1. TO DRAW PROJECTIONS OF ANY OBJECT, ONE MUST HAVE FOLLOWING INFORMATION A) OBJECT { WITH IT’S DESCRIPTION, WELL DEFINED.} B) OBSERVER { ALWAYS OBSERVING PERPENDICULAR TO RESP. REF.PLANE}. C) LOCATION OF OBJECT, { MEANS IT’S POSITION WITH REFFERENCE TO H.P. & V.P.} TERMS ‘ABOVE’ & ‘BELOW’ WITH RESPECTIVE TO H.P. AND TERMS ‘INFRONT’ & ‘BEHIND’ WITH RESPECTIVE TO V.P FORM 4 QUADRANTS. OBJECTS CAN BE PLACED IN ANY ONE OF THESE 4 QUADRANTS. IT IS INTERESTING TO LEARN THE EFFECT ON THE POSITIONS OF VIEWS ( FV, TV ) OF THE OBJECT WITH RESP. TO X-Y LINE, WHEN PLACED IN DIFFERENT QUADRANTS. ORTHOGRAPHIC PROJECTIONS OF POINTS, LINES, PLANES, AND SOLIDS. STUDY ILLUSTRATIONS GIVEN ON HEXT PAGES AND NOTE THE RESULTS.TO MAKE IT EASY HERE A POINT A IS TAKEN AS AN OBJECT. BECAUSE IT’S ALL VIEWS ARE JUST POINTS.

2. NOTATIONS FOLLOWING NOTATIONS SHOULD BE FOLLOWED WHILE NAMEING DIFFERENT VIEWS IN ORTHOGRAPHIC PROJECTIONS. IT’S FRONT VIEW a’ b’ SAME SYSTEM OF NOTATIONS SHOULD BE FOLLOWED INCASE NUMBERS, LIKE 1, 2, 3 – ARE USED. OBJECT POINT A LINE AB IT’S TOP VIEW a a b IT’S SIDE VIEW a” b”

3. X Y 1 ST Quad. 2 nd Quad. 3 rd Quad. 4 th Quad. X Y VP HP Observer THIS QUADRANT PATTERN, IF OBSERVED ALONG X-Y LINE ( IN RED ARROW DIRECTION) WILL EXACTLY APPEAR AS SHOWN ON RIGHT SIDE AND HENCE, IT IS FURTHER USED TO UNDERSTAND ILLUSTRATION PROPERLLY.

4. HP VP a’ a A POINT A IN 1 ST QUADRANT OBSERVER VP HP POINT A IN 2 ND QUADRANT OBSERVER a’ a A OBSERVER a a’ POINT A IN 3 RD QUADRANT HP VP A OBSERVER a a’ POINT A IN 4 TH QUADRANT HP VP A Point A is Placed In different quadrants and it’s Fv & Tv are brought in same plane for Observer to see clearly. Fv is visible as it is a view on VP. But as Tv is is a view on Hp, it is rotated downward 90 0, In clockwise direction.The In front part of Hp comes below xy line and the part behind Vp comes above. Observe and note the process.

5. FV & TV of a point always lie in the same vertical line FV of a point ‘P’ is represented by p’. It shows position of the point with respect to HP. If the point lies above HP, p’ lies above the XY line. If the point lies in the HP, p’ lies on the XY line. If the point lies below the HP, p’ lies below the XY line. TV of a point ‘P’ is represented by p. It shows position of the point with respect to VP. If the point lies in front of VP, p lies below the XY line. If the point lies in the VP, p lies on the XY line. If the point lies behind the VP, p lies above the XY line. Basic concepts for drawing projection of point

6. A a a’ A a A a X Y X Y X Y For Fv For Tv For Fv For Tv For Fv POINT A ABOVE HP & INFRONT OF VP POINT A IN HP & INFRONT OF VP POINT A ABOVE HP & IN VP PROJECTIONS OF A POINT IN FIRST QUADRANT. PICTORIAL PRESENTATION PICTORIAL PRESENTATION ORTHOGRAPHIC PRESENTATIONS OF ALL ABOVE CASES. XY a a’ VP HP XY a’ VP HP a XY a VP HP a’ Fv above xy, Tv below xy. Fv above xy, Tv on xy. Fv on xy, Tv below xy.

7. SIMPLE CASES OF THE LINE 1.A VERTICAL LINE ( PERPENDICULAR TO HP & // TO VP) 2.LINE PARALLEL TO BOTH HP & VP. 3.LINE INCLINED TO HP & PARALLEL TO VP. 4.LINE INCLINED TO VP & PARALLEL TO HP. 5.LINE INCLINED TO BOTH HP & VP. STUDY ILLUSTRATIONS GIVEN ON NEXT PAGE SHOWING CLEARLY THE NATURE OF FV & TV OF LINES LISTED ABOVE AND NOTE RESULTS. PROJECTIONS OF STRAIGHT LINES. INFORMATION REGARDING A LINE means IT’S LENGTH, POSITION OF IT’S ENDS WITH HP & VP IT’S INCLINATIONS WITH HP & VP WILL BE GIVEN. AIM:- TO DRAW IT’S PROJECTIONS - MEANS FV & TV.

8. X Y V.P. X Y b’ a’ b a F.V. T.V. a b a’ b’ B A TV FV A B XY H.P. V.P. a’ b’ a b Fv Tv XY H.P. V.P. a b a’b’ Fv Tv For Fv For Tv For Fv Note: Fv is a vertical line Showing True Length & Tv is a point. Note: Fv & Tv both are // to xy & both show T. L. 1. 2. A Line perpendicular to Hp & // to Vp A Line // to Hp & // to Vp Orthographic Pattern (Pictorial Presentation)

9. A Line inclined to Hp and parallel to Vp (Pictorial presentation) X Y V.P. A B b’ a’ b a   F.V. T.V. A Line inclined to Vp and parallel to Hp (Pictorial presentation) Ø V.P. a b a’ b’ B A Ø F.V. T.V. XY H.P. V.P. F.V. T.V. a b a’ b’  XY H.P. V.P. Ø a b a’b’ Tv Fv Tv inclined to xy Fv parallel to xy. 3. 4. Fv inclined to xy Tv parallel to xy. Orthographic Projections

10. X Y V.P. For Fv a’ b’ a b B A   For Tv F.V. T.V. X Y V.P. a’ b’ a b   F.V. T.V. For Fv For Tv B A X Y   H.P. V.P. a b FV TV a’ b’ A Line inclined to both Hp and Vp (Pictorial presentation) 5. Note These Facts:- Both Fv & Tv are inclined to xy. (No view is parallel to xy) Both Fv & Tv are reduced lengths. (No view shows True Length) Orthographic Projections Fv is seen on Vp clearly. To see Tv clearly, HP is rotated 90 0 downwards, Hence it comes below xy. On removal of object i.e. Line AB Fv as a image on Vp. Tv as a image on Hp,

11. XY H.P. V.P. X Y  H.P. V.P. a b TV a’ b’ FV TV b1b1 b1’b1’ TL X Y   H.P. V.P. a b FV TV a’ b’ Here TV (ab) is not // to XY line Hence it’s corresponding FV a’ b’ is not showing True Length & True Inclination with Hp. In this sketch, TV is rotated and made // to XY line. Hence it’s corresponding FV a’ b 1 ’ Is showing True Length & True Inclination with Hp. Note the procedure When Fv & Tv known, How to find True Length. (Views are rotated to determine True Length & it’s inclinations with Hp & Vp). Note the procedure When True Length is known, How to locate FV & TV. (Component a’b 2 ’ of TL is drawn which is further rotated to determine FV) a a’ b’ b  b1’b1’   TL b2b2 Ø Fv Tv Orthographic Projections Means Fv & Tv of Line AB are shown below, with their apparent Inclinations  &  Here a’b 1 ’ is component of TL ab 1 gives length of FV. Hence it is brought Up to Locus of a’ and further rotated to get point b’. a’ b’ will be Fv. Similarly drawing component of other TL(a’b 1 ‘) TV can be drawn.  b1b1 b2’b2’

12. Projection of straight line Line inclined to both HP & VP Type-I Given projections (FV & TV) of the line. To find True length & true inclination of the line with HP (θ) and with VP(Φ). End A of a line AB is 20mm above HP & 20mm in front of VP while its end B is 55mm above HP and 75mm in front of VP. The distance between end projectors of the line is 50mm. Draw projections of the line and find its true length and true inclination with the principal planes. Also mark its traces. PROBLEM

13. a’ X Y a 20 50 55 b’ 75 b1b1 b1’ b1’ b 2 ’ b2 b2 θ α Φβ TLTL TL h’ HT v VT’ b θ: True inclination of the line with HP = 24º α : Inclination of FV of the line with HP/XY Ø: True inclination of the line with VP = 41º β : Inclination of TV of the line with VP/XY

14. Type –II Given (i) T.L., θ and Ø, (ii) T.L., F.V., T.V. to draw projections, find α, β,H.T. and V.T. Line inclined to both HP & VP PROBLEM A line AB, 70mm long, has its end A 20 mm above HP and 20mm in front of VP. It is inclined at 30° to HP and 45°to VP. Draw its projections and mark its traces.

15. X Y 15 a’ 20 70 b1’b1’ a b2b2 30° 45° b1b1 b b’ b2’b2’ h’ HT v VT’

16. Q10.11 The top view of a 75mm long line AB measures 65mm,while its front view measures 50mm. Its one end A is in HP and12mm in front of VP. Draw the projections of AB and determine its inclination with HP and VP X Y a’ 12 a b1b1 Hint: Draw ab 1 =65mm // to XY. Because when TV is // to XY, FV gives TL. 75 b1’b1’ b’ 50 65 b 75 b2b2 Given, TL=75mm,TV=65mm,FV=50mm A is in HP & 12mm → VP To draw FV &TV of the line AB To find θ & Ø 31º 49º Ans. θ=31º Ans. Ø=49º

17. Q10.12 A line AB, 65mm long has its end A 20mm above H.P. and 25mm in front of VP. The end B is 40mm above H.P. and 65mm in front of V.P. Draw the projections of AB and show its inclination with H.P. and V.P. X Y 20 a’ 25 a 40 65 Given, TL=65mm A is 20mm ↑ HP & 25mm → V.P. B is 40mm ↑ & 65mm → V.P. To draw FV &TV of the line AB To find θ & Ø Hint1:Mark a’ 20mm above H.P & a 25mm below XY Hint2:Draw locus of b’ 40mm above XY & locus of b 65 mm below XY 65 b1’b1’ b1b1 b b’ b2’b2’ b2b2 65 18º 38º Ans. θ=18º Ans. Ø=38º

18. Q10.13:The projectors of the ends of a line AB are 5cm apart. The end A is 2cm above the H.P and 3cm in front of V.P. The end B is1cm below H.P. and 4cm behind the V.P. Determine the true length and traces of AB, and its inclination with the two planes X Y 50 20 a’ 30 a 40 b 10 b’ b1b1 91 Ans. θ=20º 20º b2’b2’ b2b2 50º Ans. Ø=50º h’ HT v VT’ Given, A 0 B 0 =50mm A is 20mm ↑ HP & 30mm → V.P. B is 10mm ↓ & 40mm ← V.P. To find, True Length, θ,Ø, H.T. and V.T.

19. Q10.14:A line AB, 90mm long, is inclined at 45 to the H.P. and its top view makes an angle of 60 with the V.P. The end A is in the H.P. and 12mm in front of V.P. Draw its front view and find its true inclination with the V.P. Y X a’ a 12 90 45º b1’b1’ b1b1 60º b b’ Given, T.L.=90mm, θ=45º, β=60º A is in the H.P. & 12mm→V.P. To find/draw, F.V.,T.V. & Ø 90 b2b2 38º Ans. Ø = 38º

20. Q10.16:The end A of a line AB is 25 mm behind the V.P. and is below the H.P. The end B is 12 mm in front of the VP and is above the HP The distance between the projectors is 65mm. The line is inclined at 40 to the HP and its HT is 20 mm behind the VP. Draw the projections of the line and determine its true length and the VT X Y Given, A 0 B 0 =65mm A is 25mm ←V.P.& is ↓ H.P. B is 12mm →V.P. & is above HP θ = 40º To find/draw, F.V., T.V., T.L., VT’ 25 a 65 12 b 20 HT h’ b1b1 40º b1’b1’ b’ a’ v VT’ b2b2 b2’b2’ Ans. TL= a’b 2 ’=123 mm

21. 10.17:A line AB, 90mm long, is inclined at 30 to the HP. Its end A is 12mm above the HP and 20mm in front of the VP. Its FV measures 65mm. Draw the TV of AB and determine its inclination with the VP X Y 12 a’ 20a 90 30° b1’b1’ 65 b’ b1b1 b 90 b2b2 44° Ans: Ø = 44º

22. Q10.23:Two lines AB & AC make an angle of 120 between them in their FV & TV. AB is parallel to both the HP & VP. Determine the real angle between AB & AC. X Y c’ b’ a b a’ 120° c c1c1 c1’c1’ c2c2 c2’c2’ 112° C Ans. 112º

23. Q8:A line AB 65 mm long has its end A in the H.P. & 15 mm in front of the V.P. The end B is in the third quadrant. The line is inclined at 30 to the H.P. and at 60 to the V.P. Draw its projections. X Y 15 a a’ 30º b1’b1’ b2b2 65 60º b1b1 b b’ b2’b2’ HP VP X Y 15 a” 30º 60º b” b’ a’ a b

24. Q10.19 A line AB, inclined at 40º to the V.P. has its end 50mm and 20mm above the H.P. the length of its front view is 65mm and its V.T. is 10mm above the H.P. determine.the true length of AB its inclination with the H.P. and its H.T. Given, Ø = 40º, A is 20mm↑HP, B is 50 mm ↑ HP, FV=65mm, VT is 10mm ↑ HP To find, TL, θ & HT X Y 50 b’ 20 a’ 10 VT’ h’ b2’b2’ v 40º b2b2 b a b1b1 b1’b1’ 85 21º HT Ans, TL = 85 mm, θ = 21º & HT is 17 mm behind VP

25. Q10.19 A line AB, inclined at 40º to the V.P. has its end 50mm and 20mm above the H.P. the length of its front view is 65mm and its V.T. is 10mm above the H.P. determine.the true length of AB its inclination with the H.P. and its H.T. Given, Ø = 40º, A is 20mm↑HP, B is 50 mm ↑ HP, FV=65mm, VT is 10mm ↑ HP To find, TL, θ & HT X Y 50 b’ 20 a’ 10 VT’ h’ v 65 40 º a b HT 21 º A1’A1’ B1’B1’ Ans: A1’B1’=TL=85mm Ans:HT is 17 mm behind VP Ans:θ = 21º Step1: For solving the problem by trapezoidal method, draw a line at 40º(Ø) from VT’. Then draw perpendiculars from a’ and b’ on this line. Step2: Then draw projectors from a’ and b’ and mark the distance of b’B 1 ’ on the projector of b’ below XY. Similarly mark the distance a’A 1 ’ on the projector of a’ below XY

26. Q6. The top view of a 75mm long line CD measures 50 mm. C is 50 mm in front of the VP & 15mm below the HP. D is 15 mm in front of the VP & is above the HP. Draw the FV of CD & find its inclinations with the HP and the VP. Show also its traces. X Y 15 50 Given, TL = 75 mm, FV =50 mm, C is 15mm ↓ HP & 50 mm → VP, D is 15 mm → VP To draw, FV & to find θ & Ø To mark HT & VT c’ c Locus of D Hint 1: Cut an arc of 50 mm from c on locus of D to get the TV of the line d Hint 2: Make TV (cd), // to XY so that FV will give TL d1d1 d1’d1’ d’ θ=48º Ans: θ=48º d2d2 50 75 Ø=28º Ans: Ø=28º h’ HT v VT’

27. Q10.10 A line PQ 100 mm long is inclined at 30º to the H.P. and at 45º to the V.P. Its mid point is in the V.P. and 20 mm above the H.P. Draw its projections, if its end P is in the third quadrant and Q is in the first quadrant. Given, TL = 100, θ = 30º, Mid point M is 20mm↑HP & in the VP End P in third quadrant & End Q in first quadrant To draw, FV & TV X Y 20 m’ m 30º q1’q1’ p1’p1’ 50 q2q2 p2p2 q2’q2’ q’ p’ q p q1q1 p1p1 p2’p2’ 45º

28. Problem 3: The front view of a 125 mm long line PQ measures 75 mm while its top view measures 100 mm. Its end Q and the mid point M are in the first quadrant. M being 20 mm from both the planes. Draw the projections of line PQ.

30. X Y V.P. For Fv a’ b’ a b B A   For Tv F.V. T.V. X Y V.P. a’ b’ a b   F.V. T.V. For Fv For Tv B A X Y   H.P. V.P. a b FV TV a’ b’ A Line inclined to both Hp and Vp (Pictorial presentation) 5. Note These Facts:- Both Fv & Tv are inclined to xy. (No view is parallel to xy) Both Fv & Tv are reduced lengths. (No view shows True Length) Orthographic Projections Fv is seen on Vp clearly. To see Tv clearly, HP is rotated 90 0 downwards, Hence it comes below xy. On removal of object i.e. Line AB Fv as a image on Vp. Tv as a image on Hp, B A