Projection of Planes


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Projection of Planes

  2. 2. Class A(1): Plane parallel to P.P. and hence perpendicular to both H.P. & V.P. Y V.P. a” V.P. P.P. ’ P.P a’,b’ a” a’,b A . b” d” b” D YB c’,d’ d’ c” d” c” c’, C X Y a,d a,d H.P.X b,c b,c X H.P.
  3. 3. Class A(2): Plane parallel to V.P. and hence perpendicular to both H.P. & P.P. A, a’ B, d’ Y V.P. b’ a’ D, d’ F.V. C, c’ c’ Y BX Y d’ A C c b, .P. X D H a,d a, d b, c T.V. X
  4. 4. Class A(3): Plane parallel to H.P. and hence perpendicular to both V.P. & P.P. Y .P. V d’ c’, D a’,b’ a’ ,b’ c’,d’ C F.V. A Y X Y B d a d a c . PX H. b b c X T.V.
  5. 5. Class B(1): Plane perpendicular to V.P. and inclined to H.P. by  & also inclined to P.P. Y V .P. b’, c’ b’, c’ . a’, d’  F.V. B Y C X Y a’, d’ A b a b D  .P. X a c H d d c T.V. =  X
  6. 6. Exercise 01:A regular hexagonal plateABCDEF, 30mm side, is restingon H.P. on one of thesides/edges with surface of theplate making 45º with H.P. andperpendicular to V.P. Draw theprojections of the plate.
  7. 7. Data Given:(1) Hexa. Plate Size = 30mm V.P .(2)  = 45° d’,e’ E c’,f’ Y D F f e a’,b’ d ’e’ A,a C d H. P. ’f’ F,f E,e ’ c c a’b B ,b X A,a D,d C,c B,b
  8. 8. Data Given:(1) Hexa. Plate Size = 30mm d1’,e1’(2)  = 45° c1’,f1’ a’,b’ c’,f’ d’,e’ a1’,b1’  X f f1 Y a e a1 e1 30 b d b1 c d1Scale: 1:1 c
  9. 9. Class B (2): Plane perpendicular to H.P. and inclined to V.P. by Φ & also inclined to P.P. Y P. . a’ b’ V. b’ a’ d’ c’  F.V. Ac’ B YX Y d’ . a, d  D C X a, d  c .P. b, H T.V. b, c = X
  10. 10. Exercise 02: A square plate PQRS, edge25mm size, is in space with oneof its corners on V.P. Surface ofthe plate makes 60º with V.P.and it is perpendicular to H.P.Draw its projections.
  11. 11. Data Given: V.P.- Square Plate Size=25mm s’- Φ=60º r’ S S ,s’ P,p’ R,r’ R q’ Y Φ Q P ’ p p q,s ,q’ r r Q H.P. q,s p X X
  12. 12. Data Given:(1) Square Plate Size=25mm s’ S s1’(2) Φ=60º P r’ p ’ p’ 1 r1’ R q’ Q q1’ X Y p q,s r p1 Φ q1,s1 r
  13. 13. Class B (3): Plane perpendicular to P.P. and inclined to H.P. by  & to V.P. by Φ Y P. V. b’ P.P a”,b” . a’ B  A Y   c”, d’ d” C X a  cH.P. D Z d X
  14. 14. Exercise 03:A rectangular plate PQRS 30mm X60mm size, is in space withshorter edge parallel to H.P. and20mm above it. Plate PQRS isperpendicular to V.P. and inclinedto H.P. by such an angle so thatits plan becomes square. Drawthe projections.
  15. 15. Data Given: c1’d1’- Size of rectangle=30mmX60mm-Distance of plane from H.P.=20mm . (plane is parallel to H.P.) T.L- Size of Plan=square of 30mm X 30mm θ a’,b’ c’,d’ a1’,b1’ 20 X Y A,a D,d a1 d1 30 b1 c1 B C,c ,b 60 30
  16. 16. Exercise 04:A regular pentagonal plate of30mm sides, has one of its cornerson H.P. The plane of the pentagonis inclined at 45º to the H.P. Theside of the pentagon, which isopposite to the corner, which is onH.P. is inclined at 30º to the V.P.Draw the projections of the plate.
  17. 17. Data Given - Size of Pentagonal Plate =30mm -  = 45° -  = 30° c1’,d1’ d2’ c2’ L. e2’ T. b1’,e1’ b 2’ a’ b’,e’ c’,d a1’ θX e a2’ Y ’ e1 Φ d d2 30 d1 e2 c2 a a1 c c1 a2 b2 b b1 Scale = 1:1
  18. 18. Exercise 05:Draw the projections of a circle of75mm diameter resting on theH.P. on a point A of thecircumference. Plane is inclinedto the H.P. such that the plan of itis an ellipse of minor axis 30mm.The plan of the diameter,thorough the point A, is makingan angle of 30º with the V.P.Measure the angle of the planewith the H.P.
  19. 19. Data Given:(1) Circle Dia.=75mm (2) =30° e1’ e2’ (3) Minor axis plan f2’ d1’,f1’ d2’ length=30mm g 2’ . c2’ T.L c1’,g1 75 b1’,h1 ’ h2’a’ b’,h c’,g’ d’,f’ e’ ’a1’ θ a2’ b2’X ’ g g1 g2  Y f2 h f h1 f1 h2 e 2 e a1 e1 a2 a d2 b1 d1 b2 c b d 2 c c1 30 Scale:1:
  20. 20. Exercise 06:A regular hexagonal plate40mm side is resting on one ofits edges on H.P. The planemakes an angle of 30º to H.P.and its longest diagonal makesan angle of 45 º with V.P. Drawits projections.
  21. 21. Data given :- (1) Regular hexagonal plate size = 40mm (2) Θ =30º (3) = = 45º Scale = 1:1 d1’e1’ e2’ d2’ L T. f2’ a’b’ c’f’ d’e’ a 1’b 1’ θ c1’f1’ a2’ c2’X f f1 b2 ’ e Y  f 2 2 a e a1 e1 d240 a2 b d b1 d1 c2 c c1 b2
  22. 22. Exercise 07:A square plate of side 50mmis held on a corner on H.P.with a diagonal horizontaland inclined at 40º to V.P. Theplate is seen as a rhombus inplan with one of its diagonalsmeasuring 40mm. Draw itsprojections and determine theangle it makes with H.P.
  23. 23. Data Given:(1)Plate =50mm sq.(2)Plate Diagonal =parallel to H.P. & at 40° ( ) to V.P.(3)Plate is seen as rhombus with one diagonal=40mm c1’ c2’ L d2’ R= L b2’ b1’d1’ a’ b’d’ c’ a1’ X a2’ Y d d1 = d2 50 c2 T.S. c a a1 c1 square a2 b2 b1 b 40
  24. 24. Exercise 08:A regular pentagon ABCDE, of25mm sides, has its side AB inthe V.P. and inclined at anangle of 45º to the H.P. Thecorner A is 20mm above H.P.and the corner D is 25mm infront of V.P. Draw theprojections of the plane andfind its inclination with the V.P.
  25. 25. Data Given:-(1) Regular pentagonal plate size=25mm(2)  =45° -:Answer:-(3) A= 20 mm above XY line  = 31°(4) D= 25 mm below XY line e’ e1’ d2’ c2’ a’ a1’ d’ 25 d1’ e2’ b2 ’ b’ b1’ a2’ c’ c1’  a2 02X a1,b1  b2 Y a,b c,e d c2 25 c1,e1 e2Scale=1:1 Locus of d d1 d2
  26. 26. Exercise 09:A 30º- 60º set square has itsshortest side 40mm long and is inthe H.P. The top view of the setsquare is an isosceles triangleand the hypotenuse of the setsquare is inclined at an angle of45º with the V.P. Draw theprojections of the set square andfind its inclination with the H.P.
  27. 27. Data:- Answer:- (1) T.L.(AB)=40mm (1) θ = 55º (2) Φ=45º Locus of c’ c1’ c2’ .L. R=T a’,b’ c’ a1’,b1’ θ b2 ’ a2’X Y a a1 a2 T.L Φβ 60º . P.40 40 T. L. L. P.L 30º c1 b c b1 40 b2 . c2 Scale:-1:1 Locus of c
  28. 28. Exercise 10:ABCD is a rhombus of diagonalsAC=120mm and BD=60mm. Itscorner A is in the H.P. and thePlane is inclined to the H.P.such that the plan appears to bea square. The plan of diagonalAC makes an angle of 30º to theV.P. Draw the projections ofthe plane and find its inclinationwith H.P.
  29. 29. Data:- (1) Size of rhombus = 120 mm X 60mm (2) =30º c1’ c2’ Answer:- (1) θ = 60º . T.L d2 ’ b2 ’ b1’d1’ a’ b’,d’ c’ a1’  a2’ X Y d d1 d2 c1 60 a c a1 c2 120 b 60 b1 a2 30º b2Scale:-1:1
  30. 30. Exercise 11:A regular hexagonal plate 40mm side is resting on one of its corners in H.P. The diagonal through that corner is inclined at 30º to H.P. and(a)the plan of that diagonal is inclined to V.P. by 30º and(b)diagonal is inclined at 30º. Draw its projections.
  31. 31. Data Given:- (1) Hexagonal plate size=40mm (2) =30° (3) =30° [for case (a)] (4) =30° [for case (b)] . d1’ d2’ d2’ L e 2’ e2’ T. c ’e ’ c 2’ c 2’ b1’f1’ 1 1 f2’X a’ b’f’ c’e’ d’ a1’  f 2’ b2’ b’ Y f f1 a2’ e  a2’ e2 2 d e e1 2 d2 1  f2 f2 d2 a d a1 d1 β Φ c2 a2 c2 a2 b b2 40 c b1 c1 b2 Locus of d Scale=1:1