# Tutorial 3

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INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
Department of Civil Engineering
Tutorial Sheet #03: Engineering Curves

Time: 180 minutes                                        ME 111: Engineering Drawing (2009-10)
Maximum Marks: 100

1. Draw an ellipse for which the eccentricity is 3/4 and the distance between the focus and
directrix is 70 mm, using eccentricity method. Draw normal and tangent to the curve at a
point 40 mm above the axis.                                                            [15]
2. A cricket ball is thrown and reaches a maximum height of 20 m and falls on the ground at a
horizontal distance of 70 m from the point of projection. Assuming point of projection is
from the ground level and the trajectory is a parabola, trace the path of the ball. Draw a
normal and tangent to the parabola at a point 10 m above the ground. Use rectangle method
to construct parabola and use appropriate scale.                                       [15]
3. The distance between two fixed points is 90 mm. A point P moves such that the difference of
its distance from the two fixed points is always equal to 60 mm. (i) Draw the loci of P. and
(iii) Draw a tangent to the curve at a point lying on it which is 30 mm from one of foci. [15]
4. Construct the involute of the object shown in the figure below. The thin object consists of a
semi-circular part (top portion) with diameter 60 mm (length 1-2) and a semi-hexagonal part
(bottom portion).                                                                      [20]

5. A circular disc of diameter AB = 80 mm rotates about its centre with uniform angular
velocity. During one complete revolution, a point P moves at a constant linear velocity along
the diameter AB from A to the centre of the disc. Draw the locus of the point P. Draw the
tangent to the curve at a point which is at a radial distance of 30 mm from the centre. [15]
6. A wheel of a vehicle has outer diameter of 0.75m. The vehicle passes over a small bridge
having the radius of curvature 2.5m. Draw the locus of the tip of the inflating valve of tube
for one revolution of the wheel. The tip of the valve is 0.2m inside the periphery of the
wheel. Name the curve.                                                                  [20]

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