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# Engineering Graphics - Projection of points and lines

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Engineering Graphics - Projection of Points, Projection of Lines

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### Engineering Graphics - Projection of points and lines

1. 1. Projection of Points • There are basically nine type of projections of point is space : 1. In FIRST Quadrant (Above H.P. , In front of V.P.) 2. In SECOND Quadrant (Above H.P. , Behind V.P.) 3. In THIRD Quadrant (Below H.P. , Behind V.P.) 4. In FOURTH Quadrant (Below H.P. , In front of V.P.) 5. In PLANE (On V.P. , Above H.P.) 6. In PLANE (On H.P. , Behind V.P.) 7. In PLANE (On V.P. , Below H.P.) 8. In PLANE (On H.P. In front of V.P.) 9. In PLANE (On both H.P. & V.P.)
2. 2. V.P. H.P. . . . . X Y . X Y a1’ A1 a1 a1’ a1 X Y A1- Point a1’- F.V. a1 - T.V. (3D) (2D) Position 1 In 3D In 2D Above H.P. Front View Above Reference Line In front of V.P. Top View Below Reference Line
3. 3. H.P. A2- Point a2’- F.V. Y a2 - T.V. V.P. A2 . . a2’ . . . (3D) X (2D) X Y a2 a2 a2’ In 3D In 2D Above H.P. Front View Above Reference Line Behind V.P. Top View Above Reference Line X Y Position 2
4. 4. a3 X A3- Point a3’- F.V. a3- T.V. (3D) A3 a3’ X Y .a3 . a3’ Y X Y (2D) . . . Position 3 In 3D In 2D Below H.P. Front View Below Reference Line Behind V.P. Top View Above Reference Line
5. 5. A4- Point a4’- F.V. a4- T.V. .a4 A4 a4’ a4 . . a4’ X Y (3D) X Y X Y . (2D) . Position 4 In 3D In 2D Below H.P. Front View Below Reference Line In front of V.P. Top View Below Reference Line
6. 6. A5- Point a5’- F.V. a5 - T.V. H.P. H.P. V.P. . . . . Y X a5’ A5 a5 Aa’ 5 5a X 5 Y X Y (3D) (2D) Position 5 In 3D In 2D Above H.P. Front View Above Reference Line On V.P. Top View On Reference Line
7. 7. . X Y X Y A6 a6 a6’ X Y .a6’ (2D) a6 . A6 (3D) . A6- Point a6’- F.V. a6- T.V. Position 6 In 3D In 2D Below H.P. Front View Below Reference Line On V.P. Top View On Reference Line
8. 8. A7 Point a7 - T.V. X Y A7 . . A7 a7 a7’ X Y Y (3D) X (2D) . . a7’- F.V. a7’ a7 Position 7 In 3D In 2D On H.P. Front View On Reference Line In Front of V.P. Top View Below Reference Line
9. 9. Y A8 . . A8- Point a8’- F.V. a8 - T.V. Y X X A8 a8 a8’ (3D) (2D) a8 . .a8’ X Y Position 8 In 3D In 2D On H.P. Front View On Reference Line Behind V.P. Top View Above Reference Line
10. 10. V.P. A9- Point a9 Y - T.V. (3D) H.P. (2D) X Y . A9 a9 X Y X a9’ a9’- F.V. .a9’ aA 9 9 Position 9 In 3D In 2D On H.P. Front View On Reference Line On V.P. Top View On Reference Line
11. 11. Projection Of Lines • A straight line is the shortest distance between two points. • Top views of two end points of a straight line, when joined, give the top view of the straight line. • Front views of the two end points of a straight line, when joined, give the front view of the straight line. • Both the above projections are straight lines.
12. 12. Notations for : Projection Of Lines • True length of the line: Denoted by Capital letters. e.g. AB=100 mm, means that true length of the line is 100 mm. • Front View Length: Denoted by small letters. e.g. a’b’=70 mm, means that Front View Length is 70 mm. • Top View Length: Denoted by small letters. e.g. ab=80 mm, means that Top View Length is 80 mm. • Inclination of True Length of Line with H.P.: It is denoted by θ. e.g. Inclination of the line with H.P. (or Ground) is given as 30º means that θ = 30º.
13. 13. Notations for : Projection Of Lines • Inclination of True Length of Line with V.P.: It is denoted by Φ. e.g. Inclination of the line with V.P. is given as 40º means that Φ = 40º. • Inclination of Front View Length with XY : It is denoted by α. e.g. Inclination of the Front View of the line with XY is given as 50º means that α = 50º. • Inclination of Top View Length with XY : It is denoted by β. e.g. Inclination of the Top View of the line with XY is given as 30º means that β = 30º. • End Projector Distance: It is the distance between two projectors passing through end points of F.V. & T.V. measured parallel to XY line.
14. 14. Projection Of Lines There are cases of projections of line :- 1.Line Parallel to two Planes and Perpendicular to the third plane. 2.Line Inclined to one Plane and Parallel to another 3.Line Inclined to both the Planes.
15. 15. Position 1: Parallel to two planes & perpendicular to the other In 3D In 2D Parallel to H.P. Front View – Parallel line to reference line Parallel to V.P. Top View – Parallel Line to reference line Perpendicular to P.P. Side View – Point on the side of front view V.P. a’ Fv b’ X Y a b H.P. TV Y a” P.P. . H.P. V.P. Y X B A a’ b’ b a b” z x P.P. a’’ b’’
16. 16. Position 1: Parallel to one plane and inclined to the other In 3D In 2D Inclined to H.P. Front View – Line inclined by to reference line Parallel to V.P. Top View – Parallel Line to reference line X Y V.P. A B b’ a’ b a q q F.V. T.V. V.P. a’ b’ q X Y H.P. F.V. T.V. a b True Length q
17. 17. H.P. V.P. X Y a b a’ b’   Y X B A a V.P. X Y b a H.P. b FV TV a’ b’ Position 1: Inclined to both the planes In 3D In 2D Inclined to H.P. Front View – Line inclined by to reference line Parallel to V.P. Top View – Line inclined by to reference line a b
18. 18. Problem 1 : A line PJ, 50 mm long is perpendicular to H.P. & t is below H.P. Point P is on H.P. & 30 mm behind V.P. Draw projections of line PJ. 50 30 pj j’ p’ 50 50 30 pj 30 p’ j’ X Y
19. 19. Problem 2 :A line MJ, 35 mm long, is perpendicular to the profile plane. The end M is 20 mm below H.P., 30 mm behind V.P. Draw projections on H.P. & V.P. 35 j m 30 X Y 20 j’ 35 m’ 35 30 20 m’ j’ j m
20. 20. Problem 3 : A line KP, 70 mm long, is parallel to H.P. & inclined to V.P. by 60O . Point P is 20 mm above H.P. and 30 mm in front of V.P. Point K is behind V.P. Draw to projection of line KP. k k’ p’ X Y p 20 70 60
21. 21. 25 15 Problem 4 : A Line AB, 90 mm long, is inclined to H.P. by 30° and inclined to V.P. by 45º. The line is in first quadrant with Point A 15 mm above H.P. and 25 mm in front of V.P. Draw the projection of line AB. Φ α β .. a’ a b’ b1’ X Y b b2 θ Locus of b’ Locus of b Data Given :- (1) T.L.=90 mm (2) Θ =30° (3) Φ =45° (4) Point A 15 above H.P. 25 mm in Front of V.P. F.V. T.V. Answers :- (1) F.V.= 64 mm (2) T.V = 78 mm (3)  = 45° (4)  = 55° T.L.= 90 b2’ b1 ..