Engineering Drawing - HOME - Prof. Ibrahim … Mobile: 9892128099 By Prof.Shaikh Ibrahim Ismail...

Engineering Drawing By Shaikh Ibrahim Ismail

M.H. Saboo SSiddik College Of Engineering, Mumbai

1

Mobile: 9892128099 By Prof.Shaikh Ibrahim Ismail [email protected]

Contents

ENGINEERING CURVES ........................................................................................................................................... 4

CYCLOID ................................................................................................................................................................. 4

INVOLUTE .............................................................................................................................................................. 4

PROJECTION OF LINES ............................................................................................................................................ 7

PROJECTION OF SOLIDS ....................................................................................................................................... 12

SECTIONS OF SOLIDS ............................................................................................................................................ 18

ORTHOGRAPHIC PROJECTION .............................................................................................................................. 24

2


3


Engineering Curves

4


ENGINEERING CURVES

CYCLOID

1) A circle of 64 mm. diameter rolls along a straight line without slipping. Draw the curve traced out by a point on the circumference of the rolling circle for one complete revolution. Name the curve.

2) A car travels along a straight road inclined at 300 to the horizontal. Diameter of each wheel of the car is 70 cm. Looking in the direction perpendicular to the plane of motion, draw the elevation of the path traced out by a point on the circumference of the wheel, for one complete revolution of the wheel. Name the curve.

3) A circle of 60 mm. diameter rolls on a horizontal line for a half a revolution and then on a vertical line for another half revolution. Draw the curve traced out by a point ‘P’ on the circumference of the circle.

INVOLUTE

1) Construct an involute of a regular pentagon of 30 mm. sides. 2) Construct an involute of a circle of 50 mm. diameter. 3) One end of an inelastic string is attached to the center of a semi-circle of 65 mm.

diameter. The thread is 100 mm. long. Find the locus of the other end of the string if it is wound round the semi-circle. Name the curve.

4) One end of a thread 150 mm. long is fixed to a point on the circumference of a circular disc of 42 mm. diameter. Plot the locus of the free end of the thread when the thread is wound round the disc, the thread being kept tight.

5) A line AB 120 mm. long is tangent at the top of a circular disc of 50 mm. diameter. The point A is at the top of the circumference. The line AB rolls around the circumference of the circular disc in a clockwise direction. Draw the locus of the end ‘A’, till the end B touches the circle. Name the curve.

6) Draw a semi-circle of 65 mm. diameter. An inelastic string 150 mm. long is fixed at the center of the circle. The thread is wound around the semi-circle, keeping the thread tight. Find the locus of the free end of the thread.

Helix

1) Construct a helix on a cylinder of 60 mm diameter and 80 mm length of axis. The pitch of the helix is 70 mm.

2) Draw the plan and elevation of a cylinder of 50 mm diameter and 72 mm length of axis. Mark a point P on the base of the cylinder, nearest to the observer. The point P moves on the surface of the cylinder, around it, reaching the respective top point in one turn. Plot the path of the point P, if both its motions are uniform.

3) A rectangular sheet ABCD. AB=70 CD=2. AB vertical, rotates about AB for one revolution. During this, the point C moves along CD and reaches D. Plot the path of C.

5


4) Construct a rectangle PQRS. PQ=88, QR=176. Join Q and S. This rectangle is bent and rolled to form a cylinder of 88 mm length. Show the line QS on this cylinder.

5) Construct a rectangle ABCD, AB=80, BC=150. Join AC. This paper in a rectangular form ABCD is rolled to form a cylinder so that the points B and C are together and nearest to the observer. Draw two views of a cylinder and show the line AC on the views.

6) Draw a helix on a cone of 60 mm diameter and 70 mm length of axis. 7) A hill has base diameter= 70 meters and a height of 90 meters. A car starting at the base

of the hill travels along an uphill road going around the hill and reaching the top in 11/2

turns. Draw two views of the hill and show the road on the views. 8) A rectangular sheet PQRS, PQ=70, QR=25 PQ vertical rotates about PQ for one

revolution. During this, the point R moves along the diagonal RP and reaches the corner P. Plot the path of R.

6


Projection of Lines

7


Projection of Lines

Important information:

1) If a line is parallel to the V.P., its elevation will show the true length and the plan will be a straight line parallel to the X-Y line.

2) If a line is parallel to the H.P., its plan will show the true length and the elevation will be straight line parallel to the X-Y line.

3) The inclination with the H.P. is θ, the inclination with the V.P. is Ø. 4) Whenever the plan of a line is made parallel to the X-Y line, its elevation will show the true

length, the true inclination with H.P., and the locus (path) of the moving end. 5) Whenever the elevation of a line is made parallel to the X-Y line, its plan will show the true

length, the true inclination with V.P. and the locus (path) of the moving end. 6) If a line is inclined with two planes such that angle θ + angle Ø = 90 0 Then the elevation and the

plan of that line will be perpendicular to the X-Y line. 7) For a straight line,

If the (true length) 2 = (elevation length) 2 + (plan length) 2, then also The elevation and the plan of the line will be perpendicular to the X-Y line.

EXERCISE

1. A line AB, 70mm long is inclined at an angle of 30⁰to the HP and 45⁰ to the VP .Its end point A

is10mm above the HP and 20mm in front of the VP .Draw the projection of lines AB .Assume,

complete line to be in the first quadrant.

2. A line AB ,70mm long has its end A 10mm above the HP and 20mm in front of the VP. The end B

is 45 mm above the HP and 70 mm in front of the VP .Draw the projections of line AB and finds

its inclination with the HP and VP.

3. The FV of line AB ,70 mm long is inclined at 45⁰ to the XY line .The end point A is 10mm above

the HP and 20mm in front of the VP. Draw the projection of line AB if it is inclined at 30⁰to the

HP.

4. The TV of line AB , 70mm long measures 60mm . The end point A is 10mm above the HP and

20mm in front of the VP. The other end point B is 70 mm in front of the VP and above the HP

.Draw the projections of lines AB and find its inclination with the HP and VP.

5. The distance between the end projectors of a straight line AB is 35mm. The end point A is 10mm

above the HP and 20mm in front of the VP, while the other end B is 45mm above the HP and

70mm in front of the VP. Draw the projections of line and determine its inclinations with HP and

VP .Also find its true length.

6. The distance between the end projectors of a straight line AB is 35mm.The line AB is 70mm long

and is inclined at 30⁰to the HP .The end point A is 10mm above the HP and 20mm in front of the

VP. Draw the projection of lines AB .

8


7. The FV of line AB measures 50mm and makes an angle of 45⁰ with the XY line . The end point A

is 10mm above the HP and 20mm in front of the VP. Draw the projections of lines AB if it is

inclined with the VP at 45⁰.

8. The FV and TV of line AB measures 50mm and 60mm respectively. The line is 70mm long. point

A is 10mm above the HP and 20mm in front of the VP. Draw the projections of lines AB and

determine its inclination with the HP and VP.

9. The elevation length and the plan length of line AB measures 50mm and 60mm respectively.

The line AB is inclined at 30⁰to the HP and the end point A is 10mm above the HP and 20mm in

front of the VP. Draw the projections of lines AB.

10. A line AB 70 mm long, has its end A 10mm above the HP and 15mm in front of VP. Its TV and FV

measures 60mm and 40mm respectively. Draw the projection of line and determine its true

length, true inclination with VP.(Dec 08)

11. The TV of a line AB measures 60 mm and is inclined at 56⁰ to the XY line. The end point A is

10mm above the HP and 20mm in front of the VP, while the other end B is 45mm above the HP

and in front of the VP. Draw the projection of line.(May 09)

12. Side view of a line AB is 75 mm long makes an angle of 40⁰with XY line. Draw TV and FV of line

when the length of side view is 50mm .Take point A is 15mm above the HP and 55mm in front of

the VP, the point B being closest to VP.(Dec 09)

13. The TV of 100mm long line AB measures 70mm while the length of FV is 85mm.Its one end A is

15mm above HP and 25mm in front of VP. The other end is in the 3rd quadrant. Draw the

projection of line and determine its true length, true inclination with HP. Also laocate its traces

HT and VT.(May 10)

14. The end A of a straight line AB 90mm long is in the second quadrant and 15mm in front of both

HP and VP.End B is in the 3rd quadrant.The line is inclined at an angle of 30⁰to the HP and DBEP

measured parallel to the XY line is 60mm . Draw the projection of line and determine its true

inclination with VP.(Dec 10)

Extra Problems:

1. A line AB 90 mm. long is inclined at 300 to H.P. and 400 to V.P. The end A is 15 mm. above H.P. and 30 mm. in front of V.P. Draw its projections.

2. The front view of a straight line AB is 60 mm. long and is inclined at 600 to X-Y line. The end

point A is 12 mm. above the H.P. and 25mm in front of the V.P. Draw the projections of the line if it is inclined at 450 to the H.P. and is located in the first quadrant. Find the true length and the true inclination of the line with the V.P.

3. The top view and the front view of a line AB measure 70 mm. and 58 mm. respectively. The

line is inclined at an angle of 350 to H.P. The end A is 15 mm. above H.P. and 12 mm. in front

9


of V.P. The other end B is also in the first quadrant. Draw the projections of the line AB. Find the true length and the true inclination with the V.P.

4. The plan of a 100 mm. line AB measures 70 mm. The point A is 10 mm. below the H.P. and

60 mm. in front of the V.P. The point B is above the H.P. and 15 mm. in front of the V.P. Draw the projections of the line and determine the true inclinations with the H.P. and V.P.

5. The front view of a 85 mm. long line AB measures 60- mm. while its top view measures 70

mm. Draw the projections of AB if its end A is 10 mm. above H.P. and 20 mm behind V.P., while end B is in the first quadrant. Determine the inclinations of the line AB with the reference planes.

6. The end-projectors of a line AB are 55 mm. apart. The point ‘A’ is 50 mm. below the H.P. and

60 mm. behind the V.P. The point ‘B’ is 30 mm. above the H.P. and 25 mm. in front of V.P. Draw the projections of AB, and find the true length, true inclination with the H.P. and with the V.P.

7. The plan ‘ab’ of a straight line AB is 140 mm. long and makes an angle of 450 with the XY

line. The end A is in the V.P. and 85 mm. from H.P. The end B is 20 mm. from the H.P. and the whole line is in the fourth quadrant. Draw the projections and determine the true length and the inclinations with H.P. and V.P.

8. The top view of a line AB 80 mm. long measures 65 mm. and the length of its front view is

50 mm. The end A is in H.P., and 15 mm. behind V.P. Draw the projections of AB and determine the inclinations with the H.P. and V.P.

9. The front view of a 125- mm. long line PQ measures 75 mm. and the top view measures 100

mm. Its end Q and the mid- point M are in the first quadrant. The midpoint M is 20 mm. from both the reference planes. Draw the projections of the line PQ and find its inclinations with H.P. and V.P.

10. A line MN has its end M in the H.P. and 15 mm. in front of the V.P. The end N is in the third quadrant. The line is 65 m. long and is inclined at 30 0 to H.P. and 600 to the V.P. Draw its projections.

11. A line PQ 140 mm. long is inclined at 300 to H.P. and 400toV.P. The mid-point M of PQ is 20 mm below H.P. and 25mm behind V.P. The end P is in the first quadrant. Draw the projections of PQ.

12. The front view and the top view of a line AB 125 mm. long lying in the third quadrant

measure 75 mm. and 100 mm. respectively. Its end A is 30 mm. from both the reference planes. Draw the projections of the line and determine its inclinations with H.P. and the V.P.

13. PQ is a straight line 100 mm. long. It is inclined at 300 to H.P. and 450 to V.P. Its mid- point M

is in the V.P. and 20 mm above H.P. The end P is in the third quadrant and the end Q is in the first quadrant. Draw its projections.

14. A line AB measures 120 mm. Its plan and elevation measure 81mm. and 96 mm.

respectively. A point C on the line dividing it in the ratio 1:2 (i.e. AC:CB =1:2) is contained by

10


both the reference planes. Draw the projections of the line and determine the inclinations with the reference planes.

15. A line AB is inclined at 350 to the H.P. and 550 to the V.P. The end B is 90 mm. behind the

V.P. and is in the third quadrant. The end A is 10 mm. below the H.P. and 15 mm. behind the V.P. Draw the projections of AB and state the distance of B from H.P. and the true length of AB

16. The end A of a straight- line AB 90 mm. long is in the second quadrant and 15 mm. from H.P.

and V.P. End B is in the third quadrant. The line is inclined at 300 with H.P. and the distance between the end-projectors measured parallel to the XY line is 60 mm. Draw the projections of the line, find the inclination with the V.P.

17. The projectors of the ends of a line AB are 90 mm. apart. The end A is 40 mm. above the

H.P. and 50 mm. in front of the V.P. The end B is 25 mm. below the H.P. and 70 mm behind the V.P. Determine the true length and the inclinations of the line AB with the H.P. and V.P.

18. A line PQ is 110 mm. long and its plan measures 80 mm. The point P is 50 mm in front of the

V.P. and 20 mm. below the H.P. The point Q is in the first quadrant and 15 mm. in front of the V.P. Draw its projections and find the inclinations with H.P. and V.P.

11


Projection of Solids

12


Projection of Solids

Important Information:

1) The position of a solid (prism, cylinder, cone, pyramid) is stated in the question. The position is with respect to the H.P. and the V.P. It is required that we should draw the elevation and the plan of that solid. This position cannot be plotted directly because we will not know the length of a line (edge or generator) when it is inclined to the plane. We will not know the position of a corner of a solid in space. Hence we keep the solid in a primary position either on the H.P. or the V.P., draw its views. Then we rotate the solid with respect to the plane according to the condition given. This way we can finally get the required views of that solid.

2) The outermost boundary of a solid is always visible, because it is the limit of the space occupied by the solid. The boundary lines are always dark and continuous, but never dotted.

3) The true inclination with the H.P. is seen in the elevation. The true inclination with the V.P. is seen in the plan.

4) All the points in the elevation are associated with a dash so that it will be identified as elevation and the other view will be plan.

5) Whenever the pyramid or the prism stands on the edge, initially the edge should be perpendicular to the x-y line, and then turn (swivel or rotate) the solid at the given angle. The rotation is always parallel to one of the principal planes.

6) The generators on the cone and the cylinder are purely imaginary and hence should be extremely light. 7) The inclination of the whole solid should be considered first. Then the inclination of the edge of base

should be considered. 8) If in the plan, the apex or the top of the solid is away from the observer, then in the corresponding

elevation, the base of the solid will be visible and hence dark. Conversely, if the apex or top is nearer to the observer, then in the corresponding elevation, the base will not be visible.

9) If a line (edge, axis, generator) is inclined at an angle with H.P. and also inclined with the V.P. then we have to plot the apparent angle. If the two inclinations when added, are equal to 90 degrees, then the apparent angle is equal to 90 degrees and the elevation and plan of the line will be perpendicular to the X-Y line.

10) If a solid is suspended by a thread tied to the solid at some point, then the line of action passes through the center of gravity of the solid. In the case of cylinder and prism, the mid- point of the axis is the center of gravity. In the case of pyramids and cones, the center of gravity is at a height of ¼ th the height along the axis, from the base.

EXERCISE

1. A square pyramid of base 40mm and axis length 60mm has one of the side of base in the H.P.

The axis of solid is inclined to the H.P. at an angle 30⁰ (ϴ) and the T.V. of axis is inclined at an

angle 45⁰(φ) with the V.P. Draw its projections. (i) Apex away from the observer. (ii) Apex nearer

to the observer.

2. A square pyramid side of base of 40mm, axis length 60mm has one of the side of base in the

H.P. The axis of a solid is inclined to the H.P. and the V.P. at an angle 30⁰(ϴ) and 45⁰(φ)

respectively. Draw its projections.

3. A square prism with side of base 40mm and axis length 60mm has one of its side of base in the

V.P., which makes an angle 45⁰ (ϴ) with the H.P. and axis inclined at an angle 30⁰ (φ) with the

V.P. Draw its projections.

13


4. A square Pyramid side of base 40mm and axis length 60mm has one of the side of base in the

V.P. The axis of the solid is inclined to the V.P. at an angle 30⁰ (φ) and F.V. of axis is inclined at

an angle 45⁰ (ϴ) with the H.P. Draw its projections. (i) Apex away from the observer, (ii) Apex

nearer to.

5. A square pyramid side of 40mm, axis length 60mm has one of the side of base in the V.P. The

axis of a solid is inclined to the V.P. The axis of a solid is inclined to the V.P. and the H.P. at an

angle 30⁰(φ) and 45⁰ (ϴ) respectively. Draw its projections.

6. A square prism, side of base 40mm and height 60mm is resting on one of the corner of the base

on the H.P. The longer edge containing the corner is inclined at 50⁰ to the H.P. and 20⁰ to the

V.P. Draw the projections of a prism when the top end of a prism is nearer to the V.P.

7. A square prism, base 30mm side and axis 60mm long has its corner of the base on the H.P. with

its axis inclined at 45⁰ to the V.P. and 30⁰ to the H.P.

8. Draw the plan and elevation of a cube of solid diagonal 80mm length when the solid diagonal is

perpendicular to the V.P. and the corner of a cube is in the H.P.

9. A pentagonal prism of 30mm edge of a base and 65mm length of an axis is having an edge of a

base inclined at 30⁰ to the H.P and in the V.P. Draw the projections of a prism if the rectangular

side face containing that edge is inclined at 30⁰ to the V.P.

10. A pentagonal prism of having an edge of base 25mm axis height 60mm has one of its corner in

the H.P. The axis is inclined at 30⁰ to the H.P. and the T.V. of an axis is inclined at 45⁰ to the V.P.

Draw the projections.

11. A square pyramid of 40mm edge base and 60mm length of an axis is resting in the H.P. on one of

its base edges. The axis makes an angle of 30⁰ with the H.P. Draw its projections if the top view

of an axis is inclined at 45⁰ to the V.P.

12. A square pyramid side of base 40mm and axis length 55mm has one of the corner of its base in

the H.P. with its axis inclined at 30⁰ and 45⁰ to the H.P. and the V.P. respectively. Draw its

projections if the apex is nearer to the V.P.

13. Draw the top view and the front view of a square pyramid of the side of base 35mm and height

50mm when it lies with one of its triangular faces on the H.P. The base edges contained by face

lying on the H.P. is inclined at 45⁰ to the V.P. Take apex nearer to the observer.

14. A square pyramid of 40mm side of base and 60mm length of an axis is resting in the V.P. on one

of its slant edges. Draw its projections containing that slant edge and axis is normal to the V.P.

inclined at 30⁰ to the H.P. and the base away from an observer.

15. A square pyramid, side of base 40mm, axis length 60mm is suspended by a string from one of its

corner of the base. The T.V. of an axis is inclined at 40⁰ to the V.P. and apex is nearer to the

observer. Draw its projections.

16. A hexagonal pyramid, side of base 30mm and length of axis 60mm is tilted towards the observer

on one of its base edge in such a way that the triangular face containing the edge on which the

pyramid rests, appears in front view as an isosceles triangle of 30mm base and 45mm altitude.

Draw the projection and find the inclination of the base of the pyramid which the H.P.

17. A right hexagonal pyramid, side of base 20mm and height of axis 40mm is resting on one of its

triangular faces on the ground (H.P.)and the edge of the base contained by that triangular face

makes an angle 45⁰ to the V.P. draw its projections considering the apex nearer to the V.P.

14


18. A pentagonal pyramid of 30mm edge of base and 60mm axis height is lying on one of its

triangular surface in the V.P. and the edge of base contained by a triangular face makes an angle

of 45⁰ to the H.P. Draw its Front view and top view having base nearer to the observer.

19. A hexagonal pyramid, base 40mm, side axis 100mm long is resting in the H.P. on a corner of its

base , with base surface making an angle of 30⁰ with the H.P. and axis making an angle 30⁰ with

V.P. Draw the projections of the pyramid when the apex is touching the V.P. and base of the

corner which is in the H.P. equally inclined to the H.P.

20. A hexagonal pyramid of 30mm side of base and slant edges 65mm long is lying on one of its

triangular surfaces in the V.P., so that its axis is inclined at an angle of 45⁰ to the H.P. Draw its

projection if apex is nearer to the observer.

21. A pentagonal pyramid base edge 25mm and slant edges60mm long is resting on one of its base

corners with its axis inclined at 30⁰ to the H.P. Draw its projections if the base side opposite to

the base corner on the HP. Makes an angle of 40⁰ to the V.P. and apex nearer to the observer.

22. A pentagonal pyramid, edge of base 30mm and length of axis 60mm is lying on one of its

triangular face in the H.P. with the T.V. of axis inclined at 45⁰ to the V.P. Draw its projections if

the apex is away from an observer.

23. A pentagonal pyramid, side of base 35mm and axis 70mm long is lying on one of its corner on

the H.P. such that the two base edges passing through the corner on which it rests makes an

equal inclination with the H.P. One of its triangular surface is parallel to the H.P. and

perpendicular to the V.P. and the base edge containing that triangular surface is parallel to both

the H.P. and the V.P. Draw the projection of the solid when the apex of the pyramid is nearer to

the observer.

24. A pentagonal pyramid has a height of 60mm and the side of a base 30mm. The pyramid rests

with one of the sides of a base on the H.P. such that the triangular face containing that side is

perpendicular to the H.P. and makes an angle of 30⁰ with the V.P. Draw its projections.

25. A tetrahedron of 45mm sides has one of its edge in the H.P. and inclined at 45⁰ to the H.P., while

a face containing that edge is inclined at 30⁰ to the V.P. Draw its projections.

26. A cone base 50mm diameter and axis 60mm long rests on its circular rim on the H.P. with the

axis making an angle of 30⁰ with the H.P. and its top view making an angle of 45⁰ with the V.P.

Draw its projections.

27. A cone of base 60mm diameter and axis 66mm long is lying on one of its generator on the V.P.

with its F.V. of an axis making an angle at 50⁰ with the H.P. Draw its projections considering the

apex nearer to observer.

28. A Right circular cylinder diameter of base 50mm and axis height 70mm has one of the

circumference point of base in the H.P. such that its axis is inclined at 30⁰ to the H.P. and the

axis appears to be inclined at 45⁰ to the V.P. in the T.V. Draw its projections.

15


Extra Problems

1) A square pyramid of 40 mm. edge of base and 60 mm. length of axis stands on an edge of base on the H.P., inclined at 45 0 to V.P. while the axis is inclined at 30 0 to the H.P. Draw the projections, if the apex is away from the observer.

2) A hexagonal prism- edge of base 25 mm. axis 60 mm. long has an edge of base on the H. P. and inclined at 300 to V. P. and a rectangular face containing that edge is inclined at 450 to H.P. Draw the projections.

3) A cone of 50mm. diameter of base and 60-mm. length of axis has one of its generators on the H.P. and inclined at 450 to V.P. Draw the projections if the apex is away from the observer.

4) A pentagonal pyramid of 30 mm. edge of base and 60 mm. length of axis has one of its triangular faces in the V. P .The shorter edge of that face is inclined at 600 to H.P. Draw three views of the pyramid.

5) A tetrahedron of 50 mm. edges has one of its edges on the H.P., inclined at 450 to V.P. A triangular face containing that edge is inclined at 600 to H.P. Draw three views of the solid.

6) A frustum of a square pyramid- base 50 mm x 50 mm, top 25 mm x 25 mm and height 50 mm., has one of its trapezoidal faces on the H.P. and the two parallel sides of that face are at 450to V.P. Draw its projections.

7) An equilateral triangular prism of 32 mm. edge of base and 60 mm. length of axis has a 60 mm. edge on the H.P. inclined at 450 to V.P. A rectangular face containing that edge is inclined at 450 to H.P. Draw the projections.

8) A cone of 60 mm. diameter of base and 70 mm. length of axis has a generator on H.P. and the axis is inclined at 300 to V.P. Draw the projections.

9) An equilateral triangular pyramid of 50 mm. edge of base and 65 mm. length of axis has one of its slant edges on the H.P. and the plane containing the slant edge and the axis is perpendicular to H.P. and inclined at 450 to V.P. Draw the projections.

10) A hexagonal pyramid edge of base 32 mm., axis 70 mm. has one of its triangular faces on the H.P. and the plan of the axis is inclined at 600 to X-Y line. The apex is away from the observer. Draw the projections.

11) A rectangular pyramid of base 45 X 30 and axis 50 mm. long has a 45 mm. edge of base on the H.P. inclined at 450 to V.P. and the triangular face containing that edge is perpendicular to H.P. Draw the projections.

12) A cube of 45 mm. edges has one of its corners on the H.P. The solid diagonal passing through that corner is inclined at 450 to H.P. and 300 to V P. Draw the projections of the cube.

13) A rectangular prism of base 38 x 20 and axis 70 mm. long, has a 70 mm. long edge in the V.P. inclined at 300 to the H.P. and the larger rectangular face containing that edge is inclined at 450 to the V.P. Draw the projections.

14) A cylindrical disc of 50 mm. diameter of base and 25 mm. axis length has a co-axial square hole of 25 mm. sides cut in it. Draw the projections of the disc if it stands on its curved surface with the axis parallel to H.P. and at 600 to V.P. A flat face of the square hole is inclined at 300 to H.P.

15) A tetrahedron of 50 mm. edges has one edge of base on the H.P. inclined at 450 to V.P. and the triangular face containing that edge is perpendicular to H.P. Draw the projections.

16) A square pyramid edge of base 40mm., axis 60 mm. has one edge of base in the V. P. inclined at 450 to H.P. The apex is in the H.P. and 28 mm. in front of the V.P. Draw the projections.

17) A pentagonal prism of 28 mm. edge of base and 60 mm. length of axis has a 28 mm. edge on the H.P. The axis is inclined at 350 to H.P. and 450 to V.P. Draw the projections.

16


18) A rectangular prism - base 40 x 25 and axis 65 mm. long has one of its solid diagonals parallel to H.P. and 350 to V.P. Draw the projections of the prism.

19) A square prism of 25 mm. edge of base and 40 mm. length of axis is kept standing on its square base, centrally on the flat face of a circular disc of 50 mm diameter and 30 mm. length of axis. Draw the front view and the top view of the combined solid if the disc stands on a point of its rim on H.P. and the combined axis is parallel to V.P. and at 450 to H.P. A rectangular face of the square prism is at 300 to V.P.

20) A frustum of a cone—top dia. = 25, base dia. = 55 and axis 60 has its base inclined at 600 to the H.P. and the axis is inclined at 450 to the V.P. Draw the projections.

21) A hexagonal pyramid of 35 mm. edge of base and 55 mm. length of axis has one edge of base in the V.P. inclined at 300 to H.P. the triangular face containing that edge is inclined at 450 to the V.P. Draw the projections.

22) An equilateral triangular prism of 60 mm. edge of base and 30 mm. length of axis has a co-axial circular hole of 25 mm. diameter cut in it. Draw the projections if the prism stands on one side of base on the H.P. inclined at 600 to V.P. and the combined axis is inclined at 450 to H.P.

23) A square pyramid base edge 50 mm. axis 60 mm. is suspended by a string tied to one of the corners of the base. The axis of the pyramid is inclined at 300 to V.P. Draw .the projections of the pyramid.

24) A frustum of a pentagonal pyramid – edge of base = 36 edge of top = 20 and height = 50 has one of its trapezoidal faces in the V.P., the axis is inclined at 300 to H.P. Draw its projections if the smaller pentagonal face is upwards.

25) A pentagonal pyramid of edge of base 30 axis 55, has one corner of base on H.P. The two edges of base passing through this corner are equally inclined to H.P. The triangular face opposite this corner is parallel to H.P. and perpendicular to V.P. The edge of base contained by the triangular face is parallel to V.P. The apex is nearer to the observer. Draw the projections.

26) A cube of 40 mm. edges stands on one of its corners on the H.P. and one of its solid diagonals is perpendicular to V.P. Draw its projections.

27) A hexagonal pyramid edge of base 30 axis 60 is resting on its base with an edge of the base parallel to V.P. and nearer to the observer. The pyramid is tilted on this base edge towards the observer until the apex height is 40 mm. Draw its projections. Measure the inclination of its axis with the H.P.

28) Draw the projections of a cone – diameter of base =50 mm , axis 65 mm. long when one of its generators is in the V.P. and the axis is inclined at 300 to the H.P.

29) A square pyramid of 32 mm edge of base and 50 mm. length of axis has one of its slant edges on the H.P. and the plane containing that edge and the axis is perpendicular to H.P. and inclined at 450 to V.P. Draw the projections if the apex is away from the observer and 10 mm. from the V.P.

30) A pentagonal prism , edge of base 30 mm. and height 70 mm. is resting on an edge of base, the edge being parallel to and at a distance of 40 mm. from V.P. Draw the projections if the upper 30 mm. edge opposite to the edge on which the prism rests is in the V.P.

31) A frustum of a hexagonal pyramid – side of top hexagon = 20mm. side of base hexagon = 40mm. and the axis length = 50 mm. has a 20 mm. edge of top in the V.P. inclined at 450 to the H.P. and the trapezoidal face containing this edge is inclined at 30 0 to the V.P. Draw the projections.

32) A hexagonal prism of 20 mm. side of hexagon and 55 mm. length of axis has a 20 mm. edge of base on H.P. The axis is inclined at 350 to H.P. and 550 to V.P. Draw the projections of the prism.

33) A cylindrical block ( 60 mm. diameter and 25 mm. thick) has a hexagonal hole of 25 mm. sides

cut centrally through its flat faces. Draw the top and front view of the block when its flat faces

are vertical and inclined at 300 to V.P. and the two parallel faces of the hole are parallel to H.P.

17


Sections Of Solids

18


SECTIONS OF SOLIDS

Important information:

1) The position of the solid (prism, cylinder, cone, pyramid) with respect to the H.P. and V.P. is stated in the question. Accordingly, draw two views - elevation and plan of the solid.

2) Further, the solid is cut by a cutting plane. The cutting plane may be of one of the following types— a) Cutting plane is parallel to the V.P. and perpendicular to the H.P.—it will be shown as a line on

the plan. This line will be parallel to the X -Y line. b) Cutting plane is parallel to the H.P. and perpendicular to the V.P.—it will be shown as a

line on the elevation. This line will be parallel to the X -line. c) Cutting plane is perpendicular to both the H.P. and the V.P.---it will be shown as a line on the

elevation or on the plan. d) Cutting plane is perpendicular to the V.P. and inclined to the H.P.—it will be shown as a line on

the elevation. e) Cutting plane is perpendicular to the H.P. and inclined to the V.P.---it will be shown as a line on

the plan. 3) The part of the solid in-between the observer and the cutting plane is assumed to be discarded, hence, it

should be drawn very light. 4) In the case of the prisms and the pyramids, the edges are cut. In the case of the cylinders and the cones,

the generators are cut. 5) The points where the edges and the generators get cut, should be projected from one view to the other

on the corresponding edge or the generator. 6) When joined in proper sequence this will give the apparent shape of the section. 7) The true shape of the section.- Draw X -Y line, parallel to the cutting plane line and at a suitable

distance. Project the points from the cutting plane perpendicularly to the X – Y line. In the compass, measure the distance of a point of the apparent shape from the X -Y line and transfer it to the corresponding projector from X1-Y1 line. When joined in proper sequence, this will give the true shape of the section.

8) In some cases, we have to rotate the solid to transfer the points from one view to the other. 9) In some cases, we have to transfer the points via the 450 line. 10) Indirect questions- In some questions, the position of the cutting plane is not given, instead, the

measurements of the true shape are given. Using the data, we have to fix the position of the cutting plane and then solve the problem.

a) Square prism/cube - 1) rhombus 2) equilateral triangle or largest possible triangle 3) trapezium 4) rectangle ( For Cube - regular hexagon )

b) Cone - 1) circle 2) triangle 3) ellipse 4) parabola 5) hyperbola c) Square pyramid - 1) triangle 2) trapezium d) Tetrahedron - 1) isosceles triangle 2) square e) Cylinder - 1) ellipse 2) rectangle.

EXERCISE

1. A cube of 40mm long edges on the HP on one of its face. Its vertical faces are equally inclined to

the VP. It is cut by A.I.P. in such a way that the true shape of a section is

A trapezium with two parallel side of 20mmand 60mm

A triangle with base 50mm and altitude 40mm

An equilateral triangle of maximum size

A rhombus of maximum size

19


2. A hexagonal prism base 35mm side and axis 70mm long is resting on one of its base edges on

the ground (HP) such that the axis is inclined at 30⁰ to the HP and parallel to the VP. It is cut by

an inclined plane inclined at an angle of 45⁰ to the HP perpendicular to the VP passes at a

distance of 25mm above the base along the axis. Draw FV, sectional TV and true shape of a

section.

3. A square pyramid edge of base 30mm, axis height 50mm rests on its base in the HP with one of

the edge of base parallel to VP. A sectional plane which is the HT cuts the pyramid at an angle

45⁰ to the VP and is 6mm away from the axis of a pyramid. Draw the TV, sectional FV, sectional

SV and the true shape of the section.

4. A hexagonal pyramid, side of base30mm and axis height 90mm lies in the HP on one of its

triangular face and the axis parallel to the VP. It is cut by the vertical cutting plane, inclined at

30⁰ to the VP and passing through the point and the axis 25mm from the base. The apex of a

pyramid is to be retained . Draw the sectional FV, TV and the true shape of the section.

5. A pentagonal pyramid edge of base 40mm long and height 75mm is lying in the HP on the

triangular face with an axis parallel to the VP. It is cut by the section plane perpendicular to the

HP, inclined at 30⁰ to the VP and bisecting the axis of a pyramid. Draw the sectional FV, TV and

the true shape of the section of a pyramid when the apex is retained.

6. A tetrahedron of 70mm side is resting on one of the faces in the HP with a side of that face

perpendicular to the VP. It is cut by A.I.P. so that the true shape of the section is a square. Set

the required cutting plane and draw the section plane, elevation and the true shape of the

section. Measure the side of a square.

7. A pentagonal pyramid, side of base 35mm and height 75mm rests on its base on the HP with

one side of the base perpendicular to the VP. It is cut by a plane which is perpendicular to the

VP, such that the true shape of the section is an isosceles triangle of maximum possible base and

maximum height. Draw its FV, sectional TV and true shape of the section.

8. A vertical cone base 40mm diameter and axis height 50mm is cut by a vertical section plane, HT

of which is parallel to the VP and 10mm away from the axis of a cone. Draw the TV, sectional FV

and the true shape of the section.

9. A right circular cone of base diameter 40mm, axis height 50mm has its base in the HP. It is cut by

auxiliary inclined plane which makes an angle 45⁰ to the HP and passes to through the point on

the axis 20mm below the apex. Draw the sectional TV, sectional SV, FV and the true shape of a

section.

10. A right circular cone of base circle 40mm, axis height 50mm is cut by a section plane which is

perpendicular to the VP and inclined to the HP such that the section plane is parallel to one of

the generator of a cone and is at a distance of 10mm from that generator. Draw the sectional

TV, FV, sectional SV and the true shape of a section. Name the curve obtained.

11. A cone base diameter 40mm and height 50mm is resting on its base on the HP. It is cut by a

plane inclined to the HP and perpendicular to the VP such that the true of a section is an

isosceles triangle of base 30mm. Draw the FV, sectional SV, sectional TV. Measure the

inclination of a cutting plane with the HP.

20


12. A right circular cone of diameter 60mm and length of the axis 60mm is resting on the HP on its

base. It is cut by cutting plane perpendicular to the VP and inclined to the HP such that the true

shape is a parabola of height 60mm. Draw the FV, sectional TV and the true shape of the

section, measure the angle made by the cutting plane with the HP and the base of the parabola.

13. A cone, base diameter 45mm and axis 75mm long is lying on the HP on one of its generator with

an axis parallel to the VP. It is cut by section plane parallel to the HP and perpendicular to the

VP, which bisects its axis. Draw the sectional TV and SV.

14. A cylinder of base diameter 30mm, axis height 50mm stands vertically on the base in the HP. A

section plane perpendicular to the VP, inclined to the HP at 45⁰ to pass through the point on the

axis 12mm below the top base. Draw the FV, sectional TV, sectional SV and the true shape of a

section.

15. A cylinder of 70mm base diameter and 100mm of length of an axis is resting on its base on the

HP. It has a square hole of 35mm side cut through its flat ends, so that the axis of a hole

coincides with the axis of a cylinder. The faces of a hole equally inclined to the VP. It is cut by a

cutting plane inclined to the HP and perpendicular to the VP and passing through the extreme

left point of the top surface and the extreme right point of the base of the cylinder. Draw the FV,

sectional TV, sectional SV and the true shape of a section.

Extra Problems:

1) A rectangular pyramid – base 75 mm. x 60 mm. and height 80 mm. is standing on its base in such a way that the 75 mm. edge of base is inclined at 750 V.P. It is cut by a section plane perpendicular to V.P. and inclined at 450 to H.P. and passing through a point on the axis ,measured 30 mm. from the base. Draw the front view, sectional top view and the true shape of the section.

2) A hexagonal pyramid of 30- mm. side of base and 80- mm. height is resting on its triangular face, its axis being parallel to V.P. It is cut by a section plane inclined at 400 to V.P. and bisecting the axis. Draw the sectional elevation, plan and the true shape of the section.

3) A right circular cone of 60- mm. diameter of base and 80- mm. height is lying on one of its generators on the H.P. with the axis parallel to V.P. A cutting plane making an angle of 450 to V.P. and perpendicular to H.P. cuts the cone bisecting it’s axis Draw the front view, top view and the true shape of the section.

4) A pentagonal pyramid edge of base 32 mm. and axis 65 mm. long is resting on one of its triangular faces with the axis parallel to V.P. It is cut by a section plane perpendicular to H.P. and inclined at 300 to V.P. bisecting the axis. Draw the plan, sectional front view and the true shape of the section.

5) A pentagonal prism with side of base 35 mm. and length of axis 50 mm. rests on one of its rectangular faces on the ground. The axis of the solid is parallel to both H.P. and V.P. The solid is cut by an auxiliary inclined plane making an angle of 300 to with the H.P. The cutting plane bisects the axis of the solid. Draw the apparent and the true shape of the section.

6) A cone – diameter of base 60 mm., length of axis 70 mm. is standing on its base on the ground .A section plane perpendicular to H.P. and inclined at 600 to V.P. cuts the cone and is 10 mm. away from the axis. Draw the sectional front view, the top view and the true shape of the section.

21


7) A cone – 70 -mm. diameter of base and axis 90 mm. long is resting on its base on the ground. It is cut by section plane perpendicular to V.P., parallel to and 15 mm. away from one of its end generators. Draw its front view, sectional top view, sectional side view and the true shape of the section.

8) A cube of 40 mm. long edges has its vertical faces equally inclined to the V.P. It is cut by a section plane, perpendicular to the V.P. so that the true shape of the section is a regular hexagon. Determine the inclination of the cutting plane with the H.P. and draw the sectional top view and the true shape of the section.

9) A right cylinder of 50- mm. diameter and 70 -mm. length of axis, is resting on its base on the ground. It is cut by a section plane perpendicular to V.P. and 300 to H.P. and which passes through a point on the axis 20 mm. from the top. Draw the front view sectional top view, sectional side view and the true shape of the section.

10) A pentagonal pyramid, having edge of base 30 mm. and axis 60 mm. long is resting on one of its triangular faces on the ground with its axis parallel to V.P. A cutting plane perpendicular to V.P. and inclined at 300 to H.P. cuts the pyramid and passes through the mid- point of the axis. Draw the front view, sectional top view and the true shape of the section.

11) A tetrahedron of 60 mm. edges is resting on its base with one of the edges perpendicular to V.P. It is cut by an inclined plane such that the true shape of the section is an isosceles triangle of 50- mm. base and 40- mm. altitude. Find the inclination of the cutting plane with the H.P. and draw the front view, the sectional top view and the true shape of the section.

12) A cylinder of 50- mm. diameter and 72 mm. height is resting on a point of its rim of base on the H.P. and the axis is parallel to V.P., inclined at 300 to H.P. It is cut by a plane at 900 to H.P. and at 450 to V.P. bisecting the axis. Draw to full scale the sectional front view, the top view and the true shape of the section.

13) A hollow square prism, base 50 mm. side (outside), axis 80 mm. long and thickness of walls 10 mm. is resting on the ground with the axis vertical and one of the rectangular faces inclined at 300 to V.P. It is cut by a section plane inclined at 450 to the H.P. and perpendicular to V.P. which passes through the axis at a point 15 mm. from its top end. Draw the front view, top view and the true shape of the section.

14) An equilateral triangular prism of 36 mm. base and 80 mm. length of axis lies on one of its rectangular faces on the ground with the axis at 450 to V.P. It is cut by a section plane perpendicular to V.P. and inclined at 300 to the ground and which passes through a point on the axis 30 mm. from the nearer end. Draw three views of the cut prism and show the true shape of the section.

15) A cylinder, base 64 mm. diameter and axis 70 mm. long has a square hole of 30 mm. sides cut axially in it. The vertical faces of the square hole are equally inclined to the V.P. and the common axis is vertical. The cylinder is cut by a section plane perpendicular to V.P. and inclined at 600 to H.P. passing through a point on the axis 20 mm. from the top end. Draw three views of the cut cylinder and show the true shape of the section.

16) A pentagonal pyramid, side of base 40 mm. length of axis 70 mm. stands on its base with a side of base parallel to the V.P. and away from the observer. A plane, perpendicular to H.P. and inclined at 600 V.P. cuts the pyramid and is 8 mm. away from the axis of the pyramid. Draw projections and show the true shape of the section.

17) A cone, diameter of base 75 mm. and axis 80 mm. long is held with its axis parallel to V.P. and inclined at 600 to the ground. It is cut by a plane perpendicular to both the H.P. and the V.P. and which passes through the point on the axis 50 mm. from the base. Draw three views of the cut cone.

18) A cylinder of 50 mm diameter of base and 75- mm. length of axis has one of its ends on the ground. It is cut by an A.I.P. in such a way that the true shape of the section is an ellipse of

22


largest possible major axis. Draw the front view, sectional top view, the true shape of the section State the inclination of the cutting plane with the H.P.

19) A hexagonal prism side of hexagon 36 mm. and height 75 mm. having an axial circular hole of 30 mm. diameter is resting on the ground on its hexagonal face with a side of the face parallel to V.P. It is cut by a plane at 60 degrees to the H.P. and at right angles to V.P. The plane passes through a point on the axis 15 mm. from the top. Draw front view, top view and the true shape of the section.

20) A square pyramid of 50- mm. side of base and 70- mm. height is standing on its base with one side of base perpendicular to V.P. It is cut by an inclined plane in such a way that the true shape of the section is a trapezium whose parallel sides measure 40 mm. and 20 mm. Draw the front view, sectional top view and the true shape of the section.

21) A rectangular pyramid base 45x 70 and axis 75 mm. long has a 45 mm. edge on the ground, perpendicular to V.P. and the base is inclined at 300 to the ground. A cutting plane perpendicular to the ground, inclined at 450 to the V.P. cuts the pyramid and passes through a point on the axis 30 mm. from the base. Draw three views of the cut pyramid.

22) A hexagonal prism side of base 36 mm. long has a central circular hole of 35 mm. diameter such that the axis of the hole coincides with that o\f the prism. The prism is lying on a rectangular face on the ground and the axis is inclined at 300 to V.P. A cutting plane perpendicular to V.P. and inclined at 300 to H.P. cuts the prism passing through a point on the axis m25 mm. from the nearer end. Draw two views of the cut prism and show the true shape of the section.

23) A pentagonal prism side of base 25 mm. axis 70 mm long is resting on a rectangular face on the ground with the axis inclined at 300 to the V.P. A cutting plane perpendicular to H.P. and inclined at 450 to V.P. cuts the prism passing through a point on the axis 25 mm. from the nearer end. Draw sectional front view and top view.

24) A hexagonal pyramid- side of base 25 -mm. length of axis 65 mm. has a side of base on the ground perpendicular to V.P. and the base is inclined at 450 to h.p. A plane inclined at 450 to V.P. and perpendicular to H.P. cuts the pyramid bisecting the axis. Draw sectional front view, top view and the true shape of the section.

25) A hexagonal prism- edge of base 30 mm. length of axis 85 mm. rests on one of its rectangular faces and the axis is inclined at 600 to V.P. A cutting plane perpendicular to V.P. and inclined at 450 to H.P. cuts the prism at a point on the axis 35 mm. from the nearer end Draw the front view, sectional top view and the true shape of the section.

26) A pentagonal pyramid, edge of base 30 mm. length of axis 70 mm. has one of its triangular faces in the V.P. and the axis is parallel to H.P. A cutting plane perpendicular to V.P. inclined at 300 to H.P. cuts the pyramid bisecting the axis. Draw the front view, sectional top view and the true shape of the section.

27) A circular disc of 70mm. diameter and 30mm. length of axis is resting on its circular base. A square pyramid of 35mm. edge of base and 45mm. length of axis is resting on its square base centrally on the circular disc. All the base edges of the pyramid are equally inclined to the V.P. The axis of both the solids are co-linear. A cutting plane perpendicular to V.P and inclined at 450 to H.P. cuts both the solids and passes through the mid point of the axis of the pyramid. Draw the front view, sectional top view and the true shape of the section.

28) A tetrahedron of 64 mm. edges stands on its base with an edge of base perpendicular to the V.P. The solid is cut by a plane perpendicular to V.P. and inclined to H.P. in such a way that the true shape of the section is a square. Draw the front view sectional top view and the true shape of the section.

29) A square prism of 30mm. edge of base and 70mm. length of axis stands on its square base with all the edges of base equally inclined to V.P. A cutting plane perpendicular to V.P. and inclined to H.P. cuts the prism so that the true shape of the section is the largest possible

23


equilateral triangle. Draw the front view, sectional top view and the true shape of the section.

30) A hexagonal prism of 25mm edge of base and 65mm length of axis stands on one edge of base on H.P. while the axis is inclined at 600 to H.P. and parallel to V.P. A cutting plane perpendicular to H.P. and inclined at 450 to V.P. cuts the prism at a point on the axis 30mm from the upper end. Draw sectional front view, top view and the true shape of the section.

31) A right circular cone of 60mm diameter and 70 mm length of axis rests on its base on H.P. It is cut by a plane perpendicular to V.P. and inclined to H.P. such that the true shape of the section is a parabola of 60mm height. Draw the front view, sectional top view and the true shape of the section.

32) A cone of 70 mm diameter of base and 60mm length of axis stands on its base on H.P. It is cut by an A.I.P. so that the true shape of the section is a isosceles triangle with the vertex angle of 500 Set the required cutting plane and draw front view, sectional top view and the true shape of the section.

33) A cylinder of 50mm diameter and length of axis 80mm has its axis parallel to H.P. and inclined at 300 to the V.P. It is cut by a section plane inclined to the V.P and perpendicular to H.P., so that the true shape of the section is an ellipse of 70mm. major axis. Draw the top view, sectional front view and the true shape of the section.

34) A pentagonal pyramid of 32mm side of base and 70mm axis length has one of its slant edges on the H.P. parallel to V.P. with the axis also parallel to V.P. A vertical section plane inclined at 300 to V.P. cuts the pyramid bisecting the axis. Draw the sectional front view, top view and the true shape of the section.

35) A cylinder of 50mm diameter and 80mm length of axis has its axis parallel to H.P. and inclined at 300 to the V.P. It is cut by a section plane inclined to the V.P. and perpendicular to the H.P. so that the true shape of the section is an ellipse of 70- mm major axis. Draw the top view, sectional front view and the true shape of the section.

36) A glass tumbler is in the form of a frustum of a cone—top diameter =60mm bottom diameter =35 height =60. It is completely filled with water and then tilted on the rim of its bottom face so that its axis remains at 450 to H.P. and parallel to V.P.. Obtain the projections of the tumbler and show the water surface in both the views.

37) A tetrahedron of 50mm edges has a triangular face in the V.P. with an edge of that face parallel and nearer to H.P. A cutting plane perpendicular to H.P. and at 450 to V.P. cuts the pyramid through the mid point of the axis. Draw three views and the true shape of the section.

38) A semi-cone of diameter 80mm and axis 90mm is resting on its semicircular base on H.P. such that the triangular face of the semi-cone is parallel to V.P. and away from the observer. It is cut by a section plane perpendicular to V.P. and inclined at 450 to H.P. passing through the mid-point of the axis. Draw the sectional plan, front view & the true shape of the section. Also add a right hand side view showing the sectional detail on it. (M-95)

39) A pentagonal prism with 30mm edge of pentagon and 60mm length of axis rests on one of its longer edges on the H.P. having a face containing that edge at 300 to H.P. The axis being parallel to both the H.P. and the V.P. and in this position only two faces of the prism are visible in the F.V. It is cut by a plane whose H.T. is inclined at 300 to V.P. bisecting the axis of the prism. Draw sectional front view, top view and the true shape of the section.

40) A cube of 50mm edges is kept on its square base on H.P. with all the edges of the base equally inclined to the H.P. A cutting plane perpendicular to V.P. and inclined to the H.P. cuts the cube so that the true shape of the section is a trapezium. One side of the trapezium is equal to the diagonal of the square and the opposite parallel side is half the diagonal. Draw the front view, sectional top view and the true shape of the section.

24


Orthographic Projection

Sectional Orthographic Projection

Isometric Projection

25


26


27


28


29


30


31


32


33


34


Engineering Drawing - HOME - Prof. Ibrahim … Mobile: 9892128099 By Prof.Shaikh Ibrahim Ismail...

Documents

Transcript of Engineering Drawing - HOME - Prof. Ibrahim … Mobile: 9892128099 By Prof.Shaikh Ibrahim Ismail...