Projection of Points (Revised) ( * Problems to be practiced on computer )

1. Draw the projections of the following points keeping convenient distance between each

projectors. Name the quadrants in which they lie. A - 25mm.above H.P. and 30 mm infront of V.P. B - 30mm above H.P. and 30 mm behind V.P. C - 40mm above H.P. and on V.P. D - 35 mm below H.P. and 30 mm infront of V.P.

2. A point P is 20mm infront of V.P. , 45mm above H.P. and 40mm from/ infront/ behind L.P.P. Draw projections. 3. A point M is 25mm above H.P. , 50mm behind V.P. and 35mm from/ infront/ behind R.P.P. Draw 3 principle views of the point. 4. Draw all the 3 views of a point lying 50mm below H.P. , 60mm infront of V.P. and 30mm from the R.P.P. 5. A point is 35mm below H.P. , 20mm behind V.P. and 25mm from R.P.P. Draw projections. 6. A point is lying on V.P. ,30mm below H.P. and 40mm behind/infront/ from L.P.P.. Draw projections. * 7. A point 30mm above XY line is the front view of 3 points P,Q,R. The top view of R is 50mm . in front of V.P. , top view of P is on xy and top view of Q is 25mm behind V.P. Draw the projections of points and state the quadrants in which the points are situated. Draw the left view for point P only. 8. A point A is 35mm in front of V.P. and 50mm above H.P. . Another point B is 25mm. behind V.P. and 45 mm below H.P. The length of the line connecting the two front views is 120mm.Draw the projections of the points. 9. A point P is on H.P. and 35mm in front of V.P. Another point Q is on V.P. and below H.P. The line joining their front views makes an angle of 600 to xy line., while the line joining their top views makes an angle of 250 with xy line .Find the distance of point Q from H.P. 10. A point G is 35mm below H.P. and is situated in 3rd quadrant . Its shortest distance from the intersection of xy and x1y1 is 50mm. Draw the projections and find the distance from V.P. * 11. A point C is in I quadrant and equidistant of 50mm. from all planes. Draw all the 3 views. 12. A point A is 30mm. above H.P. and in the I – quadrant. Its shortest distance from the xy line is 50mm. Draw projections . Determine its distance from V.P.

Assignment - 1 (Revised)

1. A point Q is on both HP and VP. Another point P is 45mm above HP and 30mm in front of V.P. Draw its projections when the line joining their elevation is 60mm. Also draw and measure the line joining their plan .

2. The front and left views of a point is 30mm above xy line. And are at distances of 40mm

and 20mm on either side of the X1Y1 line respectively. Draw top ,front and left views of the point. How far the point is from V.P.?

3. The difference between the distances of the views of a point lying above XY line are

30mm. The top view itself is 45mm above XY line. Draw all the 3 views of the point and state the quadrant in which the point lies.

4. A point A is 40mm in front of VP and is situated in the fourth quadrant. Its shortest

distance from the line of intersection of HP and VP is 45mm. Draw its projections and find its distance from HP.

5.A point 40mm below XY line is the front view of two points A and B . The top view of A is 45mm behind VP and the top view of B is 35mm in front of VP . Draw the projections of the points and state the quadrants in which the points are situated.

6..A point M is 30mm in front of VP and 20mm above HP. Another point N is 15mm behind VP and 40mm below H.P. The horizontal distance between the points is 50mm Draw the projections of the points M and N and join their front and top views. Draw the right view for the point N only.

7.. Two points A and B are on VP. The point A is 35mm above HP , while B is 50mm below HP . The line joining their front views makes an angle of 600 with XY . Draw the projections and find the horizontal distance between the points.

8 A point P is 35mm above HP and 28mm in front of VP .Another point Q is on HP and

45mm behind VP . The distance between the projectors is 50mm. Draw the projections and find the distance between front view of P and top view of Q.

Projection of Lines (Revised) ( * Problems to be practiced on computer )

1. Draw the projections of a line 50mm. long when it is parallel to both H.P. and V.P.

The line is 30mm. above H.P. and 20mm. infront of V.P. and one of its ends is 25mm. infront of right PP.

2. A line 60mm. long is perpendicular to H.P. and parallel to V.P. and 30mm. in front of it. The top end is 90mm. above HP. The line is 25mm infront of left PP. Draw its projections.

3. Draw the projections of a line 60mm. long parallel to VP and inclined at 600 to HP . The lower end is 20mm above H.P. ,15mm infront of V.P. and 20mm infront of left PP.

4. Draw the projections of a line 70mm long when it lies on HP and inclined at 300 to VP. One end of the line is 10mm infront of VP and 20mm infront of left PP.

5. A line AB 80mm long has its end A 20mm. above HP and 30mm infront of V.P.It is inclined at 300 to HP and 450 to V.P. Draw the projections of the line and find apparent lengths and apparent inclinations.

6. The distance between end projectors of a line AB is 60mm .The line appears 70mm long in front view and in the top view the line appears inclined at 300 to XY line.The end A is 30mm above HP and 40mm infront of VP.Draw its projections and determine the true length and true inclinations. *

7. The top view PQ of a straight line is 70mm and makes an angle of 600 with xy line. The end P is 10mm infront of V.P. and 30mm above H.P. The difference between the distances of P and Q above HP is 45mm. Draw the projections and determine true length and true inclinations with H.P. and V.P.

8. The front view of a line PQ80mm long measures 55mm and is inclined at 450 to the XY line . End P is 25mm above XY line and is in V.P. Draw the projections of the line and find its inclinations with H.P. and V.P. *

9. The point B on a line AB is in H.P. , the top view of the line makes an angle of 450 with xy line , being 70mm. The point A is on V.P. and 40mm . above horizontal plane. Draw the top and front views of the line and obtain the true length and true inclinations of the line with HP and VP.

10. Draw the projections of a straight line PQ , 100mm long , inclined at 450 to HP and 300 to V.P. The end P is in HP and the end Q is in V.P. Find the shortest distance between the straight line PQ and the line of intersection of planes of projection.

11. The top view of a line PQ measuring 90 mm long is 75mm. and front view is 60mm long. The end Q is nearer to both HP and VP. Than the end P. and is 15mm above HP and 20mm infront of VP .Draw the projections of the line and determine the inclinations with HP and VP.

12. Draw the projections of a line PQ and find its true length and inclinations when the line is inclined at 300 to HP and 450 to VP. The line is having one of its end15mm above HP and 20mm in front of VP The distance between the end projectors on the XY line is 60mm.

Projection of Lines -2 (Revised)

1. The mid point of a line AB is 60mm above HP and 50mm. infront of VP.The line measures 80mm and inclined at 300 to HP.and 450 to V.P. Draw the projections.

2. A straight line AB measuring 80mm has the end A in HP and 25mm infront of VP. Its

mid point M is 25mm above HP and 40mm infront of VP. Draw all the 3 views of the line & determine the inclination of the line with HP and V.P. and also find distance between end projectors. *

3. Draw the projections of of a line AB 90mm long and find its true and apparent inclinations with HP and VP ,when its end A is on HP and 20mm infront of VP .Its mid point M is 20mm above HP and 40mm infront of VP.

4. The top view of a line AB 80mm long measures 65mm. The mid point of the line is 20mm infront of VP & 40mm above HP. The point A is in VP. Draw its projections and find its inclinations.

5. A line AB 100mm long measures 80mm in front view and 70mm in top view .The mid point M of the line is 40mm from both HP and VP. Draw its projections and find inclinations.

6. A line MN 90mm long has a point P on it which divides the line in the ratio of 2:1.The point P is 50mm above HP and 60mm infront of V.P. The line is inclined at 300 to HP and 450 to V.P. Draw the projections and find the distance between end projectors .

Assignment -2 (Revised)

1.A straight line PQ is inclined at 400 to VP has pq =60mm and p1q1 = 50mm. The end P is both in HP and VP, and 40mm to the right of the left profile plane . a) Draw the projections and find the true length and true inclination with HP. B) Draw the profile view of the straight line c) Find the position of the end Q with HP and VP.

2.) The plan of a line PQ measures 60mm . The line is inclined at 300 to VP and its front view is inclined at 450 to XY line. One of its ends is at 25mm from both HP and VP.Draw the projections and determine true length and true inclination with HP .

3. The top view of a line PQ 65mm long measures 40mm. The end P is 20mm in front of VP and 25mm above HP. The end Q is 10mm in front of VP and above HP . Draw the projections of the line and find its true inclinations with HP and VP Find the length of the front view and distance between end projectors. 4.The mid point M of a line AB is 50mm above HP and 40mm in front of VP . The line is inclined at 450 to HP and its top view is inclined at 300 to XY line.The line appears to be 80mm in the front view. Draw all the 3 views of the line and determine its true length and true inclination to VP. 5 A line PQ is inclined to both HP and VP by 300 and 450 respectively. The end P is at a distance of 25mm from HP and 15mm from VP. The distance between the end projectors is 45mm.Draw the top and front views of the line and determine the true length and the distances of the end Q from VP and HP.

2.) A line MN 90mm long has a point P on it which divides the line in the ratio 2:1. This point P is 40mm above HP and 50mm in front of VP. The line is inclined at 500 to HP and 200 to VP . Draw the projections of the line , find the distance between the end projector and the position of the ends of the line from HP and VP.

2.) The distance between the end projectors of a straight line AB is zero with its top view

and front view measuring 35mm and 50mm respectively. One end of the line is 20mm above HP and the other end 35mm in front of VP. A) Draw the projections of AB b) Find the true length and true inclinations. C) Find the position of the other end with respect to HP and VP.

2.) A line PQ 60mm long has its end Q in VP and the end P in HP . The line is inclined at

600 to HP and 300 to VP . Draw its projection

Projection of Plane Surfaces – 1 (revised)

( * Problems to be practiced on computer ) (Assign. - Assignment )

1. An equilateral triangular lamina 40mm side rests on one of its sides on H.P. The lamina

makes 300 to H.P. and the side on which it rests makes 450 to V.P. Draw its projections.- Assign.

2. A pentagonal lamina of edges 30mm is resting with one of its edges such that the corner opposite to this edge is 20mm above H.P and is in VP. Draw the top view and front views of the lamina and determine its inclination with H.P. *

3. A hexagonal lamina of 30mm. sides rests on H.P. with one of its edges touching V.P. and

surface inclined at 300 to it. The diagonal is inclined at 600 to HP Draw the top view and front view of the lamina in its final position. Assign.

4. A 300 – 600 setsquare of 70mm. longest side is so kept such that the longest side is in

VP , making an angle of 450 with HP. The setsquare itself is inclined at 300 to VP. Draw the projections. Assign.

5. A hexagonal lamina of sides 25mm rests on one of its corners on HP The lamina makes

30o to HP and two of its parallel sides appear perpendicular to xy in plan and elevation. Draw its projections. *

Projection of Plane Surfaces – 2

6. abc is an equilateral triangle of altitude 50mm with ac in XY line. And b below it.ab1c is

an isosceles triangle of altitude 65mm and above XY line. Determine the true shape of the triangular lamina ABC of which abc is the top view and ab1c is the front view. Measure the sides of the triangle.* Assign.

7. A rectangular lamina of 35mm. x 20mm rests on H.P. on one of its shorter edges . The

lamina is rotated about the edge on which it rests till it appears as a square in top view . The edge on which the lamina rests being parallel to both H.P. and V.P. Draw its projections and find its inclination to H.P. and V.P.

8. A mirror 30mm x 40mm is inclined to the wall such that its front view is a square of

30mm .side. The longer sides of the mirror appear perpendicular to both H.P. and V.P. Find the inclination of the mirror with the wall. Assign.

9. A regular pentagonal lamina of 25mm side is resting on one of its corners on H.P. while

the side opposite to this corner touches V.P. If the lamina makes an angle of 600 with HP and 300 to V.P. , draw the projections of the lamina.

10. A regular hexagonal lamina of sides 30mm is lying in such a way that one of its sides touches both the reference planes. If the side opposite to the side on which it rests is 45mm above HP , draw the projections of the lamina. Assign .

11. A circular lamina of 50mm diameter is standing with one of its points on the rim on HP and the lamina is inclined at 450 to HP. The diameter at right angles to the diameter which is passing through the point on which the lamina rests is parallel to VP. Draw its projections. *

Projection of Plane Surfaces – 3

12. A pentagonal lamina having edges 25mm is placed on one of its corners on HP such that

the perpendicular bisector of the edge passing through the corner on which the lamina rests is inclined at 300 to HP and 450 to VP. Draw the top and front views of the lamina. *

13 . A hexagonal lamina of sides 30mm is resting with one of its corners in VP and its surface is inclined at 300 to VP. The diagonal passing through that corner which is in VP is inclined at 450 to HP. Draw the projections of the lamina. Assign. 14 . Draw the projections of a circular lamina of 60mm diameter when it is resting on HP on one of its points on its circumference and making an angle of 400 to HP with its opposite point on the circumference touching VP. *

15. A hexagonal lamina of side 25mm. has its plane inclined at 500 to HP. Two of its sides are parallel to both HP and VP. The nearest edge is at a distance of 25mm from HP and VP. Draw the projections. 16. A square lamina of 30mm side has its one diagonal inclined at 450 to HP and the other diagonal inclined at 400 to VP and parallel to HP. Draw its top and front views. * Assign. 17 . A circular lamina of 70mm in diameter is resting on a point A on HP. The lamina is inclined to HP at such an angle that its top view is an ellipse of minor axis 40mm. , the top view of the diameter through point makes an angle of 450 with V.P.Draw its projections and determine the inclination of the lamina to H.P. Assign.

Projection of solids -1 (Revised)

1. A square pyramid 30mm. sides of base and 60mm axis length rests on HP on one of its corners of the base such that the two base edges containing the corner on which it rests make equal inclinations with HP. Draw the projections of the pyramid when the axis of the pyramid is inclined to HP at 300 and to VP at 450. Assign

2. A triangular pyramid 35mm sides of base and 50mm axis length rests on HP on one of its edges of the base such that the base is inclined at 600 to HP and the axis appears to make 450 to VP. Draw the projections when the apex is nearer to the observer than the base. *

3. A pentagonal pyramid 30mm sides of base and 50mm axis length rests on HP on one of its slant edges and the axis appears to be inclined to VP at 450 . Draw the projections when the base is nearer to the observer. Assign.

4. A hexagonal pyramid 30mm sides of base and 60mm axis length rests on HP such that one of its slant edges is inclined to HP in such a way that the opposite base corner is 15mm above HP and the axis is inclined to VP at 300. Assign.

5. A pentagonal pyramid 25mm sides and axis 60mm rests on HP on one of its corners of

the base such that the apex is 40mm above HP and the side opposite to the corner on which it rests is inclined at 450 to VP. Draw the projections. *

6. A pentagonal pyramid 25mm sides and axis 40mm rests on HP on its base such that one of the triangular faces is perpendicular to HP and parallel to VP and away from it .Draw the projections. Assign.

7. A rectangular pyramid of 45 x 25mm and axis 50mm is resting on HP on its vertex such that its triangular face is inclined at 300 to HP .Draw the top , front and side view .*

Projection of solids -2 (Revised)

1. A triangular prism 35mm sides of base and 60mm.axis length rests on HP on one of its edges of the base. Draw the projections of the prism when the axis is inclined at 600 to HP and 300 to VP. Assign.

2. A pentagonal prism 25mm. sides of base and axis 60mm length rests on HP on one of its edges of the base which is inclined to VP at 450 .Draw the projections of the prism when the axis is inclined to HP at 300 *

3. A hexagonal prism 30mm. sides of base and 50mm axis length is resting on HP on one of its base edges such that the top face diagonally opposite edge of the prism lies exactly above the edge on which it rests with the top view of axis inclined at 300 to VP. Draw the projections . Assign

4. A cube of 30mm sides rests on HP on an edge which is inclined to VP at 450 . Draw the projections when the lateral square face containing the edge on which it rests makes an angle of 600 to H.P. *

5. A hexahedron ( cube) of sides 35mm is resting on one of its corners on HP such that one of its solid diagonals is perpendicular to VP. Draw the projections of the solid. Assign

Projection of solids -3 (revised)

1. A cone of 40mm base diameter and 60mm axis length rests on HP on one of its generators. Draw its projections when the axis is inclined at 450 to VP, apex is away from the observer. * Assign

2. A cone of base diameter 50mm and axis 50mm is resting on HP on a point on the

circumference of its base such that its apex is 25mm above HP and the top view

of the axis is inclined at 300 to VP. Draw the top and front views when the base is nearer to the observer. Assign

3. A cylinder of 40mm and height 60mm is resting on one of its base point on HP such that the axis is inclined at 300 to HP and 600 to VP .Draw the projections. *

Assign

4. A cone of base 60mm and height 80mm rests on HP with its axis inclined to HP such that the top view of the base is an ellipse with minor axis 40mm.Draw the projections and determine the inclination of the axis with HP. *

5. A cone of diameter of base 50mm and height 60mm rests with its apex on HP such that the axis is inclined at 300 to HP and 600 to VP The apex of the cone is nearer to VP than base . Draw its top and front views. Assign

Projection of solids – 4 (revised) 1. A regular pentagonal pyramid side of base 30mm and axis 60mm is freely suspended

from a corner of its base Draw the projections of the pyramid when the axis is parallel to the profile plane. Find inclination of the axis with HP and VP. Assign

2. A cube of edges 50mm is hung by a string attached to one of its corners and the axis appears to make 300 to VP. Draw the top and front views of the cube.Assign

3…A pentagonal prism of 30mm side of base and height 60mm is suspended freely from a corner. The axis of the prism is inclined at 300 to VP. Draw its plan and elevation. *

4. A cone of 50mm diameter of base and height 60mm is freely suspended from a point on its base such that the projection of axis on HP is inclined at 450 to VP. The apex is nearer to the observer than base. Draw the projections. Assign

5. A cylinder of diameter 60mm and height 60mm is suspended freely from a point on its circular rim. The axis appears to be inclined at 450 to VP . Draw the projections. *

6. A rectangular prism 50m x 20mm and height 60mm rests with one of its longer edges of the base on HP. The axis is inclined at 450 to HP and top view of the axis inclined at 300 to VP. Draw its projections. *

Isometric Projection – 1 (revised)

1.Construction of Isometric scale

2.Isometric projection of circle in horizontal position and vertical position. 3 . A cube of side 25mm is resting centrally on a rectangular slab 100mm x 40mm and 30mm thick. Draw the isometric projection of the combination.

4.A cone of base diameter 50mm and height 40mm is centrally placed over a cube of side 60mm . Draw the isometric projection of the combination of solids. Assign *

5.A hexagonal pyramid of side 30mm and height 40mm is placed centrally on a cylindrical slab of diameter 80mm and thickness 35mm. Draw the isometric projection of the combination. Assign . *

6. A hemisphere of 60mm is placed centrally on the top face of a hexagonal prism side 35mm and height 50mm. Draw the isometric projection of the combination. Assign *

7.A hemisphere of diameter 60mm is resting on its curved surface centrally on the top face of frustum of a rectangular pyramid base 80 mm x 60mm and top 60mm x 40mm height 55mm. Draw the isometric projection of the combination. Assign * 8. A sphere of diameter 50mm is placed centrally on an equilateral triangular prism of side 70mm and 30mm thick . Draw the isometric projection of the combination. Assign

Isometric projection -2

1. A square pyramid of side 40mm and height 30mm rests on the frustum of a hexagonal pyramid base 50mm , top face 40mm side and height 35mm , such that their axes coincide. Draw the isometric projection of the combined solids. Assign *

2. Draw the isometric projection of the combination of solids formed by a frustum of

Cone and co – axial frustum of pentagonal pyramid. The lower frustum of cone is 80mm diameter , 60mm top diameter and height 30mm. The upper frustum of pyramid is of 30mm side of base, 20mm side of top face and height 40mm. Assign *

3. Following figure shows the front and top views of solid. Draw the isometric

projection of the solid. i) Assign ii) Assign iii) Assign iv) *

Development of lateral surfaces of Solids – 1

1. A cube of side 40mm is resting on HP with its base on HP such that one of its vertical faces is inclined at 300 to VP. It is cut by a section plane perpendicular to VP , inclined to HP at an angle of 450 and passes through the midpoint of the axis. Draw the development of the lower lateral surface of the cube. Assign *

2. A pentagonal prism of 30mm side of base and height 50mm lies with its base on HP such that one of its rectangular faces is inclined at 400 to VP . It is cut to the shape of a truncated pyramid with the truncated surface inclined at 300 to the axis so as to pass through a point on it 30mm above the base. Develop the truncated portion of the prism. Assign *

3. A hexagonal prism of base side 20mm and height 50mmis resting on HP on its base such that one of the base edges is parallel to VP. The prism is cut in this position as shown in the following front view. Draw the development of the lateral surface of the prism. Assign

4. A vertical cylinder of base diameter 50mm and axis 60mm is cut by two planes which

are perpendicular to VP. And inclined at 450 to HP. And passing through either side of the centre point of the top face . Draw the development of the lateral surface of the cylinder.Assign *

5. Develop the lateral surface of the cylinder of 40mm diameter and

height 60mm which is cut in the following way. Assign

Development of lateral surfaces of Solids – 2

1. Draw the development of the lateral surface of cone , whose front view is shown below.

a) Assign b) *

2 . A square pyramid base 40mm side and axis 65mm long has its base on HP and all the edges of the base are equally inclined to VP. It is cut with an inclined section plane at 450 to its axis. Bisecting it. Draw the

development of the truncated pyramid. * 2.) A pentagonal pyramid 30mm edges of base and 50mm height rests vertically with one of its base edges parallel to VP and nearer to it. It is cut as shown in figure. Draw the development of the upper portion of the

pyramid . Assign

4. A hexagonal pyramid 25 mm side of base and axis 60mm is resting on its base on HP with one of the edges of the base parallel to VP. It is cut by a vertical section plane at a distance of 8mm from the axis towards right. Draw the development of the

left part of the pyramid. * 5. A right circular cone of 75mm diameter and axis 90mm rests on its base on HP. A point P initially situated at the extreme right end of the base , moves around the surface of the cone and finally comes back to the starting point. Find the length of the shortest path , the point P will take , in covering the distance along the surface of the cone. Also show the path in front and top views.

Assi

Development of lateral surfaces of Solids – 3

2.) Draw the development of the lateral surface of the solids shown below.