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Projections of lines.pptx

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Praveen Kumar

1. The document discusses projections of lines and includes examples of lines oriented in different positions relative to the horizontal and vertical planes. It provides data such as lengths of lines, positions of endpoints, and inclinations with the planes. Accompanying diagrams show the projections of the lines along with traces and other details. 2. Examples give information about lines and ask the reader to draw the projections, determine lengths, angles, or other values. Data may include true lengths of lines, positions of endpoints in relation to the planes, and angles of inclination. Diagrams are included with solutions. 3. Projection techniques are demonstrated for lines oriented in various positions, including parallel or inclined to one or both reference planes. Traces

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x y A B a’ b’ a b 50 50 1. Line parallel to both the planes Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x y • A. Line inclined to HP and parallel to VP • B. Line inclined to VP and parallel to HP 2. Line inclined to one plane and parallel to other A C D a’ b’ a b c’ d’ c d B θ φ TV – Apparent TV length (reduced TV length) FV – Apparent FV length (reduced FV length) TV – shows true length FV – shows true length Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x y VP HP x y VP HP θ a’ b’ a b FV – shows true length TV – Apparent length (reduced length) φ a’ b’ a b FV – Apparent length (reduced length) TV – shows true length Line inclined to HP with angle θ and parallel to VP Line inclined to VP with angle φ and parallel to HP locus of b’ locus of a’ locus of a locus of a locus of a’ locus of b 50 25 50 25 Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x y 3. Line inclined to both the planes B b’ a’ A a b FV – Apparent length (reduced length) TV – Apparent length (reduced length) Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x y VP HP locus of a’ locus of b’ locus of a locus of b 20 65 20 50 a’ a b’ b1’ b b2 b1 b2’ • a’ = 20 ↑, a = 20 ↓ • b’ = 65 ↑, b = 50 ↓ • TL AB = 70 Given Data θ φ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Shades Views i.e. ab and a’b’ → DARK x-y lines, dimensions lines → MEDIUM DARK Projectors, locus lines, arc and extensions → LIGHT Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x y Concept of HT and VT Point of intersection with HP (HT) Point of intersection with VP (VT) h h’ v’ v b’ a’ a b B A a’ b’ h’ v’ a b h v VT HT x-y x-y Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x y a’ b1’ a b1 b2 b b’ h’ h v v’ b2’ • a’ = 25 ↑; a = 25 ↓ • b’ = 75 ↑; b = 50 ↓ • TL AB = 65 Given Data VP HP locus of b’ locus of a’ locus of a locus of b 50 75 25 25 Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x Y VP HP locus of p’ locus of p Given Data TLPQ = 150 mm P’ = 35 ↓, p = 55 ↑ Θ = 30° o’ = 0 ↑↓, o = 0 ↑↓ Ф = ? 35 p’ p 30° 55 q1’ o1’ locus of o’ locus of o locus of q q q’ locus of q’ q2’ 1. A line PQ 150 mm long has its end P 55 mm behind VP and 35 mm below HP. The line makes an angle of 30º with HP and has a point on it contained in both reference planes. Draw the projection of line. Find the inclination with VP and the distance of a point in both the planes from end P. o’ o Since pt. P is in 3rd quadrant and a pt. on a line contained in both RP (i.e. intersecting at xy), other pt. Q must be in 1st quadrant Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x HP locus of a Given Data FVAB = 50 mm locus of a’ 1. The FV of a line AB measures 50 mm and makes an angle of 45⁰ with xy, whereas its TV makes an angle of 30⁰ with xy. Its end A is 10 mm above HP and is 15 mm in front of VP. Draw the projections of line AB and show its traces. Also find out the true length of line and its True angle with the two reference planes. y α = 45⁰ Β = 30⁰ a’= 10 ↑, a = 15 ↓ θ = ?, ф = ? 10 15 a’ a 45° 30° b’ locus of b’ b locus of b h’ h v’ b1’ b1 b2 b2’ Required Ans. θ = 41⁰ θ ф ф = 22⁰ VP v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x Given Data a’ = 0 ↓↑, a = 25 ↑ locus of a 2. The end A of line AB is in HP and is 25 mm behind VP. The end B is in VP and is 50 mm above HP. The distance between the end projectors is 75 mm. Draw the projections of line AB and determine its true length, True angle with two plane and show traces. y 25 50 b’ = 50 ↑, b = 0 ↑↓ L = 75 mm locus of a’ locus of b locus of b’ VP HP a a’ 75 b’ b b1’ b1 b2’ Required Ans. TLAB = 94 mm θ θ = 33⁰ ф ф = 16⁰ h’ v h v’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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2. The projectors of the ends of a line PQ are 90 mm apart. P is 20 mm above the H.P. while Q is 45 mm behind the V.P. The H.T. and V.T. of line coincide with each other on xy, between the two end projectors and 35 mm away from the projector of the end P. Draw the projections of PQ and determine its true length and inclination with the two planes. (W – 2009) Given Data L = 90 mm p’ = 20 ↑, a = __ b’ = __ , q = 45 ↑ x y locus of p’ 20 locus of q 45 P Q 90 p’ q h 35 p q’ v’ locus of q’ q1‘ q1 q2 q2‘ locus of q Required Ans. θ θ = 24⁰ ф ф = 34⁰ TLAB = 128 mm Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x Given Data TLCD = 75 mm 2. The TV of a 75 mm long line CD measures 50 mm. Pt. C is 50 mm in front of VP and is 15 mm above HP. Point D is 15 mm in front of VP and is above the HP. Draw the projection of line CD. And find out its true inclination with HP and VP. Show also its traces. [x(b)] y TVCD = cd = 50 mm c’ = 15 ↓, c = 50 ↓ d’ = __ ↑, d = 15 ↓ locus of c’ 15 50 locus of c c’ c locus of d d d1 d1’ locus of d’ d’ d2’ d2 h v’ Required Ans. θ = 48⁰ ф = 28⁰ θ ф VP HP h’ v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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x Given Data TLAB = 75 mm 2. The TV of a 75 mm long line AB is measures 65 mm while the length of its FV is 50 mm. Its one end A is 10 mm above HP and 15 mm in front of VP. The other end is in first quadrant. Draw the projection of AB and determine its inclinations with HP and VP. Also show its traces. HP y TVAB = ab = 65 mm FVAB = a’b’ = 50 mm a’ = 10 ↑, a = 15 ↓ b’ = __ ↑, b = __ ↓ locus of a’ 10 locus of a 15 a’ a b1 b2’ 50 b1’ locus of b’ locus of a’ b2 b b’ Required Ans. θ = 30⁰ ф = 48⁰ θ ф v v’ 65 VP h’ h Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data TLAB = 75 mm 2. The TV of a 75 mm long line AB is measures 65 mm while the length of its FV is 50 mm. Its one end A is 10 mm above HP and 15 mm in front of VP. The other end is in third quadrant. Draw the projection of AB and determine its inclinations with HP and VP. Also show its traces. TVAB = ab = 65 mm FVAB = a’b’ = 50 mm a’ = 10 ↑, a = 15 ↓ b’ = __ ↓, b = __ ↑ x HP y locus of a’ 10 locus of a 15 a’ a b1 65 b2’ 50 b1’ locus of b b2 locus of b b h’ v v’ h Required Ans. θ = 30⁰ ф = 48⁰ θ ф VP b’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data 2. The point A of line AB is 30 mm above HP and in the VP, while end B is 10 mm below HP and behind VP. Draw the projections of line if it is inclined at 30⁰ to HP and 45⁰ to VP. Locate its traces. HP locus of a’ 30 locus of a a’ = 30 ↑, a = 0 ↑↓ b’ = 10 ↓, b = __ ↑ θ = 30⁰ ф = 45⁰ x y 10 a’ a θ b2 locus of b ф b1 b b’ VP h’ v h v’ locus of b’ b1’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line, 75 mm long is inclined at 30⁰ to HP. The end P is 15 mm above the HP and Q is 40 mm in front of VP. Draw projections of the line if its front view measures 50 mm. Locate traces. Given Data TLPQ = 75 mm x VP HP locus of p’ 15 locus of q 20 θ = 30⁰ a’ = 15 ↑, a = ___ q’ = ___ , q = 40 ↓ FVAB = p’q’ = 50 mm y q1’ θ locus of p’ q’ p2’ q2 p’ locus of q h’ v q p

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TLAB = 75 mm 2. A line AB is 75 mm long and is inclined at 45⁰ with HP and 30⁰ with VP. Its end B is in HP and is 40 mm in front of VP. Show the projection and show the traces. locus of b 40 θ = 45⁰ ф = 30⁰ b’ = 0 ↑↓, a = 25 ↓ y locus of b’ b x a1’ θ locus of b b2 ф a1 a locus of a a’ h’ HP b’ v h V’ VP

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Given Data TLAB = 90 mm 2. Draw the projection of line AB which is 90 mm long and is having its midpoint M at 50 mm above HP and 40 mm in front of VP. The end A is 20 mm above HP and 10 mm in front of VP. Show the traces and find out the true inclination of the line with the two reference planes. x VP HP locus of m’ locus of m 40 TLAM = TLMB = 90 mm m’ = 50 ↑, m = 40 ↓ a’ = 20 ↑, a = 10 ↓ locus of m’ 20 locus of a’ 10 m1’ m2 50 θ ф b1’ locus of b’ y a’ b2 locus of b’ b1’ b’ h’ a v h v’ Required Ans. θ = 42⁰ ф = 41⁰ b’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data 2. A line AB inclined at 400 to the VP, has its ends 20 mm and 50 mm above the HP. The length of its Front View is 65 mm and its VT is 10 mm above HP. Determine the true length of AB, its inclination with HP and its HT. ф = 30⁰ a’ = 20 ↑, a = ___ b’ = 50 ↑, b = ___ FVAB = a’b’ = 65 mm (VT) v’ = 10 ↑ x y VP HP locus of b’ 50 locus of a’ 20 locus of v’ 10 b’ v’ h’ a’ v b1’ ф b1 locus of a locus of a b a h b2 b2‘ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data TLAB = 100 mm 2. A line PQ 100 mm long is inclined at 45⁰ to the HP and 30⁰ to VP. Its end P is in the second quadrant and Q is in fourth quadrant. A point R on PQ, 40 mm from P is in both the planes. Draw the projections of PQ. (W 2000, 7 marks) x HP θ = 45⁰ ф = 30⁰ p’ = __ ↑, p = __ ↑ q’ = __ ↓, q = __ ↓ r’ = 0 ↑↓, r = 0 ↑↓ y r Consider a line RQ for the time being θ locus of q’ q2 locus of q r’ ф p1’ locus of q’ locus of p p2 locus of r’ locus of r q1’ q q’ p VP p’ q1’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data FVPQ = p’q’ = 75 mm 2. The FV of a 125 mm long line PQ measures 75 mm and its TV measures 100 mm. Its end Q and midpt. M are in 1st quadrant. M being 20 mm from both the planes. Draw the projection of line PQ. Determine its traces x VP HP locus of m’ 20 20 TLPQ = 125 mm m’ = 20 ↑, m = 20 ↓ TVPQ = p’q’ = 100 mm TLPM = TLMQ = 100/2 = 50 mm FVPM = FVMQ = p’m’ = m’q’ = 75/2 = 35.5 mm TVPM = TVMQ = pm = mq = 70/2 = 35 mm m 35.3 50 q2’ q2 locus of m’ q1’locus of q’ locus of p’ locus of p q q’ p p’ p2 m’ p1’ locus of m q1 θ ф Point to be noted here that pq and p’q’ are perpendicular to xy. i.e. angle α = β = 90⁰. It means that line PQ is in profile plane. The method of finding traces in such a case will be studied in details in coming session of the topic. In above drawing, it can be found out that θ = 37⁰ and ф = 53⁰ (θ+ф ) = 90⁰

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line AB 100 mm long has its FV inclined at 45⁰ with xy. Point A is in VP and 25 mm above HP. FV measures 60 mm. Draw the projections of line AB and find its true length, true angle with HP and VP and show the traces. Given Data TLAB = 100 mm x HP locus of a’ 20 y α = 45⁰ a’ = 25 ↑, a = 0 ↑↓ FVAB= a’b’ = 60 mm locus of a a α locus of a’ b’ b1’ b b2’ locus of a’ b2 a’ h’ v h v’ β θ ф VP

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Given Data H↔ v’ = 25 mm 2. The projections of HT and VT of a line PQ are 25 mm apart. The HT is 20 mm behind VP and VT is 10 mm above HP. The end P is 15 mm above HP. The length of the TV of a line is 60 mm. Draw the projection and find true length and inclinations of line with HP and VP. x HP locus of h 20 h = 20 ↑ v’ = 10 ↑ p’ = 15 ↑, p = __ TVPQ= ab = 60 mm y locus of v’ 10 locus of p’ 15 25 h v’ h’ v VP p’ locus of p p q locus of q q’ locus of q’ q1’ q2 q2 q2’ Required Ans. θ ф TLPQ = 63.2 mm θ = 18⁰ ф = 37⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data a’ = 15 ↑, a = __ ↓ b’ = __ ↑, b = 10 ↓ TLAB = 75 mm θ = 30⁰ ф = 45⁰ 2. The end A of a line is 15 mm above HP and end B is 10 mm in front of the VP. The length of the line is 75 mm. Draw its projection if the line is inclined at 30⁰ to the HP and 45⁰ to VP. Also locate its traces. (W-03, 7 marks) x VP HP locus of a’ 15 locus of b 10 y a’ b1’ θ Apparent TV length b ф a2 Apparent FV length locus of b’ locus of a a’ b1’ a b h’ v h v’ α β Point to be noted here that we are given the position of one end w.r.t. HP i.e. a’ and position of other end w.r.t. VP i.e. b and also we are given True Length and θ & ф. In this type normally we draw the drawing in 3 stages as shown. If in such a case, the angle θ & ф are such that θ + ф = 90⁰, then in final fig. we have to draw the views which are perpendicular to xy .

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Given Data TLAB = 50 mm 2. A line AB, 50 mm long, is in fourth quadrant with one end A in HP and other end B in VP. The line is inclined at 30⁰ with HP and 45⁰ with VP. Draw the projection of line and determine its traces. x HP a’ = 0 ↑↓, a = __ ↓ b’ = __ ↓, b’ = 0 ↑↓ y θ = 30⁰ ф = 45⁰ a’ b1’ θ Apparent TV length b ф locus of b’ locus of a Apparent FV length a’ b’ b Point to be noted here that we are given the position of one end w.r.t. HP i.e. a’ and position of other end w.r.t. VP i.e. b and also we are given True Length and θ & ф. In this type normally we draw the drawing in 3 stages as shown. If in such a case, the angle θ & ф are such that θ + ф = 90⁰, then in final fig. we have to draw the views which are perpendicular to xy . a2 a VP Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data TLAB = 90 mm 2. Draw the projection o line AB which is 90 mm long and is having its midpoint M at 50 mm above HP and 40 mm in front of VP. The end A is 20 mm above HP and 10 mm if front of VP. Show the traces and find out the true inclination of the line with the two reference planes. x VP HP locus of a’ 10 locus of a 15 TLAM = TLMB = 90 mm m’ = 50 ↓, m = 40 ↓ a’ = 20 ↓, a’ = 10 ↓ y Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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y A B ф θ a’ b’ a b α=90⁰ β=90⁰ v’ h h’ v x y VP HP locus of b’ b’ a’ locus of a’ locus of b b a locus of a Profile Plane (PP), plane which is perpendicular to both the RP Projection of line in Profile Plane … Concept Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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y Projection of line in Profile Plane … way to obtain A B ф θ a’ a b α=90⁰ β=90⁰ v’ h B1 A1 b’ x VP HP locus of b’ b’ a’ locus of a’ locus of b a b locus of a Profile Plane (PP), plane which is perpendicular to both the RP A1 B1 v’ v θ ф h’ v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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y Projection of line in Profile Plane … way to obtain A B ф θ a’ a b α=90⁰ β=90⁰ v’ b’ Profile Plane (PP), plane which is perpendicular to both the RP A2 B2 h h’ v x y VP HP locus of b’ b’ a’ locus of a’ locus of b a b locus of a A2 B2 ф θ h h’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data 2. A line AB is in profile plane. Its end A is 50 mm above HP and is 10 mm in front of VP. Its end B is 15 mm above HP and is 40 mm in front of VP. Draw the projection of line AB. Find out its true length and true angle with both the reference plane and show the traces. x VP HP locus of a’ 50 locus of a 10 a’ = 50 ↑, a = 10 ↓ b’ = 15 ↑, b = 40 ↓ α = β = 90⁰ y locus of b’ 15 locus of a 40 a b A1 B1 a’ b’ A2 B2 v’ h h’ v θ Required Ans. TLAB = 46 mm θ = 50⁰ ф = 40⁰ ф ф θ

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Given Data 2. A line AB is in profile plane. Its end A is 10 mm above HP and is 15 mm if front of VP. The line is 60 mm long and makes an angle of 60⁰ with HP and makes an angle of 30⁰ with VP. Draw the projection of line AB and show its traces. Assume that the end B is in first quadrant. x VP HP locus of a’ 10 locus of a 15 y a’ = 10 ↑, a = 15 ↓ θ = 60⁰ TLAB = 60 mm ф = 30⁰ a’ θ b1’ locus of a’ b’ b2 locus of a’ b ф A1 A2 B2 B1 v’ h h’ v b’ = __ ↑, b = __ ↓ a Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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2. A line AB, 75 mm long, has its one end A in VP and other end B 15 mm above HP and 50 mm in front of VP. Draw the projection of line when the sum of inclination with HP and VP is 90⁰. Determine true angle of inclination with HP and VP, of line AB. (S-97, 7 marks) Given Data TLAB = 75 mm x VP HP locus of b’ 15 locus of b 15 a’ = __ ↑, a = 0 ↑ ↓ Θ + ф = 90⁰ y b’ = 15 ↑, b = 50 ↓ Θ = ? ф = ? locus of a a b b’ B2 A2 a’ locus of b’ A1 B1 θ Required Ans. θ = 48⁰ ф ф = 42⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data 2. A line AB is in profile plane. Its end A is 10 mm above HP and is 15 mm if front of VP. The line is 60 mm long and makes an angle of 60⁰ with HP and makes an angle of 30⁰ with VP. Draw the projection of line AB and show its traces. Assume that the end B is in first quadrant. x VP HP locus of a’ 10 locus of a 15 y a’ = 10 ↑, a = 15 ↓ θ = 60⁰ TLAB = 60 mm ф = 30⁰ a’ a θ b’ = __ ↓, b = __ ↑ b1’ b’ locus of b’ b2 locus of b b ф A1 B1 A2 B2 v’ h Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Concept of Side View x y 50 40 a a' VP HP x1 y1 a‘’ x2 y2 a‘’’ RHSV LHSV

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Side View of a Line x y VP HP a b x1 y1 a’’ b’’ α β γ δ b’ a’

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Side View of a Line having one pt. in 1st quadrant and other in 2nd quadrant x y VP HP x1 y1 a’’ b’’ h’’ v’’ δ γ b’ h’ v β α b h v’ a a’

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer To obtain Traces when line is in profile plane using side view x VP HP b’ a’ a b h’ v x1 y1 a’’ b’’ v’’ v’ y h’’ h’

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Points to keep in mind ……… The Side View (SV) of an object is the projection of the object on the side plane which is actually a Profile Plane. TWO types of SVs: 1. Left Hand Side View (LHSV), 2. Right Hand Side View (RHSV). LHSV is the projection of an object on Right Hand Side Plane. RHSV is the projection of an object on Left Hand Side Plane. The LHSV, say a’’ is lies on the same locus as that of a’ so that dist. of a’’ from x1y1 = dist. of TV a from xy. The RHSV, say a’’’ is lies on the same locus as that of a’ so that dist. of a’’’ from x2y2 = dist. of TV a from xy. LHSV a’’ is marked on right side of x1y1 if TV a, is below xy. LHSV a’’ is marked on left side of x1y1, if TV a is above xy. LHSV a’’ is lies on xy, if FV a’ in on xy. LHSV a’’ is lies on x1y1, if TV a in on xy. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Points to keep in mind (Contt.) ……… h’’ is the point of intersection of SV a’’b’’ with xy. v’’ is the point of intersection of SV a’’b’’ with xy. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data TLAB = 100 mm 2. A line AB, 100 mm long is so placed that its side view measures 100 mm. End A is 40 mm above HP and 30 mm in front of VP. A line is inclined at 35⁰ to HP and end B is in third quadrant. Draw the three views of line AB and find its inclination with VP. Locate its HT and VT. (s-2003, 6 marks) x HP locus of a’ 40 locus of a 30 y Side View (SV) = 100 mm a’ = 40 ↑, a = 30 ↓ θ = 35⁰ b’ = __ ↓, b = __ ↑ Since TLAB and SVAB is same, line must be in profile plane, i.e. θ+ф = 90⁰ Therefore, ф = 90 – 35 = 55⁰ a x1 y1 a’’ θ b’’ b a’ b’ v’ h v’’ h’’ VP h’ v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line AB is in profile plane. Its HT is 15 mm behind VP, VT is 20 mm above HP while point B is 50 mm in front of VP. Point A is 10 mm below HP. Show its projection with HP and VP of line AB Given Data Line in Profile Plane locus of h 15 locus of b 50 h = 15 ↑ v’ = 20 ↑ y b’ = __ , b = 50 ↓ a’ = 10 ↓, a = __ locus of v’ 20 locus of a’ 10 a’ b x1 h’’ v’’ a’’ b’’ b’ x VP HP h h’ v a v’

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Given Data SVPQ = 70 mm 2. The side view of line PQ 70 mm long makes an angle of 45⁰ the ground and measures 50 mm. The end P is on ground and is 15 mm away from VP. Draw the TV and FV of line. Also determine its traces. x HP locus of p 15 p’ = 0 ↑↓, p = 15 ↓ y γ = 45⁰ Assuming point P is in front of VP p’ x1 p’’ q’’ γ locus of q’ q1’ q’ VP p locus of p’ locus of q q h’ v h’’ q1 h v’ v’’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer y1

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Given Data FVAB = a’b’ =65 mm 2.(Type V – Rotation about traces) The FV of line AB measures 65 mm and makes an angle of 45º with xy. Point A is in HP and VT of the line is 15 mm below HP. The line is inclined at 30° to VP. Draw the projections of line AB and find its true length and true angle with HP and also show its HT. x VP HP locus of a’ locus of v’ 15 α = 45⁰ Assuming point A and B are in I quadrant a’ = 0 ↑↓, a = __ ↑↓ b’ = __↑, b’ = __ ↓ V’ = 15 ↓, v = 0 ↑ ↓ TLAB = ? θ = ? HT = ? y v’ α a’ b’ locus of b’ b2’ θ = 30⁰ b θ b2 locus of v’ a locus of a b1 b1’ h’ v h Required Ans. TLAB = 74 mm θ θ = 38⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TVAB = ab = 80 mm 2. The TV of a straight line AB measures 80 mm. The line is inclined at 35⁰ to the VP and 45⁰ to the HP. The end B is 80 mm in front of VP. Draw projection of the line when its VT is 15 mm above the HP and line is completely in the first quadrant. Find the length of line and locate its HT. x VP HP locus of b 80 y ф= 35⁰ θ = 45⁰ b’ = __ ↑, a = 80 ↓ v’ = 15↑ locus of v’ 15 v’ v ф b2 θ b1’ locus of b’ b1 b a locus of a a’ a’ locus of a’ a1’ a1 h’ h Required Ans. TLAB = 113 mm

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Given Data TVPQ = pq = 70 mm 2. The TV of a line PQ measures 70 mm and makes an angle of 55⁰ with xy and P is in VP and HT of line is 20 mm above xy. The line is inclined at 35⁰ to HP. Draw the projection of line PQ and determine its true length, true inclination with VP and traces. (S-2000, 7 marks) x HP locus of h 20 p’ = __ ↑, p = 0 ↑↓ y β= 55⁰ h = 20 ↑ θ = 35⁰ TLPQ = ? Ф = ? locus of p h β p q locus of q h’ q1 θ q1’ locus of h q’ p’ locus of p’ q2’ q2 VP Required Ans. TLAB = 84.8 mm φ θ = 43⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TLAB = 75 mm 2. A line AB measures 75 mm and is in first quadrant. FV and TV of line are inclined at 45⁰ to xy. End A is 20 mm in front of VP and 30 mm above HP. Draw the projection of the line, determine its true inclination with HP and VP and its traces. x HP locus of a’ 30 a’ = 30 ↑, a = 20 ↓ y α = β = 45⁰ h = 20 ↑ θ = ? Ф = ? locus of a’ 20 a’ a α h’ v locus of v’ β a1 a1’ b1’ locus of b’ b’ b locus of a’ h b2’ b2 θ φ Required Ans. θ = 35⁰ φ = 35⁰ VP v’

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TLPQ = 100 mm 2. A line PQ 100 mm long is inclined at 30⁰ with HP and 45⁰ with VP. Its end P is 10 mm behind VP and is below HP whereas its HT is 20 mm in front of VP. Draw the projection of line PQ and locate its VT. x HP locus of p 10 p’ = __ ↓, p = 10 ↑ y θ = 30⁰ h = 20 ↓ locus of h 20 Ф = 45⁰ Assuming point Q is also in III quadrant h p2 locus of q q2 θ φ locus of h q1’ q p q’ p’ locus of p’ h’ VP v v’ q1

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data FVAB = a’b’ = 55 mm 2. The FV of a line AB 75 mm long measures 55 mm. Point A is 15 mm above HP and point B is 50 mm above HP. The VT is 10 mm below HP. Draw the projection and determine the inclination of line AB with HP and VP. And find its HT. (S – 97, 7 marks) x HP locus of a’ 15 a’ = 15 ↑, b = __ ↓ y locus of b’ TLAB = 75 mm b’ = 50 ↑, b = __ ↓ v’ = 10 ↓ 50 locus of v’ 10 b’ b1’ a’ v’ h’ v θ b3’ b2 locus of a’ a locus of a θ b VP b2’

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Given Data TLAB = 75 mm 2. The TV of a 75 mm long line AB measures 60 mm. Point A is 15 mm above HP while its VT is 10 m below HP. Line is inclined at 45⁰ with VP. Draw the projection of the line and find its inclination with HP. (W-95, 7 m) x VP HP locus of a’ 15 a’ = 15 ↑, a = __ ↓ y locus of v’ 10 TVAB = ab = 60 mm v’ = 10 ↓ Ф = 45⁰ v’ v Ф θ = TV Length/True Length = 60/75 = 37⁰ a1’ b1’ locus of a’ θ=37⁰ b2 locus of a’ b1 b b’ a’ a locus of a h’ h Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Given Data 2. A line AB, inclined at 40⁰ to VP has its ends 50 mm and 20 mm above HP. The length of its FV is 65 mm and its VT is 10 mm above HP. Determine the true length of AB, its inclination with HP and its HT. (W-99, 7 marks) x VP HP 20 a’ = 20 ↑, a = __ ↓ y locus of b’ 50 Ф = 45⁰ b’ = 50 ↑, a = __ ↓ FVAB = a’b’ = 65 mm v’ = 10 ↑ locus of v’ 10 locus of a’ a’ b’ v’ h’ v b2 locus of b’ b a locus of a’ b1 b1’ θ Required Ans. TLAB = 91 mm θ = 20⁰ b2’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line AB is inclined at 30⁰ to HP. Its ends A and B are 25 mm and 60 mm in front of VP respectively. The TV of line measures 65 mm and its VT is 15 mm above HP. Draw the three views of line AB and determine its true length and true inclination with VP. Locate its traces. x y x1 y1 locus of v’ 15 locus of a 25 locus of b 60 v b v’ θ b1 b1’ locus of b’ b’ a a’ locus of a’ a’’ b’’ v’’ h’ h h’’

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Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data 2. A line AB is in first quadrant. Its ends A and B are 15 mm and 55 mm in front of VP respectively. The distance between the end projector is 80 mm. The line is inclined at 30⁰ to HP and its HT is 10 mm above xy. Draw projection of line AB and determine its true length and VT. x VP HP 15 a’ = __ ↓, a = 15 ↓ b’ = __ ↓, b = 55 ↓ y θ = 30⁰ h = 10 ↑ A -- B = 80 mm 55 locus of b locus of a b a locus of h 10 80 v h h’ b1 θ b2 b2’ v’ a’ b1’ locus of b’ b’ locus of a’ A B

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• A. Auxiliary Vertical Plane (AVP) • B. Auxiliary Inclined Plane (AIP) Auxiliary Planes 08-Jul-09 SBT 54 Vertical Plane (VP) Horizontal Plane (HP) Auxiliary Vertical Plane (AVP) α β Auxiliary Inclined Plane (AIP) x y1 x1 y1 x1 a’ a a1’ a’ a a1 A A Turn about HP to which they are perpendicular

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08-Jul-09 SBT 55 x y HP VP a’ a y1 x1 a1’ o o1 a1’01 = a’o Dist. of AFV from x1y1 = Dist. of previous FV from xy

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g l 7.5 m locus of b’ locus of c’ 9 m locus of o’ x VP HP y locus of o o’ a1’ o 350 b1’ c1’ a1 a locus of a a’ b1 b b’ c1 c c’ locus of c locus of a’

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l 7.5 m 9 m locus of o’ x y o’ a1’ o 350 c1’ a1 a’ b1 b b’ c1 c’ locus of c’ 30 m locus of a’ 450 300 b2’ c2’ g b1’ locus of a’ a locus of a locus of o locus of c

More Related Content

Projections of lines.pptx

  • 1. x y A B a’ b’ a b 50 50 1. Line parallel to both the planes Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 2. x y • A. Line inclined to HP and parallel to VP • B. Line inclined to VP and parallel to HP 2. Line inclined to one plane and parallel to other A C D a’ b’ a b c’ d’ c d B θ φ TV – Apparent TV length (reduced TV length) FV – Apparent FV length (reduced FV length) TV – shows true length FV – shows true length Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 3. x y VP HP x y VP HP θ a’ b’ a b FV – shows true length TV – Apparent length (reduced length) φ a’ b’ a b FV – Apparent length (reduced length) TV – shows true length Line inclined to HP with angle θ and parallel to VP Line inclined to VP with angle φ and parallel to HP locus of b’ locus of a’ locus of a locus of a locus of a’ locus of b 50 25 50 25 Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 4. x y 3. Line inclined to both the planes B b’ a’ A a b FV – Apparent length (reduced length) TV – Apparent length (reduced length) Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 5. x y VP HP locus of a’ locus of b’ locus of a locus of b 20 65 20 50 a’ a b’ b1’ b b2 b1 b2’ • a’ = 20 ↑, a = 20 ↓ • b’ = 65 ↑, b = 50 ↓ • TL AB = 70 Given Data θ φ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 6. Shades Views i.e. ab and a’b’ → DARK x-y lines, dimensions lines → MEDIUM DARK Projectors, locus lines, arc and extensions → LIGHT Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 7. x y Concept of HT and VT Point of intersection with HP (HT) Point of intersection with VP (VT) h h’ v’ v b’ a’ a b B A a’ b’ h’ v’ a b h v VT HT x-y x-y Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 8. x y a’ b1’ a b1 b2 b b’ h’ h v v’ b2’ • a’ = 25 ↑; a = 25 ↓ • b’ = 75 ↑; b = 50 ↓ • TL AB = 65 Given Data VP HP locus of b’ locus of a’ locus of a locus of b 50 75 25 25 Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 9. x Y VP HP locus of p’ locus of p Given Data TLPQ = 150 mm P’ = 35 ↓, p = 55 ↑ Θ = 30° o’ = 0 ↑↓, o = 0 ↑↓ Ф = ? 35 p’ p 30° 55 q1’ o1’ locus of o’ locus of o locus of q q q’ locus of q’ q2’ 1. A line PQ 150 mm long has its end P 55 mm behind VP and 35 mm below HP. The line makes an angle of 30º with HP and has a point on it contained in both reference planes. Draw the projection of line. Find the inclination with VP and the distance of a point in both the planes from end P. o’ o Since pt. P is in 3rd quadrant and a pt. on a line contained in both RP (i.e. intersecting at xy), other pt. Q must be in 1st quadrant Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 10. x HP locus of a Given Data FVAB = 50 mm locus of a’ 1. The FV of a line AB measures 50 mm and makes an angle of 45⁰ with xy, whereas its TV makes an angle of 30⁰ with xy. Its end A is 10 mm above HP and is 15 mm in front of VP. Draw the projections of line AB and show its traces. Also find out the true length of line and its True angle with the two reference planes. y α = 45⁰ Β = 30⁰ a’= 10 ↑, a = 15 ↓ θ = ?, ф = ? 10 15 a’ a 45° 30° b’ locus of b’ b locus of b h’ h v’ b1’ b1 b2 b2’ Required Ans. θ = 41⁰ θ ф ф = 22⁰ VP v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 11. x Given Data a’ = 0 ↓↑, a = 25 ↑ locus of a 2. The end A of line AB is in HP and is 25 mm behind VP. The end B is in VP and is 50 mm above HP. The distance between the end projectors is 75 mm. Draw the projections of line AB and determine its true length, True angle with two plane and show traces. y 25 50 b’ = 50 ↑, b = 0 ↑↓ L = 75 mm locus of a’ locus of b locus of b’ VP HP a a’ 75 b’ b b1’ b1 b2’ Required Ans. TLAB = 94 mm θ θ = 33⁰ ф ф = 16⁰ h’ v h v’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 12. 2. The projectors of the ends of a line PQ are 90 mm apart. P is 20 mm above the H.P. while Q is 45 mm behind the V.P. The H.T. and V.T. of line coincide with each other on xy, between the two end projectors and 35 mm away from the projector of the end P. Draw the projections of PQ and determine its true length and inclination with the two planes. (W – 2009) Given Data L = 90 mm p’ = 20 ↑, a = __ b’ = __ , q = 45 ↑ x y locus of p’ 20 locus of q 45 P Q 90 p’ q h 35 p q’ v’ locus of q’ q1‘ q1 q2 q2‘ locus of q Required Ans. θ θ = 24⁰ ф ф = 34⁰ TLAB = 128 mm Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 13. x Given Data TLCD = 75 mm 2. The TV of a 75 mm long line CD measures 50 mm. Pt. C is 50 mm in front of VP and is 15 mm above HP. Point D is 15 mm in front of VP and is above the HP. Draw the projection of line CD. And find out its true inclination with HP and VP. Show also its traces. [x(b)] y TVCD = cd = 50 mm c’ = 15 ↓, c = 50 ↓ d’ = __ ↑, d = 15 ↓ locus of c’ 15 50 locus of c c’ c locus of d d d1 d1’ locus of d’ d’ d2’ d2 h v’ Required Ans. θ = 48⁰ ф = 28⁰ θ ф VP HP h’ v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 14. x Given Data TLAB = 75 mm 2. The TV of a 75 mm long line AB is measures 65 mm while the length of its FV is 50 mm. Its one end A is 10 mm above HP and 15 mm in front of VP. The other end is in first quadrant. Draw the projection of AB and determine its inclinations with HP and VP. Also show its traces. HP y TVAB = ab = 65 mm FVAB = a’b’ = 50 mm a’ = 10 ↑, a = 15 ↓ b’ = __ ↑, b = __ ↓ locus of a’ 10 locus of a 15 a’ a b1 b2’ 50 b1’ locus of b’ locus of a’ b2 b b’ Required Ans. θ = 30⁰ ф = 48⁰ θ ф v v’ 65 VP h’ h Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 15. Given Data TLAB = 75 mm 2. The TV of a 75 mm long line AB is measures 65 mm while the length of its FV is 50 mm. Its one end A is 10 mm above HP and 15 mm in front of VP. The other end is in third quadrant. Draw the projection of AB and determine its inclinations with HP and VP. Also show its traces. TVAB = ab = 65 mm FVAB = a’b’ = 50 mm a’ = 10 ↑, a = 15 ↓ b’ = __ ↓, b = __ ↑ x HP y locus of a’ 10 locus of a 15 a’ a b1 65 b2’ 50 b1’ locus of b b2 locus of b b h’ v v’ h Required Ans. θ = 30⁰ ф = 48⁰ θ ф VP b’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 16. Given Data 2. The point A of line AB is 30 mm above HP and in the VP, while end B is 10 mm below HP and behind VP. Draw the projections of line if it is inclined at 30⁰ to HP and 45⁰ to VP. Locate its traces. HP locus of a’ 30 locus of a a’ = 30 ↑, a = 0 ↑↓ b’ = 10 ↓, b = __ ↑ θ = 30⁰ ф = 45⁰ x y 10 a’ a θ b2 locus of b ф b1 b b’ VP h’ v h v’ locus of b’ b1’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 17. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line, 75 mm long is inclined at 30⁰ to HP. The end P is 15 mm above the HP and Q is 40 mm in front of VP. Draw projections of the line if its front view measures 50 mm. Locate traces. Given Data TLPQ = 75 mm x VP HP locus of p’ 15 locus of q 20 θ = 30⁰ a’ = 15 ↑, a = ___ q’ = ___ , q = 40 ↓ FVAB = p’q’ = 50 mm y q1’ θ locus of p’ q’ p2’ q2 p’ locus of q h’ v q p
  • 18. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TLAB = 75 mm 2. A line AB is 75 mm long and is inclined at 45⁰ with HP and 30⁰ with VP. Its end B is in HP and is 40 mm in front of VP. Show the projection and show the traces. locus of b 40 θ = 45⁰ ф = 30⁰ b’ = 0 ↑↓, a = 25 ↓ y locus of b’ b x a1’ θ locus of b b2 ф a1 a locus of a a’ h’ HP b’ v h V’ VP
  • 19. Given Data TLAB = 90 mm 2. Draw the projection of line AB which is 90 mm long and is having its midpoint M at 50 mm above HP and 40 mm in front of VP. The end A is 20 mm above HP and 10 mm in front of VP. Show the traces and find out the true inclination of the line with the two reference planes. x VP HP locus of m’ locus of m 40 TLAM = TLMB = 90 mm m’ = 50 ↑, m = 40 ↓ a’ = 20 ↑, a = 10 ↓ locus of m’ 20 locus of a’ 10 m1’ m2 50 θ ф b1’ locus of b’ y a’ b2 locus of b’ b1’ b’ h’ a v h v’ Required Ans. θ = 42⁰ ф = 41⁰ b’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 20. Given Data 2. A line AB inclined at 400 to the VP, has its ends 20 mm and 50 mm above the HP. The length of its Front View is 65 mm and its VT is 10 mm above HP. Determine the true length of AB, its inclination with HP and its HT. ф = 30⁰ a’ = 20 ↑, a = ___ b’ = 50 ↑, b = ___ FVAB = a’b’ = 65 mm (VT) v’ = 10 ↑ x y VP HP locus of b’ 50 locus of a’ 20 locus of v’ 10 b’ v’ h’ a’ v b1’ ф b1 locus of a locus of a b a h b2 b2‘ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 21. Given Data TLAB = 100 mm 2. A line PQ 100 mm long is inclined at 45⁰ to the HP and 30⁰ to VP. Its end P is in the second quadrant and Q is in fourth quadrant. A point R on PQ, 40 mm from P is in both the planes. Draw the projections of PQ. (W 2000, 7 marks) x HP θ = 45⁰ ф = 30⁰ p’ = __ ↑, p = __ ↑ q’ = __ ↓, q = __ ↓ r’ = 0 ↑↓, r = 0 ↑↓ y r Consider a line RQ for the time being θ locus of q’ q2 locus of q r’ ф p1’ locus of q’ locus of p p2 locus of r’ locus of r q1’ q q’ p VP p’ q1’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 22. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data FVPQ = p’q’ = 75 mm 2. The FV of a 125 mm long line PQ measures 75 mm and its TV measures 100 mm. Its end Q and midpt. M are in 1st quadrant. M being 20 mm from both the planes. Draw the projection of line PQ. Determine its traces x VP HP locus of m’ 20 20 TLPQ = 125 mm m’ = 20 ↑, m = 20 ↓ TVPQ = p’q’ = 100 mm TLPM = TLMQ = 100/2 = 50 mm FVPM = FVMQ = p’m’ = m’q’ = 75/2 = 35.5 mm TVPM = TVMQ = pm = mq = 70/2 = 35 mm m 35.3 50 q2’ q2 locus of m’ q1’locus of q’ locus of p’ locus of p q q’ p p’ p2 m’ p1’ locus of m q1 θ ф Point to be noted here that pq and p’q’ are perpendicular to xy. i.e. angle α = β = 90⁰. It means that line PQ is in profile plane. The method of finding traces in such a case will be studied in details in coming session of the topic. In above drawing, it can be found out that θ = 37⁰ and ф = 53⁰ (θ+ф ) = 90⁰
  • 23. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line AB 100 mm long has its FV inclined at 45⁰ with xy. Point A is in VP and 25 mm above HP. FV measures 60 mm. Draw the projections of line AB and find its true length, true angle with HP and VP and show the traces. Given Data TLAB = 100 mm x HP locus of a’ 20 y α = 45⁰ a’ = 25 ↑, a = 0 ↑↓ FVAB= a’b’ = 60 mm locus of a a α locus of a’ b’ b1’ b b2’ locus of a’ b2 a’ h’ v h v’ β θ ф VP
  • 24. Given Data H↔ v’ = 25 mm 2. The projections of HT and VT of a line PQ are 25 mm apart. The HT is 20 mm behind VP and VT is 10 mm above HP. The end P is 15 mm above HP. The length of the TV of a line is 60 mm. Draw the projection and find true length and inclinations of line with HP and VP. x HP locus of h 20 h = 20 ↑ v’ = 10 ↑ p’ = 15 ↑, p = __ TVPQ= ab = 60 mm y locus of v’ 10 locus of p’ 15 25 h v’ h’ v VP p’ locus of p p q locus of q q’ locus of q’ q1’ q2 q2 q2’ Required Ans. θ ф TLPQ = 63.2 mm θ = 18⁰ ф = 37⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 25. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data a’ = 15 ↑, a = __ ↓ b’ = __ ↑, b = 10 ↓ TLAB = 75 mm θ = 30⁰ ф = 45⁰ 2. The end A of a line is 15 mm above HP and end B is 10 mm in front of the VP. The length of the line is 75 mm. Draw its projection if the line is inclined at 30⁰ to the HP and 45⁰ to VP. Also locate its traces. (W-03, 7 marks) x VP HP locus of a’ 15 locus of b 10 y a’ b1’ θ Apparent TV length b ф a2 Apparent FV length locus of b’ locus of a a’ b1’ a b h’ v h v’ α β Point to be noted here that we are given the position of one end w.r.t. HP i.e. a’ and position of other end w.r.t. VP i.e. b and also we are given True Length and θ & ф. In this type normally we draw the drawing in 3 stages as shown. If in such a case, the angle θ & ф are such that θ + ф = 90⁰, then in final fig. we have to draw the views which are perpendicular to xy .
  • 26. Given Data TLAB = 50 mm 2. A line AB, 50 mm long, is in fourth quadrant with one end A in HP and other end B in VP. The line is inclined at 30⁰ with HP and 45⁰ with VP. Draw the projection of line and determine its traces. x HP a’ = 0 ↑↓, a = __ ↓ b’ = __ ↓, b’ = 0 ↑↓ y θ = 30⁰ ф = 45⁰ a’ b1’ θ Apparent TV length b ф locus of b’ locus of a Apparent FV length a’ b’ b Point to be noted here that we are given the position of one end w.r.t. HP i.e. a’ and position of other end w.r.t. VP i.e. b and also we are given True Length and θ & ф. In this type normally we draw the drawing in 3 stages as shown. If in such a case, the angle θ & ф are such that θ + ф = 90⁰, then in final fig. we have to draw the views which are perpendicular to xy . a2 a VP Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 27. Given Data TLAB = 90 mm 2. Draw the projection o line AB which is 90 mm long and is having its midpoint M at 50 mm above HP and 40 mm in front of VP. The end A is 20 mm above HP and 10 mm if front of VP. Show the traces and find out the true inclination of the line with the two reference planes. x VP HP locus of a’ 10 locus of a 15 TLAM = TLMB = 90 mm m’ = 50 ↓, m = 40 ↓ a’ = 20 ↓, a’ = 10 ↓ y Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 28. y A B ф θ a’ b’ a b α=90⁰ β=90⁰ v’ h h’ v x y VP HP locus of b’ b’ a’ locus of a’ locus of b b a locus of a Profile Plane (PP), plane which is perpendicular to both the RP Projection of line in Profile Plane … Concept Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 29. y Projection of line in Profile Plane … way to obtain A B ф θ a’ a b α=90⁰ β=90⁰ v’ h B1 A1 b’ x VP HP locus of b’ b’ a’ locus of a’ locus of b a b locus of a Profile Plane (PP), plane which is perpendicular to both the RP A1 B1 v’ v θ ф h’ v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 30. y Projection of line in Profile Plane … way to obtain A B ф θ a’ a b α=90⁰ β=90⁰ v’ b’ Profile Plane (PP), plane which is perpendicular to both the RP A2 B2 h h’ v x y VP HP locus of b’ b’ a’ locus of a’ locus of b a b locus of a A2 B2 ф θ h h’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 31. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data 2. A line AB is in profile plane. Its end A is 50 mm above HP and is 10 mm in front of VP. Its end B is 15 mm above HP and is 40 mm in front of VP. Draw the projection of line AB. Find out its true length and true angle with both the reference plane and show the traces. x VP HP locus of a’ 50 locus of a 10 a’ = 50 ↑, a = 10 ↓ b’ = 15 ↑, b = 40 ↓ α = β = 90⁰ y locus of b’ 15 locus of a 40 a b A1 B1 a’ b’ A2 B2 v’ h h’ v θ Required Ans. TLAB = 46 mm θ = 50⁰ ф = 40⁰ ф ф θ
  • 32. Given Data 2. A line AB is in profile plane. Its end A is 10 mm above HP and is 15 mm if front of VP. The line is 60 mm long and makes an angle of 60⁰ with HP and makes an angle of 30⁰ with VP. Draw the projection of line AB and show its traces. Assume that the end B is in first quadrant. x VP HP locus of a’ 10 locus of a 15 y a’ = 10 ↑, a = 15 ↓ θ = 60⁰ TLAB = 60 mm ф = 30⁰ a’ θ b1’ locus of a’ b’ b2 locus of a’ b ф A1 A2 B2 B1 v’ h h’ v b’ = __ ↑, b = __ ↓ a Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 33. 2. A line AB, 75 mm long, has its one end A in VP and other end B 15 mm above HP and 50 mm in front of VP. Draw the projection of line when the sum of inclination with HP and VP is 90⁰. Determine true angle of inclination with HP and VP, of line AB. (S-97, 7 marks) Given Data TLAB = 75 mm x VP HP locus of b’ 15 locus of b 15 a’ = __ ↑, a = 0 ↑ ↓ Θ + ф = 90⁰ y b’ = 15 ↑, b = 50 ↓ Θ = ? ф = ? locus of a a b b’ B2 A2 a’ locus of b’ A1 B1 θ Required Ans. θ = 48⁰ ф ф = 42⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 34. Given Data 2. A line AB is in profile plane. Its end A is 10 mm above HP and is 15 mm if front of VP. The line is 60 mm long and makes an angle of 60⁰ with HP and makes an angle of 30⁰ with VP. Draw the projection of line AB and show its traces. Assume that the end B is in first quadrant. x VP HP locus of a’ 10 locus of a 15 y a’ = 10 ↑, a = 15 ↓ θ = 60⁰ TLAB = 60 mm ф = 30⁰ a’ a θ b’ = __ ↓, b = __ ↑ b1’ b’ locus of b’ b2 locus of b b ф A1 B1 A2 B2 v’ h Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 35. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Concept of Side View x y 50 40 a a' VP HP x1 y1 a‘’ x2 y2 a‘’’ RHSV LHSV
  • 36. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Side View of a Line x y VP HP a b x1 y1 a’’ b’’ α β γ δ b’ a’
  • 37. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Side View of a Line having one pt. in 1st quadrant and other in 2nd quadrant x y VP HP x1 y1 a’’ b’’ h’’ v’’ δ γ b’ h’ v β α b h v’ a a’
  • 38. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer To obtain Traces when line is in profile plane using side view x VP HP b’ a’ a b h’ v x1 y1 a’’ b’’ v’’ v’ y h’’ h’
  • 39. Points to keep in mind ……… The Side View (SV) of an object is the projection of the object on the side plane which is actually a Profile Plane. TWO types of SVs: 1. Left Hand Side View (LHSV), 2. Right Hand Side View (RHSV). LHSV is the projection of an object on Right Hand Side Plane. RHSV is the projection of an object on Left Hand Side Plane. The LHSV, say a’’ is lies on the same locus as that of a’ so that dist. of a’’ from x1y1 = dist. of TV a from xy. The RHSV, say a’’’ is lies on the same locus as that of a’ so that dist. of a’’’ from x2y2 = dist. of TV a from xy. LHSV a’’ is marked on right side of x1y1 if TV a, is below xy. LHSV a’’ is marked on left side of x1y1, if TV a is above xy. LHSV a’’ is lies on xy, if FV a’ in on xy. LHSV a’’ is lies on x1y1, if TV a in on xy. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 40. Points to keep in mind (Contt.) ……… h’’ is the point of intersection of SV a’’b’’ with xy. v’’ is the point of intersection of SV a’’b’’ with xy. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 41. Given Data TLAB = 100 mm 2. A line AB, 100 mm long is so placed that its side view measures 100 mm. End A is 40 mm above HP and 30 mm in front of VP. A line is inclined at 35⁰ to HP and end B is in third quadrant. Draw the three views of line AB and find its inclination with VP. Locate its HT and VT. (s-2003, 6 marks) x HP locus of a’ 40 locus of a 30 y Side View (SV) = 100 mm a’ = 40 ↑, a = 30 ↓ θ = 35⁰ b’ = __ ↓, b = __ ↑ Since TLAB and SVAB is same, line must be in profile plane, i.e. θ+ф = 90⁰ Therefore, ф = 90 – 35 = 55⁰ a x1 y1 a’’ θ b’’ b a’ b’ v’ h v’’ h’’ VP h’ v Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 42. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line AB is in profile plane. Its HT is 15 mm behind VP, VT is 20 mm above HP while point B is 50 mm in front of VP. Point A is 10 mm below HP. Show its projection with HP and VP of line AB Given Data Line in Profile Plane locus of h 15 locus of b 50 h = 15 ↑ v’ = 20 ↑ y b’ = __ , b = 50 ↓ a’ = 10 ↓, a = __ locus of v’ 20 locus of a’ 10 a’ b x1 h’’ v’’ a’’ b’’ b’ x VP HP h h’ v a v’
  • 43. Given Data SVPQ = 70 mm 2. The side view of line PQ 70 mm long makes an angle of 45⁰ the ground and measures 50 mm. The end P is on ground and is 15 mm away from VP. Draw the TV and FV of line. Also determine its traces. x HP locus of p 15 p’ = 0 ↑↓, p = 15 ↓ y γ = 45⁰ Assuming point P is in front of VP p’ x1 p’’ q’’ γ locus of q’ q1’ q’ VP p locus of p’ locus of q q h’ v h’’ q1 h v’ v’’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer y1
  • 44. Given Data FVAB = a’b’ =65 mm 2.(Type V – Rotation about traces) The FV of line AB measures 65 mm and makes an angle of 45º with xy. Point A is in HP and VT of the line is 15 mm below HP. The line is inclined at 30° to VP. Draw the projections of line AB and find its true length and true angle with HP and also show its HT. x VP HP locus of a’ locus of v’ 15 α = 45⁰ Assuming point A and B are in I quadrant a’ = 0 ↑↓, a = __ ↑↓ b’ = __↑, b’ = __ ↓ V’ = 15 ↓, v = 0 ↑ ↓ TLAB = ? θ = ? HT = ? y v’ α a’ b’ locus of b’ b2’ θ = 30⁰ b θ b2 locus of v’ a locus of a b1 b1’ h’ v h Required Ans. TLAB = 74 mm θ θ = 38⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 45. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TVAB = ab = 80 mm 2. The TV of a straight line AB measures 80 mm. The line is inclined at 35⁰ to the VP and 45⁰ to the HP. The end B is 80 mm in front of VP. Draw projection of the line when its VT is 15 mm above the HP and line is completely in the first quadrant. Find the length of line and locate its HT. x VP HP locus of b 80 y ф= 35⁰ θ = 45⁰ b’ = __ ↑, a = 80 ↓ v’ = 15↑ locus of v’ 15 v’ v ф b2 θ b1’ locus of b’ b1 b a locus of a a’ a’ locus of a’ a1’ a1 h’ h Required Ans. TLAB = 113 mm
  • 46. Given Data TVPQ = pq = 70 mm 2. The TV of a line PQ measures 70 mm and makes an angle of 55⁰ with xy and P is in VP and HT of line is 20 mm above xy. The line is inclined at 35⁰ to HP. Draw the projection of line PQ and determine its true length, true inclination with VP and traces. (S-2000, 7 marks) x HP locus of h 20 p’ = __ ↑, p = 0 ↑↓ y β= 55⁰ h = 20 ↑ θ = 35⁰ TLPQ = ? Ф = ? locus of p h β p q locus of q h’ q1 θ q1’ locus of h q’ p’ locus of p’ q2’ q2 VP Required Ans. TLAB = 84.8 mm φ θ = 43⁰ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 47. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TLAB = 75 mm 2. A line AB measures 75 mm and is in first quadrant. FV and TV of line are inclined at 45⁰ to xy. End A is 20 mm in front of VP and 30 mm above HP. Draw the projection of the line, determine its true inclination with HP and VP and its traces. x HP locus of a’ 30 a’ = 30 ↑, a = 20 ↓ y α = β = 45⁰ h = 20 ↑ θ = ? Ф = ? locus of a’ 20 a’ a α h’ v locus of v’ β a1 a1’ b1’ locus of b’ b’ b locus of a’ h b2’ b2 θ φ Required Ans. θ = 35⁰ φ = 35⁰ VP v’
  • 48. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data TLPQ = 100 mm 2. A line PQ 100 mm long is inclined at 30⁰ with HP and 45⁰ with VP. Its end P is 10 mm behind VP and is below HP whereas its HT is 20 mm in front of VP. Draw the projection of line PQ and locate its VT. x HP locus of p 10 p’ = __ ↓, p = 10 ↑ y θ = 30⁰ h = 20 ↓ locus of h 20 Ф = 45⁰ Assuming point Q is also in III quadrant h p2 locus of q q2 θ φ locus of h q1’ q p q’ p’ locus of p’ h’ VP v v’ q1
  • 49. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data FVAB = a’b’ = 55 mm 2. The FV of a line AB 75 mm long measures 55 mm. Point A is 15 mm above HP and point B is 50 mm above HP. The VT is 10 mm below HP. Draw the projection and determine the inclination of line AB with HP and VP. And find its HT. (S – 97, 7 marks) x HP locus of a’ 15 a’ = 15 ↑, b = __ ↓ y locus of b’ TLAB = 75 mm b’ = 50 ↑, b = __ ↓ v’ = 10 ↓ 50 locus of v’ 10 b’ b1’ a’ v’ h’ v θ b3’ b2 locus of a’ a locus of a θ b VP b2’
  • 50. Given Data TLAB = 75 mm 2. The TV of a 75 mm long line AB measures 60 mm. Point A is 15 mm above HP while its VT is 10 m below HP. Line is inclined at 45⁰ with VP. Draw the projection of the line and find its inclination with HP. (W-95, 7 m) x VP HP locus of a’ 15 a’ = 15 ↑, a = __ ↓ y locus of v’ 10 TVAB = ab = 60 mm v’ = 10 ↓ Ф = 45⁰ v’ v Ф θ = TV Length/True Length = 60/75 = 37⁰ a1’ b1’ locus of a’ θ=37⁰ b2 locus of a’ b1 b b’ a’ a locus of a h’ h Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 51. Given Data 2. A line AB, inclined at 40⁰ to VP has its ends 50 mm and 20 mm above HP. The length of its FV is 65 mm and its VT is 10 mm above HP. Determine the true length of AB, its inclination with HP and its HT. (W-99, 7 marks) x VP HP 20 a’ = 20 ↑, a = __ ↓ y locus of b’ 50 Ф = 45⁰ b’ = 50 ↑, a = __ ↓ FVAB = a’b’ = 65 mm v’ = 10 ↑ locus of v’ 10 locus of a’ a’ b’ v’ h’ v b2 locus of b’ b a locus of a’ b1 b1’ θ Required Ans. TLAB = 91 mm θ = 20⁰ b2’ Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer
  • 52. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer 2. A line AB is inclined at 30⁰ to HP. Its ends A and B are 25 mm and 60 mm in front of VP respectively. The TV of line measures 65 mm and its VT is 15 mm above HP. Draw the three views of line AB and determine its true length and true inclination with VP. Locate its traces. x y x1 y1 locus of v’ 15 locus of a 25 locus of b 60 v b v’ θ b1 b1’ locus of b’ b’ a a’ locus of a’ a’’ b’’ v’’ h’ h h’’
  • 53. Mechanical Engineering Department, PCE, Nagpur Subject: Engineering Drawing Sub. Code: 6ME1 Unit 1: Projections of lines Topic Code: 1.1 Slide No. 01 Prof.P.R.Wankhede, Lecturer Given Data 2. A line AB is in first quadrant. Its ends A and B are 15 mm and 55 mm in front of VP respectively. The distance between the end projector is 80 mm. The line is inclined at 30⁰ to HP and its HT is 10 mm above xy. Draw projection of line AB and determine its true length and VT. x VP HP 15 a’ = __ ↓, a = 15 ↓ b’ = __ ↓, b = 55 ↓ y θ = 30⁰ h = 10 ↑ A -- B = 80 mm 55 locus of b locus of a b a locus of h 10 80 v h h’ b1 θ b2 b2’ v’ a’ b1’ locus of b’ b’ locus of a’ A B
  • 54. • A. Auxiliary Vertical Plane (AVP) • B. Auxiliary Inclined Plane (AIP) Auxiliary Planes 08-Jul-09 SBT 54 Vertical Plane (VP) Horizontal Plane (HP) Auxiliary Vertical Plane (AVP) α β Auxiliary Inclined Plane (AIP) x y1 x1 y1 x1 a’ a a1’ a’ a a1 A A Turn about HP to which they are perpendicular
  • 55. 08-Jul-09 SBT 55 x y HP VP a’ a y1 x1 a1’ o o1 a1’01 = a’o Dist. of AFV from x1y1 = Dist. of previous FV from xy
  • 56. g l 7.5 m locus of b’ locus of c’ 9 m locus of o’ x VP HP y locus of o o’ a1’ o 350 b1’ c1’ a1 a locus of a a’ b1 b b’ c1 c c’ locus of c locus of a’
  • 57. l 7.5 m 9 m locus of o’ x y o’ a1’ o 350 c1’ a1 a’ b1 b b’ c1 c’ locus of c’ 30 m locus of a’ 450 300 b2’ c2’ g b1’ locus of a’ a locus of a locus of o locus of c