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module no 1 - engineering drawing

Q1. Draw an involute of a circle of 40 mm diameter. Also draw the normal and tangent to the curve at a point 80mm from the centre of the circle. - (6 Marks) (D-15)

Ans: Step 1: Draw a circle of 40mm diameter and mark its center C and point P. draw a horizontal line PP’ equal to the circumference of a circle.

Step 2: Divide the line PP’ in to a number of parts (Say 8). Name the point as 1’,2’,....etc. divide the circumference of the circle also into same number of equal parts and mark them as 1,2,,....etc.

Step 3: From point 1 on the circle draw a tangent. With P1’ as radius and point 1 as center cut the tangent into a point P1. tp obtained corrected center for curve, with P as center & P8 as radius draw a small arc near 8. With P1 as center and P8 as radius cut previou arc to get new center for curve. With new center =draw an arc between P & P1. Similarly obtain points P2,P3,.....etc. on tangents through corresponding points 2,3,....etc.

Step 4: Draw an arc with C as center and 80 mm radius to cut at point Q on involute.

Step 5: Draw a tangent to circle such that it passes point Q this will be the tangent to the curve. Draw a line right angle to normal at point Q. this will be the tangent to the curve.

Q2. A line AB 100mm long is tangent at the op of a circular disc of 70 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. - (Extra)

Q3. One end of an inelastic string AB 150.5 mm long is attached to the circumference of a half circular, half hexagonal disc of 49 mm diameter. Draw the curve traced out by the other end of the string A when it is completely wound round the circumference of the disc, keeping the string always tight. Take initial position of the string tangent at the midpoint of the circular portion. - (Extra)

Q4. Draw an involute of a circle of 60 mm diameter.Also draw the normal and tangent at a point on the curve at a distance of 120 mm from the centre of the circle. - (Extra)

Q5. Draw a helix on a cylinder of 50mm diameter of two turns, given pitch equal to 40 mm. - (Extra)

Q6. Draw a cycloid of a point on the generating circle of 40 mm diameter. - (Extra) Ans: Step 1: Draw a circle of 40 mm diameter and mark the center C and point P. draw a horizontal line PP’ along which the circle rolls without slipping.

Step 2: Divide the circumference of the circle into a number of equal parts (Say 8) and name the points as 1,2,3,4,....etc. draw a line CC’ equal to the circumference of the circle and divide into 8 equal parts i.e C1,C2,....etc.

Step 3: through the points 1,2,....etc on the circle draw lines parallel to PP’. with center C1 and radius CP cut the line through point 1 to obtain point P1

Step 4: Similarly, with the centers C2,C3….etc obtain points P2,P3,........etc, on the corresponding lines through [points 2,3,....etc. Join P,P1,P2,......,P’ with a smooth curve.

Step 5: Draw a line parallel to and 30 mm above baseline to cut the cycloid at point Pm. Draw arc equal to radius of circle to cut CC’ at point Cm. Draw a line perpendicular from Cm at baseline PP’ at N.

Step 6: Draw line from N to meet Pm on curve. This will be normal to the curve at Q. draw [perpendicular line to normal at Q which will be tangent to the curve at Q.

Q7. A wheel of 50 mm diameter rolls on a horizontal straight surface for half revolution and then on a vertical surface downward for the next half revolution. Draw the locus of a point ‘P’ on the circumference of the wheel if initial position of the point ‘P’ is in contact with the horizontal surface. - (Extra)

Q8. A wheel of 50 mm diameter rolls downwards on a vertical wall for half revolution and then on the horizontal floor for half revolution. Draw the locus of a point ‘P’ on the circumference of the wheel. The initial position of the point ‘P’ is on opposite of contact with the wall. - (Extra)

Q9. A circular plate of diameter 60 mm rolls without slipping along a straight line inclined at 30 degrees to the horizontal.Draw locus of point of its contact with the line if it completes one rotation. Name the curve. - (M-13)

Q10. An equilateral triangle PQR of side 60 mm is inscribed in a circle rolls without slipping along a straight line at 30 degrees to the horizontal. Trace the path of vertices P,Q and R for one complete revolution. Assume initial position of the vertex point ‘P’ in contact with the inclined line. - (Extra)

Q11. A circle of 50 mm diameter rolls along a straight line without slipping. Draw the curve traced by a pointy ‘P’ on the circumference of the circle for one complete revolution. - (Extra)

Q12. A circle of diameter 50 mm rolls without slip on a horizontal surface by half a revolution and then it rolls up on a vertical surface by another half revolution.Draw the locus of a point P which is initially at the bottom of the circle. - (M-14)

module no 2 - projection of points and lines & projection of planes

Projection of Lines:

Read carefully: 1.When a line is perpendicular to one of the principle plane it must be parallel to other principle plane. 2.Projection of a line on a plane to which it is perpendicular is a point view and projection on other principal planes are line view of true length and parallel to respective ground line 3.When a line is parallel to one and inclined to other principle planes, its projection plane to which it is parallel will show true length and also so true inclination with other two planes.projection on plane to which it is inclined and not parallel are shorter than the true line and they will be parallel to corresponding ground lines. 4.When a line is inclined to all the three principle planes,its projections on all the principle plane will show apparent length and will also show apparent inclination. 5.Apparent inclination are always greater than the true inclination. 6.Apparent length and apparent inclination go together,similarly true length and true inclination go together. 7, Whenever Θ + 𝜙= 90 , the line will be parallel to the PROFILE PLANE.Hence the side view will give true length and true angles i.e Θ & 𝜙.Distance between the end projector will be zero

Q1. The front view of a line AB 80 mm long, measures 60 mm. The end A is 15 mm in front of VP and 10 mm above HP. The end B is in third quadrant, Draw the projections of the line, if the line is inclined 30° to HP. Also find the inclination of line with VP. - (7 Marks) (D-15)

Ans: Given: T.L. = 80 F.V. = 60 A’ = 10 (above) A = 15 (in front) θ = 300300 B is in 3rd quadrant. Steps to draw:

Locate A’ and A as per given information

Draw a line A’B’(T.L) = 80 at an angle of 300300 from point A’. Project a line till locus of A and draw an arc to get T.V.

Now project a direct line from T.V. to get F.V. on locus of B’.

Project an arc from F.V. till locus of A’ and then draw a straight line upto locus of B. This way we will get T.L.

Now measure the respective angles.

Q2. A straight line PQ has its end point P 10mm above HP and 15mm in front of the VP. The line is 50mm long & its front and top views are included at an angle of 60° and 45° respectively. Draw the projections of the line PQ and find its inclination with the HP & VP. - (9 Marks) (D-17)

Ans: Data: p’ 10↑ , p 15↓, TL=50,α=60,β=45 Find a’b’,ab, Θ and 𝜙. Solution: (I) As the position of p’ and p and α and β are know, projection of some part of the line PQ(say PR) can be draw,where R is a point on line PQ. Then, p’r’ and pr will be drawn. (ii)As the true length is known , it can be used to draw either p’q’, or pq2, for which either Θ or 𝜙 should be known , or the path of q1’ or the path of q,should be known.As Θ or 𝜙 for part length of the line or full length of the line should be the same,either Θ or 𝜙 for PR should be found.Those can then be used for drawing p’q1’ or pq2. (iii)Draw the various lines in the following order. Keep figure 4.24 as a reference with a the same as p here and b same as q, and r a point in between.That should help us know various line positions: 1. Locate p’,p and draw p’r’ ∠ at α and of some length (say x). 2. Locate p and draw pr ∠ at β, and vertically in line with r’ so that pr is part length of pq. 3. Draw vertical line r’r .Assuming PR to be similar to the AB of figure 4,34 ,draw arc r’r2’, r2’r2, rr2,pr2 , which will be inclined to XY at 𝜙. 4. Extend pr2 to q2 so that pq2=TL=50mm. 5. Draw the path of q ,extend pr to q ,draw qq’, extend p’r’ to q’, and draw q’q1’, p’q1’ of TL. Then p’q’ and pq are the required projections.Angles made by p’q1’ and pq with XY are the required angles Θ and 𝜙 made by the line with the HP and the VP.

Q3. The distance between the end projectors of a line AB is 60mm. The end A is 25mm above H.P. and 45mm in front of V.P. while the order end B is 60mm above H.P. and 15mm in front of V.P. Draw projections and find the true length and also inclination of the line with H.P. and V.P. - (9 Marks) (M-16) Ans: Given: DBEP = 60 A’ = 25 (above H.P.) A = 45 (infront of V.P.) B’ = 60 (above H.P.) B = 25 (infront of V.P.) ∴ Here line is in 1st Quadrant

T.L = 77 Inclination of line with H.P. is α = 300 and θ = 270 Inclination of line with H.P. is β = 250 and ø = 270 Steps:

Draw x-y line. Mark points A and A’ as per the given information

Draw a locus from points A and A’

Then locate the points B and B’ and draw their respective locus

Join A’ and B1’ to get F.V. project the line downward to get T.V.

Draw an arc from F.V. to get the T.L. as well as draw an arc from T.V. to get T.L. on locus of B’ as per given fig.

Now measure the respective angles.

Q4. The distance between end projectors of a straight line AB is 35mm. The end point A is 10 mm above HP(HRP) and 20mm in front of VP(FRP).The end point B is 45 mm above HP and 70 mm in front of VP.Draw projections of the line and determine its inclination with HP and VP.Also find its true length. - (Extra) Ans: Data:- DBEP=35 a’=10↑ XY a=20↓ XY b’=45↑ XY b= 70↓ XY TL=? θ=? ø=?

Q5. The distance between end projectors of a line AB is 35 mm .The end point A is 10 mm above HP and 20 mm in front VP.The end point B is 40 mm from both reference planes.Draw the projections and determine the inclination with HP and VP when point B is in third quadrant .Also Find TL. - (Extra) Ans: Data:- DBEP=35 a’=10↑ XY a=20↓ XY b’=40↑ XY b= 40↓ XY TL=? θ=? ø=?

Q6. The Top View of 75 mm tang line AB Measures 65 mm while the length of Its front view is 50 mm. Its one end A is 10 mm above HP and 15 mm In front of VP while the other end is in the third quadrant. Draw projections of AB and determine its inclinations with HP and VP. - (Extra)

Q7. A line AB, 75 mm long, has its end A in HP and 15 mm in front of VP. The end B is in first quadrant. The line HP inclined at 350 to HP and 550 to VP. Draw its projections. - (Extra)

Q8. The end projectors of a line MN are on the same projector. The end point M is 25 mm below HP and 5mm behind VP. Point N is 50mm above HP and 40 mm in front of VP. Draw projections of the Me. Determine Its true length and true inclination with reference planes. - (Extra)

Q9. A straight line AB, equally inclined to HP and VP has its end A in front of VP and 20 mm above HP. The and B is behind VP and 40 mm below HP. A point on the line Is on VP and 10 mm below HP. Draw the projections and find its True length. Also find inclination of One the with HP. if the distance between the end projectors is 60 mm. - (Extra) Ans: DBEP=60 θ=ø a =↓ XY a’=20↑ XY b=↑ XY b’= 40↓ XY TL=? θ=? ø=?

Q10. End projectors of a line PQ are 80 mm apart. The point P is 20 mm above HP and 60 mm behind VP. Another point R on the line which divides the line In the ratio (PQ:QR) of 3:5 and lies in both the reference planes. Draw the projections of the line and determine True length and inclinations with reference planes. Also state the position of the point Q with the reference planes. - (Extra) Ans: DBEP=80 p=60↓ XY p’=20↑ XY PQ:QR=3:5 r & r’ on XY TL=? θ=? ø=?

Q11. line AB has its end A 10 mm above HP and 50 mm In front of VP. The point P on the line 60 mm from A is In VP. The line is Inclined at 200 to HP. The other end points B Is In second quadrant and equidistant from both reference planes. Draw Its projections. - (Extra) Ans: P=60 from A p on XY a =50↓ XY a’=10↑ XY b=↑ XY b’= ↑ XY θ=200 b’ from XY = b from XY

Q12. A 70 mm long line AB has Its end A on HP and point B on VP. The fine is inclined at 30° to HP and 45° to VP. Draw Its projections when the line Is In first quadrant. - (Extra)

Q13. Line AB inclined at 300. To HP and its top view is inclined at 450 to VP.The end point A is 10mm above HP and 20mm in front of VP.Draw the projections when FV length of the line measures 60mm.Find the length of AB and its inclination with VP. - (Extra) Ans: EL=60 a=20↓ XY a’=10↑ XY EL=60 Θ=300 β=450 ø=? TL=?

Q14. The end P of a line PQ 120 mm Iong is In 2nd quadrant and 20 mm from both the reference planes. End Q is in 3rd quadrant. The line is inclined at 30* with HP and the distance between the end projectors measured parallel to XY Ione is 80 mm. Draw the projections. - (Extra)

Q15. A line AB 70mm long, has its end A 10 mm above HP and 15mm in front of VP. Its top view and front view measures 60mm and 400mm respectively. Draw the projections of the line and determine its inclinations with HP and VP. - (Extra)

SOLUTION: DATA: TL = 70 A’ = 10 XY (up) A =15 XY (down) TV = PL = 60 FV= EL = 40 θ=? ø=?

Q16. The TV of line AB measures 60mm and is inclined at 56° to the axis XY line. Point A is 10 mm above HP and 20 mm in front of the VP. Point B is 45mm above the HP and in front of the VP. Draw the projections of line AB. - (Extra) SOLUTION:

DATA: TV =60 beta =56° a’ = 10 XY (up) a= 20 XY (down) b’ = 45 XY (up) b XY (down)

Q17. Side view of a line AB 75mm long, makes an angle of 40° with XY line. Draw TV and FV of line when length of side view is 50mm. Take point A tp be 15mm above HP and 55mm infront of VP, the point B being closet to VP. - (Extra)

Q18. The top view of 100mm long line AB measures 70mm while the length of its F.V. is 85mm. Its one end A is 15mm above H.P. and 25mm in front of V.P. The other end is in the 3rd quadrant. Draw projection of the line and find its inclination with H.P. and V.P. - (Extra) SOLUTION: DATA: TL = 100mm TV = PL = 70mm FV = EL = 85mm a’ = 15 XY (up) a = 25 XY (down) b XY (up); b' XY (down) θ=? ø=?

Q19. The end A of a line AB 90mm long is in 2nd quadrant and 15mm from both the HP and VP. End B is in 3rd quadrant. The line is inclined at 30° with HP and the distance between the end projectors measured parallel to XY line is 60mm. Draw the projections of line and find its inclinatio with VP. - (Extra) SOLUTION: DATA: TL = 90 a’ & a = 15 XY (up) b XY (up); b' XY (down) theta = 30° DBEP = 60

Q20. A line PQ, 110mm long has its plan and elevation length 80mm and 90mm long. One end of the line P is in HP and the other end Q in VP. Assume the line in 3rd quadrant. Draw the projection of the line and find its inclination with HP and VP. - (Extra) SOLUTION: DATA: TL = 110 TV = PL = 80 FV = EL =90 p’ on XY q on XY theta =? phi= ?

Q21. A line AB, 100mm long is inclined at an angle of 30° to HP and 45° to VP. Its endpoint ‘A’ is 10mm above HP and 20mm in front of VP. Draw the projections when point B is in the fourth quadrant. - (Extra) SOLUTION: DATA: T.L. = 100 theta =30° phi =45° a’ = 10 XY (up) a = 20 XY (down) b’ XY (down), b XY (down)

Q22. A pentagonal pyramid has an edge of base in the H.P. and inclined at an angle 30° to the V.P. while the triangular face containing that edge makes an angle of 45° with the H.P. Draw the projections of the pyramid when the apex in nearer to the observer. The length to the side of the base of the pyramid is 35 mm and axis 70 mm. - (15 Marks) (D-15)

Q23. A pentagonal pyramid of 28mm. Edge of base and 60mm length of axis has a 28mm. Edge on the H.P. The axis is inclined at 35° to H.P. 45° to V.P. Draw the Projection - (15 Marks) (M-16)

Q24. A cone, base 50 mm diameter and axis 60 mm long rests on its circular rim on the HP with the axis making an angle of 30 degree with the HP and its top view making an angle of 45 degree with the VP. draw its projections if apex is nearer to observer. - (Extra) (15 marks)

Q25. A cylinder of 50 mm diameter of base and 70 mm length of an axis is resting on one of the points on circumference in the VP. Draw its projections if one of the generators is inclined at 300 to the VP. - (Extra) (M-16)

Q26. A pentagonal pyramid of base 30mm and axis 60mm stands on an edge of base on HP. The edge makes an angle 450 with VP. Draw its projections if the apex is 40 mm above HP and nearer to the observer. - (Extra) (M-13)

Q27. A pentagonal pyramid has a height of 60 mm and the side of base 30 mm. The pyramid rests with one of the sides of a base oh HP. such that the triangular face containing that side is perpendicular of Hp and makes an angle 30 with VP. Draw its projections. - (Extra)

Q28. A hexagonal pyramid of base edge 30mm and axis 80mm long has one of its triangular face 45° to V.P. Draw projection when the base edge of that triangular face is inclined at 50° H.P. and parallel to V.P. - (Extra)

Q29. A pentagonal pyramid, base edges 40mm and axis length 75mm rests on its slant edge on HP, which is inclined at 30° to VP. Draw its projections with apex nearer to the observer. - (Extra)

Q30. A pentagonal prism of 30 mm edge of base and 65mm length of axis is having an edge of a base in Vp. Draw the projection of the prism, if the rectangular side face containing that edge, is inclined at 30 degrees to the VP. Also draw the side view of the prism. - (Extra)

Q31. A pentagonal pyramid side of base 35mm and axis 70mm long, is lying on one of its corners on the H.P. such that, the two 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 HP. and the V.P. Draw the projections of the solid, when the apex of the pyramid is nearer to the observer. - (Extra)

module no 3 - projection solids, section of solids, development of lateral surfaces of sectioned solids

Q1. A square prism, edge of base 35 mm and axis length 70mm, is resting on HP on one of its base edges and the axis makes an angle 40° to HP and parallel to VP. Draw its projections. - (6 Marks) (D-15)

Q2. A cylinder 40mm diameter and 60mm long is resting on its base on H.P. It is cut by a section plane perpendicular to VP, inclined at 45° to HP and passing through the midpoint of the axis. Draw the front view, sectional top view and true shape of the section. Also develop the lateral surface of the cut cylinder. - (15 Marks) (D-15)

Q3. A square pyramid of base side 25mm and altitude 50mm rests on its base on the HP with two sides of the base parallel to VP. It is cut by a plane bisecting the axis and inclined at 30° to the base. Draw front view, sectional top view and true shape of the section. Also draw the development of the lower part of the pyramid. - (15 Marks) (M-16)

Q4. A right circular cone of base circular diameter 50mm and axis 60mm long is resting on its base on HP. It is cut by a section plane which is perpendicular to VPand inclined to HP such that the plane is parallel to the end generator and 10mm away from it. Draw the front view, the sectional top view and the true shape of section. Also draw the development of the cone after removing the portion containing the apex. - (D-14)

Q5. A tetrahedron of 50 mm long edges is resting on one edge on HP while one triangular face containing this edge is vertical and 45 degrees inclined to VP. draw projections. - (Extra) Ans: Steps:

As it is resting assume it standing on HP

Begin with TV, an equilateral triangle as side case as shown:

First project base points of FV on XY, name those and axis line.

From ‘a’ with TL of edge, 50 mm, cut on axis line and mark o’

Then complete FV

In 2nd FV make face o’b’c’ vertical as said in problem.

And solve completely.

Q6. A cone of base 70mm diameter and axis 90mm long is resting on its base on HP. It is cut by a section plane perpendicular to the VP and parallel to and 15mm away from one of its end generators. Draw the sectional top view, front view and sectional side view. Also draw the true shape of the section. Also draw development of the lateral surface of the cone - (15 Marks) (D-17)

Q7. A pentagonal pyramid side of base 35mm and height 70mm rests on its base on H.P. with one side of base perpendicular to V.P. It is cut by on A.I.P. Such that the true shape of section is an isosceles triangle of maximum possible base and minimum height. Draw its Front View, Sectional Top View and true shape of the section. - (Extra)

Q8. A cone, diameter of 40mm, axis 50mm, is resting on its base on the H.P. It is cut by a section plane perpendicular to both the reference planes in such a way that the section plane is at the distance 8mm from the axis of a cone. Draw the F.V, T.V. and the sectional side vie. Name the Sectional True shape obtained. - (Extra)

Q9. A cone of diameter 60mm and height 70mm rests on H.P on its base. A cutting plane (A.V.P.) perpendicular to H.P. and inclined to V.P. at 45°, cuts the cone 10mm in front of the axis. Draw top view, sectional front view and true shape of section. - (15 MARKS)

Q10. A cylinder base, 45mm diameter, axis height 75mm long is lying on the H.P. with the axis parallel to both the H.P. and V.P. It is cut by an auxiliary vertical plane inclined to the V.P. at 45°, which bisects the axis. Draw its sectional F.V., T.V. and true shape of the section. - (Extra)

Q11. A cube of edge 60mm is resting on H.P. with all vertical faces equally inclined to V.P. it is cut by section plane perpendicular to V.P., inclined to H.P. Such that true shape of cut face is trapezium with parallel sides 65mm apart. One of the parallel side which is longer measures 70mm. Draw F.V. sect. T.V. and true shape of cut face. Find inclination of section plane and length of smaller parallel side of trapezium. - (Extra)

Q12. A square prism 80mm long is cut in two halves, so that the true shape of the cute surfaces is rhombus of 40mm side and one of its angles beings 70°. Draw the F.V., sectional T.V. & T.S.S. Also find the cutting plane inclination with H.P., if the prism is resting on H.P with rectangular faces equally inclined to V.P. - (Extra)

module no 4 - orthographic projection

Q1. Figure given below shows two views of an object. Draw the following views to full scale:- (9 Marks) (D-15) i) Front view(5 Marks) ii) Left hand Side view.(4 Marks)

Q2. Figure given below shows two views of an object. Draw the following views to full scale: - (15 Marks) (M-17) (D-15)

Sectional front view section P-P(5 Marks)

Top view (4 Marks)

Left hand side view(4 Marks)

Insert minimum 10 dimensions(2 Marks)

Q3. Figure given below shows two views an object. Draw the following views to full scale: - (9 Marks) (M-17)

Front View from X(4 Marks)

Top View(4 Marks)

Insert minimum 6 dimensions(1 Marks)

Q4. For the object shown in figure draw the following views - (15 Marks) (D-17)

Sectional front view along section A-A.(4 Marks)

Side view from left(4 Marks)

Top view(5 Marks)

Insert the major dimensions(2 Marks)

Q5. Figure given below shows the pictorial view of an object. Draw to full scale the following views. - (M-14) i) Sectional Front view ii) Top view iii) R.H.S view iv) Insert 10 major dimensions

Q6. Figure given below shows the pictorial view of an object. Draw to full scale the following views - (M-8) i) Sectional elevation along plane AA in the direction of arrow X ii) End view in the direction of arrow Y iii) Plan iv) Insert 10 major dimensions

Q7. Figure given below shows the pictorial view of an object. Draw to full scale the following views. (D-08) i) Sectional Front view along AA ii) Top view iii) L.H.S view iv) Insert 10 major dimensions

Q8. Figure given below shows the pictorial view of an object. Draw to full scale the following views - (M-09) (D-09) i) Sectional Front view along section AA ii) L.H.S view iii) Top view iv) Insert 10 major dimensions

Q9. Figure shows a pictorial view of an object. - (Extra) Draw the following views:-

Front view along arrow X

Top view

Sectional side view along P-Q

Insert at least 8 major dimensions.

module no 5 - isometric views

Q1. Draw the isometric view of the following using the natural scale. - (7 Marks) (M-17) (D-15)

Q2. Draw the isometric view of the following using the natural scale. - (7 Marks) (M-17) (D-15)