DHANALAKSHMI COLLEGE OF ENGINEERING,
Chennai 601 301.
Question bank
(Unit 1 and Unit 2)
Unit 1
Conic Sections, Cycloids, Involutes
1. The focus of a conic is 50 mm from the directrix. Draw the locus of a point P moving in such a way that its distance from the directrix is equal to its distance from focus. Name the curve. Draw a tangent to the curve at a point 60 mm from the directrix.
2. Construct a curve traced by the point when the distance of focus from the directrix is 50 mm and the eccentricity is 3/2. Draw the tangent and normal at any point on the curve.
3. 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 F. Name the curve. Draw normal and tangent at a point 6 cm from F.
4. A roller of 40 mm diameter rolls over a horizontal table without slipping. A point on the circumference of the roller is in contact with the table surface in the beginning and after one complete revolution. Draw the path traced by the point
5. Draw the curve traced by a point on the circle of diameter 40 mm when it rolls inside another
circle of diameter 160 mm diameter for one complete revolution in counterclockwise direction.
Draw the tangent and normal at a point 65 mm from the centre of the circle. Name the curve.
6. A circle of 50 mm diameter rolls on a horizontal line for one and half revolution. Draw the path traced by a point P on the circumference of the circle.
7. Draw the curve traced by a point on the circle of diameter 40 mm when it rolls outside another
circle of diameter 150 mm for one revolution in clockwise direction. Draw the tangent and
normal to it at a point 95 mm from the centre of the directing circle.
8. An inelastic string of 100 mm long has one stone end attached to the circumference of a circular disc of 26 mm diameter. Draw the curve traced out by the other end of the string, when it is completely wound around the disc keeping it always tight. Draw the tangent and normal at any point on the curve.
9. Draw the path traced by the end of the string when it wound around a hexagon of side 40 mm.
Unit 2
Projection of points
1. The projections of the different points are shown in the figure 1. Define the position of the
points
in relation to the reference planes. The distances marked are in millimeters
2. Draw the projections of the following points on a common reference line.
(a) M, 35 mm behind VP and 20 mm below HP
(b) N, 40 mm infront of VP and 30 mm above HP
(c) O, 50 mm behind VP and 15 mm above HP
(d) P, 40 mm below HP and on VP
(e) Q, 30 mm infront of VP and 50 mm below HP
(f) R, 35 mm behind VP and on HP
3. Projections of various points are given in the figure. Determine their position of the
with respect to HP and VP and mention their quadrant. Distances are given in mm.
4. Mark the projections of the following points on a common reference line.
(a) P, 25 mm below the HP and in the VP
(b) Q, 40 mm behind the VP and in the HP
(c) R, 30 mm below the HP and 30 mm infront of the VP
(d) S, 25 mm above the HP and 25 mm behind the VP
(e) T, 25 mm above the HP and 30 mm infront of the VP
(f) U, is in both HP and VP
(g) V, 35 mm below the HP and 30 mm behind the VP
(h)W, 30 mm above the HP and 35 mm behind the VP.
Projection of straight lines
1. Draw the projections of a straight line AB of 80 mm long when one of its end A, is in both
HP and VP. The angle of inclinations with HP and VP are 40°and 50° respectively.
2. A line AB measuring 75 mm long has one of its ends 50 mm infront of VP and 15 mm above HP. The top view of the line is 50 mm long. Draw and measure the front view. The other end is 15 mm infront of VP and is above HP. Determine true inclinations and apparent angles.
3. A line AB 85 mm long has its end A 25mm above HP and 20 mm infront of VP. The end B is 60 mm above HP and 50 mm infront of VP. Draw the projections and find its inclinations with HP and VP.
4. The midpoint of a straight line AB 90 mm long is 60 mm above HP and 50 mm infront of VP. It is inclined at 30° to HP and 45° to VP. Draw its projections.
5. The projections of a line measure 60 mm in the top view and 70 mm in the front view. The midpoint of the line is 45 mm infront of VP and 35 mm above HP. One end is 10 mm infront of VP and nearer to it. The other end is nearer to HP. Draw the projections of the line. Find its true length and inclinations.
6. The end A of a line AB is 10 mm infront of VP and 20 mm above HP. The line inclined at 30° to HP and front view is inclined at 45° to xy line. The top view is 60 mm long. Complete the two
views. Find true length and true inclinations.
7. A line of length 75 mm has one of its ends 50 mm infront of VP and 15 mm above HP. The top view of the line is 50 mm long. The other end is 15 mm infront of VP and is above HP. Draw the projections and finds its true inclinations.
8. A straight line AB has its end A 20 mm above HP and 25 mm infront of VP. The other end B is 60 mm above HP and 65 mm infront of VP. The ends of the line are on same projector. Find the true length and true inclinations of the line with HP and VP.
9. A line AB 85 mm long has its end A 25 mm above the HP and 20 mm infront of VP. The top and front views of the line have the lengths of 55 mm and 70 mm respectively. Draw the projections of the line and find its true inclinations with VP and HP.
10. A straight line 70 mm long has one end 15 mm infront of VP and 60 mm above HP, while the other end is 35 mm infront of VP and 20 mm above HP. Draw the plan and elevation of the line.
Projections of planes
1. A triangular lamina of sides 40 mm is resting on HP with one of its corners touching it such that the lamina makes 60° to HP. If the side opposite to this corner makes 30° to VP, draw its
projections.
2. A circular plate of negligible thickness and diameter 60 mm has a point ‘a’ on the circumference in the VP. The surface of the point is inclined to the VP in such a way that the front view is seen as an ellipse of 30 mm long minor axis. Draw the projections of the plate when front view of diameter AB makes 45° with HP. Find the inclination of the plate with VP.
3. A semi circular plane of 60 mm diameter is inclined to the VP at 30°. The straight edge is in the VP and inclined to the HP at 45°. Draw elevation and plan.
4. A hexagonal lamina of side 30 mm is resting on VP on one of its sides and the resting edge is inclined at 40° to HP. Its surface is inclined at 35° to VP. Draw the projections.
5. A pentagonal lamina of side 30 mm is resting on HP with one of its corners. The surface is
inclined at 60° to HP. The edge opposite to this corner is parallel to VP and nearer to it. Draw its
projections.
6. A hexagonal lamina of 20 mm side rests on one of its corners in the HP. The diagonal passing through the corner is inclined at 45° to the HP. The lamina is then rotated through 90° such that the top view of the diagonal is perpendicular to the VP and the surface is still inclined at 45° to HP. Draw the projections of the lamina
7. A square lamina PQRS of side 40 mm rests on the ground on its corner P in such a way that the diagonal PR is inclined at 45° to the HP and apparently inclined at 30° to VP. Draw its projections.
8. A rectangular plate 70 x 40 mm has one of its shorter edges in the VP and inclined at 40° to the HP. Draw its top view if its front view is a square of side 40 mm.
9. A triangular plate PQR has sides PQ 50mm QR 70 mm and RP 40 mm. The side PQ rests on the HP and is inclined at 30o to VP. The surface of the plate is inclined at 40o to the HP. Draw the projections.
10. A circular plate of 50 mm diameter appears as an ellipse in the front view, having its major axis 50mm long and minor axis 30mm long. Draw the top view, when the minor axis of the ellipse is horizontal.
Chennai 601 301.
Question bank
(Unit 1 and Unit 2)
Unit 1
Conic Sections, Cycloids, Involutes
1. The focus of a conic is 50 mm from the directrix. Draw the locus of a point P moving in such a way that its distance from the directrix is equal to its distance from focus. Name the curve. Draw a tangent to the curve at a point 60 mm from the directrix.
2. Construct a curve traced by the point when the distance of focus from the directrix is 50 mm and the eccentricity is 3/2. Draw the tangent and normal at any point on the curve.
3. 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 F. Name the curve. Draw normal and tangent at a point 6 cm from F.
4. A roller of 40 mm diameter rolls over a horizontal table without slipping. A point on the circumference of the roller is in contact with the table surface in the beginning and after one complete revolution. Draw the path traced by the point
5. Draw the curve traced by a point on the circle of diameter 40 mm when it rolls inside another
circle of diameter 160 mm diameter for one complete revolution in counterclockwise direction.
Draw the tangent and normal at a point 65 mm from the centre of the circle. Name the curve.
6. A circle of 50 mm diameter rolls on a horizontal line for one and half revolution. Draw the path traced by a point P on the circumference of the circle.
7. Draw the curve traced by a point on the circle of diameter 40 mm when it rolls outside another
circle of diameter 150 mm for one revolution in clockwise direction. Draw the tangent and
normal to it at a point 95 mm from the centre of the directing circle.
8. An inelastic string of 100 mm long has one stone end attached to the circumference of a circular disc of 26 mm diameter. Draw the curve traced out by the other end of the string, when it is completely wound around the disc keeping it always tight. Draw the tangent and normal at any point on the curve.
9. Draw the path traced by the end of the string when it wound around a hexagon of side 40 mm.
Unit 2
Projection of points
1. The projections of the different points are shown in the figure 1. Define the position of the
points
in relation to the reference planes. The distances marked are in millimeters
2. Draw the projections of the following points on a common reference line.
(a) M, 35 mm behind VP and 20 mm below HP
(b) N, 40 mm infront of VP and 30 mm above HP
(c) O, 50 mm behind VP and 15 mm above HP
(d) P, 40 mm below HP and on VP
(e) Q, 30 mm infront of VP and 50 mm below HP
(f) R, 35 mm behind VP and on HP
3. Projections of various points are given in the figure. Determine their position of the
with respect to HP and VP and mention their quadrant. Distances are given in mm.
4. Mark the projections of the following points on a common reference line.
(a) P, 25 mm below the HP and in the VP
(b) Q, 40 mm behind the VP and in the HP
(c) R, 30 mm below the HP and 30 mm infront of the VP
(d) S, 25 mm above the HP and 25 mm behind the VP
(e) T, 25 mm above the HP and 30 mm infront of the VP
(f) U, is in both HP and VP
(g) V, 35 mm below the HP and 30 mm behind the VP
(h)W, 30 mm above the HP and 35 mm behind the VP.
Projection of straight lines
1. Draw the projections of a straight line AB of 80 mm long when one of its end A, is in both
HP and VP. The angle of inclinations with HP and VP are 40°and 50° respectively.
2. A line AB measuring 75 mm long has one of its ends 50 mm infront of VP and 15 mm above HP. The top view of the line is 50 mm long. Draw and measure the front view. The other end is 15 mm infront of VP and is above HP. Determine true inclinations and apparent angles.
3. A line AB 85 mm long has its end A 25mm above HP and 20 mm infront of VP. The end B is 60 mm above HP and 50 mm infront of VP. Draw the projections and find its inclinations with HP and VP.
4. The midpoint of a straight line AB 90 mm long is 60 mm above HP and 50 mm infront of VP. It is inclined at 30° to HP and 45° to VP. Draw its projections.
5. The projections of a line measure 60 mm in the top view and 70 mm in the front view. The midpoint of the line is 45 mm infront of VP and 35 mm above HP. One end is 10 mm infront of VP and nearer to it. The other end is nearer to HP. Draw the projections of the line. Find its true length and inclinations.
6. The end A of a line AB is 10 mm infront of VP and 20 mm above HP. The line inclined at 30° to HP and front view is inclined at 45° to xy line. The top view is 60 mm long. Complete the two
views. Find true length and true inclinations.
7. A line of length 75 mm has one of its ends 50 mm infront of VP and 15 mm above HP. The top view of the line is 50 mm long. The other end is 15 mm infront of VP and is above HP. Draw the projections and finds its true inclinations.
8. A straight line AB has its end A 20 mm above HP and 25 mm infront of VP. The other end B is 60 mm above HP and 65 mm infront of VP. The ends of the line are on same projector. Find the true length and true inclinations of the line with HP and VP.
9. A line AB 85 mm long has its end A 25 mm above the HP and 20 mm infront of VP. The top and front views of the line have the lengths of 55 mm and 70 mm respectively. Draw the projections of the line and find its true inclinations with VP and HP.
10. A straight line 70 mm long has one end 15 mm infront of VP and 60 mm above HP, while the other end is 35 mm infront of VP and 20 mm above HP. Draw the plan and elevation of the line.
Projections of planes
1. A triangular lamina of sides 40 mm is resting on HP with one of its corners touching it such that the lamina makes 60° to HP. If the side opposite to this corner makes 30° to VP, draw its
projections.
2. A circular plate of negligible thickness and diameter 60 mm has a point ‘a’ on the circumference in the VP. The surface of the point is inclined to the VP in such a way that the front view is seen as an ellipse of 30 mm long minor axis. Draw the projections of the plate when front view of diameter AB makes 45° with HP. Find the inclination of the plate with VP.
3. A semi circular plane of 60 mm diameter is inclined to the VP at 30°. The straight edge is in the VP and inclined to the HP at 45°. Draw elevation and plan.
4. A hexagonal lamina of side 30 mm is resting on VP on one of its sides and the resting edge is inclined at 40° to HP. Its surface is inclined at 35° to VP. Draw the projections.
5. A pentagonal lamina of side 30 mm is resting on HP with one of its corners. The surface is
inclined at 60° to HP. The edge opposite to this corner is parallel to VP and nearer to it. Draw its
projections.
6. A hexagonal lamina of 20 mm side rests on one of its corners in the HP. The diagonal passing through the corner is inclined at 45° to the HP. The lamina is then rotated through 90° such that the top view of the diagonal is perpendicular to the VP and the surface is still inclined at 45° to HP. Draw the projections of the lamina
7. A square lamina PQRS of side 40 mm rests on the ground on its corner P in such a way that the diagonal PR is inclined at 45° to the HP and apparently inclined at 30° to VP. Draw its projections.
8. A rectangular plate 70 x 40 mm has one of its shorter edges in the VP and inclined at 40° to the HP. Draw its top view if its front view is a square of side 40 mm.
9. A triangular plate PQR has sides PQ 50mm QR 70 mm and RP 40 mm. The side PQ rests on the HP and is inclined at 30o to VP. The surface of the plate is inclined at 40o to the HP. Draw the projections.
10. A circular plate of 50 mm diameter appears as an ellipse in the front view, having its major axis 50mm long and minor axis 30mm long. Draw the top view, when the minor axis of the ellipse is horizontal.
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