.
3.
A regular pentagonal plate of side 28mm is place with one side on VP such that
the surface is inclined at 450 to VP and perpendicular to VP. Draw
its projections.
4. A thin circular metal plate of 40mm diameter,
having its plane vertical and inclined at 400 to VP. Its centre is
33mm above HP and 25mm in front of VP. Draw its projections.
Plane
surface inclined to both HP and VP
1.
Draw the projections of a pentagonal sheet of 26mm side, having its surface inclined
at 300 to VP. Its one side is parallel to VP and inclined at 450
to HP.
2.
A hexagonal lamina of 26mm side has a side 10mm in front of VP and inclined at
300 to HP. Its surface is inclined at 450 to VP. Draw its
projections.
3.
A regular pentagonal lamina of 30mm sides has one edge 15mm above HP and
inclined at an angle of 300 to VP. Draw its projections when its
surface inclined at 450 to HP.
4.
A hexagonal lamina of 20mm side rests on one of its corners on the HP. The
diagonal passing through this corner is inclined at 450 to the HP.
The lamina is then rotated through 900 such that the top view of
this diagonal is perpendicular to the VP and the surface is still inclined at
450 to the HP. Draw the projections of the lamina.
5.
A regular hexagonal lamina of 26mm side has a central hole of 30mm diameter.
Draw the front and top views when the surface of the lamina is inclined at 450
to HP. A side of lamina is inclined at 350 to VP.
6.
A circular lamina of 60mm diameter rests on HP on a point 1 on the
circumference. The lamina is inclined to HP such that the top view of it is an
ellipse of minor axis 35mm. The top view of the diameter through the point 1
makes an angle of 450 with VP. i. Draw the projections. Ii.
Determine the andgle made by the lamina with HP.
7.
A semi-circular lamina of 64 mm diameter has its straight edge in VP and
inclined at an angle of 450 to HP. The surface of the lamina makes
an angle of 300 with VP. Draw the projections.
Unit-3
Projection
of solids
Axis
of solid perpendicular to any one of the plane (either HP or VP)
1.
Draw the top and front views of a cube of 40mm side resting with one of its
square faces on HP such that one of its vertical faces is parallel to and 20mm
in front of VP.
2.
Draw the projections of a square prism of side of base 30mm and height 50mm
resting with its base on HP such that one of its rectangular faces is
perpendicular to VP. The nearest edge parallel to VP is20mm in front of it.
3.
A rectangular prism side of base 40mm x 25mm and height 60mm rests with its
base on HP such that one of its larger rectangular faces is parallel to VP.
Draw its projections.
4.
Draw the projections of a regular pentagonal prism side of base 30mm and axis
55mm resting with its base on HP such that one of its rectangular faces is
perpendicular to VP.
5.
Draw the projections of a pentagonal prism side of base 30mm and axis 60mm long
resting with its base on HP such that one of its rectangular faces is parallel
to and 10mm in front of VP.
6.
Draw the projections of a hexagonal prism of side of base 25mm and height 50mm
resting with its base on VP such that one of its rectangular faces is
perpendicular to HP.
7.
Draw the projections of a cylinder of base 30mm diameter and axis 50mm long resting
with its base on HP and axis 50mm long resting with its base on HP and axis
25mm in front of VP.
8.
Draw the projections of a pentagonal pyramid, side of base 30mm and height 60mm
resting with its base on HP such that one of the edges of the base is perpendicular
to VP.
9.
A hexagonal pyramid side of base 30mm and height 60mm rests with its base on VP
such that one of the edges of the base is parallel to and 15mm above HP. Draw
its projections.
10.
Draw the projections of a right circular cone of base 40mm diameter and height
60mm when resting with its base on HP.
Axis
of the solid is inclined to one plane and parallel to other plane
1.
A pentagonal prism side of base 25mm and axis 50mm long, rests with one of its
edges on HP such that the base containing that edges makes an angle of 300
to HP and its axis is parallel to VP. Draw its projections.
2.
A hexagonal pyramid side of base 25mm and axis 50mm long rests with one of the
edges of its base on HP and its axis is inclined at 300 to HP and
parallel to VP. Draw its projections.
3.
Draw the projections of a cylinder base 30mm diameter and axis 40mm long
resting with a point of its base circle on VP such that the axis is making an
angle of 300 with VP and parallel to HP.
4.
Draw the projections of a pentagonal pyramid of base 25mm side axis 60mm long
when it is lying on HP on one of its base edges such that the axis is parallel
to VP and inclined at 300 to HP.
5.
A hexagonal prism side of base 25mm and axis 50mm long rests with one of its
base corners on VP such that its base makes an angle of 600 to VP
and its axis is parallel to HP. Draw its projections.
6. Draw the projections of a cone, base 30mm
diameter and axis 50mm long resting on HP on a point of its base circle with
the axis making an angle of 450 with HP and parallel to VP.
7.
Draw the top and front views of a cone of base diameter 46mm and height 65mm
lying with one of its generators on HP. The axis is parallel to VP.
8.
Draw the projections of pentagonal prism of 30mm side of base and 65mm long it
is lying on one of its longer edges on HP with one rectangular face
perpendicular to HP such that the axis makes 600 with VP.
9.
A square pyramid of base end 40mm and axis 60mm is lying on VP on one of its
triangular faces with the plane containing the axis parallel to HP and 30mm
above it. Draw the projections of the pyramid.
10.
A cone of base 40mm diameter and axis 50mm long touches VP on a point of its
base circle. Its axis is inclined at 300 to VP and parallel to HP.
Draw its projections.
11.
A cone of diameter 40mm and height 60mm is freely suspended from one of its
base points such that the axis is parallel to VP. Draw its front and top view.
Projection of solid using auxiliary
plane method
1. A hexagonal
prism, side of base 20mm and axis 48mm long, rests with its base on HP such
that an edge of the base is parallel to VP. Draw the projection of the prism on
an Auxiliary Inclined Plane (A.I.P) which makes an angle of 600 with
the HP
2. A hexagonal
prism, side of base 25mm and axis 60mm long, lies with one of its rectangular
faces on HP, such that the axis is inclined at 450 to VP. Draw its
projections using auxiliary plane method.
3. A hexagonal
pyramid, side of base 22mm and axis 50mm long, rests with one of the corners of
its base on HP. The axis is inclined at 300 to HP and parallel to
VP. Draw its projections using auxiliary plane method.
