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Isometric Projections

Isometric Projections. Hareesha N G Dept of Aeronautical Engg Dayananda Sagar College of Engg Bangalore-78. L. D. H. D. L. L. D. H. H. ISOMETRIC DRAWING. TYPICAL CONDITION. IN THIS 3-D DRAWING OF AN OBJECT, ALL THREE DIMENSIONAL AXES ARE MENTAINED AT EQUAL INCLINATIONS

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Isometric Projections

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  1. Isometric Projections Hareesha N G Dept of Aeronautical Engg DayanandaSagar College of Engg Bangalore-78 Hareesha N G, DSCE, Bengaluru

  2. L D H D L L D H H ISOMETRIC DRAWING TYPICAL CONDITION. IN THIS 3-D DRAWING OF AN OBJECT, ALL THREE DIMENSIONAL AXES ARE MENTAINED AT EQUAL INCLINATIONS WITH EACH OTHER.( 1200) IT IS A TYPE OF PICTORIAL PROJECTION IN WHICH ALL THREE DIMENSIONS OF AN OBJECT ARE SHOWN IN ONE VIEW AND IF REQUIRED, THEIR ACTUAL SIZES CAN BE MEASURED DIRECTLY FROM IT. 3-D DRAWINGS CAN BE DRAWN IN NUMEROUS WAYS AS SHOWN BELOW. ALL THESE DRAWINGS MAY BE CALLED 3-DIMENSIONAL DRAWINGS, OR PHOTOGRAPHIC OR PICTORIAL DRAWINGS. HERE NO SPECIFIC RELATION AMONG H, L & D AXES IS MENTAINED. NOW OBSERVE BELOW GIVEN DRAWINGS. ONE CAN NOTE SPECIFIC INCLINATION AMONG H, L & D AXES. ISO MEANS SAME, SIMILAR OR EQUAL. HERE ONE CAN FIND EDUAL INCLINATION AMONG H, L & D AXES. EACH IS 1200 INCLINED WITH OTHER TWO. HENCE IT IS CALLED ISOMETRIC DRAWING Hareesha N G, DSCE, Bengaluru PURPOSE OF ISOMETRIC DRAWING IS TO UNDERSTAND OVERALL SHAPE, SIZE & APPEARANCE OF AN OBJECT PRIOR TO IT’S PRODUCTION.

  3. L D A H SOME IMPORTANT TERMS: ISOMETRIC AXES, LINES AND PLANES: The three lines AL, AD and AH, meeting at point A and making 1200 angles with each other are termed Isometric Axes. The lines parallel to these axes are called Isometric Lines. The planes representing the faces of of the cube as well as other planes parallel to these planes are called Isometric Planes. ISOMETRIC SCALE: When one holds the object in such a way that all three dimensions are visible then in the process all dimensions become proportionally inclined to observer’s eye sight and hence appear apparent in lengths. This reduction is 0.815 or 9 / 11 ( approx.) It forms a reducing scale which Is used to draw isometric drawings and is called Isometric scale. In practice, while drawing isometric projection, it is necessary to convert true lengths into isometric lengths for measuring and marking the sizes. This is conveniently done by constructing an isometric scale as described on next page. Hareesha N G, DSCE, Bengaluru

  4. H H L L D D CONSTRUCTION OF ISOM.SCALE. From point A, with line AB draw 300 and 450 inclined lines AC & AD resp on AD. Mark divisions of true length and from each division-point draw vertical lines upto AC line. The divisions thus obtained on AC give lengths on isometric scale. TYPES OF ISOMETRIC DRAWINGS ISOMETRIC VIEW ISOMETRIC PROJECTION Drawn by using True scale ( True dimensions ) Drawn by using Isometric scale ( Reduced dimensions ) D 4 3 C 2 4 TRUE LENGTHS 3 1 2 ISOM. LENGTHS 0 1 450 0 300 A B Isometric scale [ Line AC ] required for Isometric Projection Hareesha N G, DSCE, Bengaluru

  5. 1 Isometric view if the Shape is F.V. or T.V. SHAPE ISOMETRIC OF PLANE FIGURES D H D RECTANGLE L A D A L C D C A B C B B B H B 3 L 1 3 B 1 L A D A 3 1 2 A 2 2 4 H PENTAGON E E 1 1 4 D 4 D E D A A D L L 1 3 3 C A C 2 B 3 B B C 2 2 AS THESE ALL ARE 2-D FIGURES WE REQUIRE ONLY TWO ISOMETRIC AXES. IF THE FIGURE IS FRONT VIEW, H & L AXES ARE REQUIRED. IF THE FIGURE IS TOP VIEW, D & L AXES ARE REQUIRED. Shapes containing Inclined lines should be enclosed in a rectangle as shown. Then first draw isom. of that rectangle and then inscribe that shape as it is. TRIANGLE Hareesha N G, DSCE, Bengaluru

  6. Z STUDY ILLUSTRATIONS A B B A D C C D 2 DRAW ISOMETRIC VIEW OF A CIRCLE IF IT IS A TV OR FV. FIRST ENCLOSE IT IN A SQUARE. IT’S ISOMETRIC IS A RHOMBUS WITH D & L AXES FOR TOP VIEW. THEN USE H & L AXES FOR ISOMETRIC WHEN IT IS FRONT VIEW. FOR CONSTRUCTION USE RHOMBUS METHOD SHOWN HERE. STUDY IT. 2 2 4 3 4 3 1 1 Hareesha N G, DSCE, Bengaluru

  7. Z STUDY ILLUSTRATIONS 25 R 50 MM IF TOP VIEW 100 MM 3 DRAW ISOMETRIC VIEW OF THE FIGURE SHOWN WITH DIMENTIONS (ON RIGHT SIDE) CONSIDERING IT FIRST AS F.V. AND THEN T.V. IF FRONT VIEW Hareesha N G, DSCE, Bengaluru

  8. SHAPE IF F.V. IF T.V. ISOMETRIC OF PLANE FIGURES HEXAGON AS THESE ALL ARE 2-D FIGURES WE REQUIRE ONLY TWO ISOMETRIC AXES. IF THE FIGURE IS FRONT VIEW, H & L AXES ARE REQUIRED. IF THE FIGURE IS TOP VIEW, D & L AXES ARE REQUIRED. CIRCLE SEMI CIRCLE 4 For Isometric of Circle/Semicircle use Rhombus method. Construct Rhombus of sides equal to Diameter of circle always. ( Ref. topic ENGG. CURVES.) For Isometric of Circle/Semicircle use Rhombus method. Construct it of sides equal to diameter of circle always. ( Ref. Previous two pages.) Hareesha N G, DSCE, Bengaluru

  9. Z STUDY ILLUSTRATIONS 4 4 D D E E D D L L 1 1 3 3 C C A A B B 2 2 5 ISOMETRIC VIEW OF PENTAGONAL PYRAMIDSTANDING ON H.P. (Height is added from center of pentagon) ISOMETRIC VIEW OF BASE OF PENTAGONAL PYRAMIDSTANDING ON H.P. Hareesha N G, DSCE, Bengaluru

  10. Z STUDY ILLUSTRATIONS 4 H E 1 D A L 3 C B 2 6 ISOMETRIC VIEW OF PENTAGONALL PRISM LYING ON H.P. ISOMETRIC VIEW OF HEXAGONAL PRISM STANDING ON H.P. Hareesha N G, DSCE, Bengaluru

  11. Z STUDY ILLUSTRATIONS 7 CYLINDER STANDING ON H.P. CYLINDER LYING ON H.P. Hareesha N G, DSCE, Bengaluru

  12. Z STUDY ILLUSTRATIONS 8 HALF CYLINDER STANDING ON H.P. ( ON IT’S SEMICIRCULAR BASE) HALF CYLINDER LYING ON H.P. ( with flat face // to H.P.) Hareesha N G, DSCE, Bengaluru

  13. Z STUDY ILLUSTRATIONS 60 X Y 40 20 9 ISOMETRIC VIEW OF A FRUSTOM OF SQUARE PYRAMIDSTANDING ON H.P. ON IT’S LARGER BASE. FV TV Hareesha N G, DSCE, Bengaluru

  14. STUDY ILLUSTRATION E A SOLUTION STEPS: FIRST DRAW ISOMETRIC OF IT’S BASE. THEN DRAWSAME SHAPE AS TOP, 60 MM ABOVE THE BASE PENTAGON CENTER. THEN REDUCE THE TOP TO 20 MM SIDES AND JOIN WITH THE PROPER BASE CORNERS. 60 60 D FV 20 B y x C 1 4 TV 20 40 40 2 3 10 PROJECTIONS OF FRUSTOM OF PENTAGONAL PYRAMID ARE GIVEN. DRAW IT’S ISOMETRIC VIEW. ISOMETRIC VIEW OF FRUSTOM OF PENTAGONAL PYRAMID Hareesha N G, DSCE, Bengaluru

  15. Z STUDY ILLUSTRATIONS 60 X Y 40 20 11 ISOMETRIC VIEW OF A FRUSTOM OF CONE STANDING ON H.P. ON IT’S LARGER BASE. FV TV Hareesha N G, DSCE, Bengaluru

  16. Z STUDY ILLUSTRATIONS 30 50 12 PROBLEM: A SQUARE PYRAMID OF 30 MM BASE SIDES AND 50 MM LONG AXIS, IS CENTRALLY PLACED ON THE TOP OF A CUBE OF 50 MM LONG EDGES.DRAW ISOMETRIC VIEW OF THE PAIR. 50 Hareesha N G, DSCE, Bengaluru

  17. Z STUDY ILLUSTRATIONS a o c p b 13 c PROBLEM: A TRIANGULAR PYRAMID OF 30 MM BASE SIDES AND 50 MM LONG AXIS, IS CENTRALLY PLACED ON THE TOP OF A CUBE OF 50 MM LONG EDGES. DRAW ISOMETRIC VIEW OF THE PAIR. a o p b SOLUTION HINTS. TO DRAW ISOMETRIC OF A CUBE IS SIMPLE. DRAW IT AS USUAL. BUT FOR PYRAMID AS IT’S BASE IS AN EQUILATERAL TRIANGLE, IT CAN NOT BE DRAWN DIRECTLY.SUPPORT OF IT’S TV IS REQUIRED. SO DRAW TRIANGLE AS A TV, SEPARATELY AND NAME VARIOUS POINTS AS SHOWN. AFTER THIS PLACE IT ON THE TOP OF CUBE AS SHOWN. THEN ADD HEIGHT FROM IT’S CENTER AND COMPLETE IT’S ISOMETRIC AS SHOWN. Hareesha N G, DSCE, Bengaluru

  18. Z STUDY ILLUSTRATIONS 30 10 30 30 D + 50 50 14 PROBLEM: A SQUARE PLATE IS PIERCED THROUGH CENTRALLY BY A CYLINDER WHICH COMES OUT EQUALLY FROM BOTH FACES OF PLATE. IT’S FV & TV ARE SHOWN. DRAW ISOMETRIC VIEW. FV TV Hareesha N G, DSCE, Bengaluru

  19. Z STUDY ILLUSTRATIONS 30 10 30 40 SQUARE 60 D 15 PROBLEM: A CIRCULAR PLATE IS PIERCED THROUGH CENTRALLY BY A SQUARE PYRAMID WHICH COMES OUT EQUALLY FROM BOTH FACES OF PLATE. IT’S FV & TV ARE SHOWN. DRAW ISOMETRIC VIEW. FV TV Hareesha N G, DSCE, Bengaluru

  20. Z STUDY ILLUSTRATIONS F.V. & T.V. of an object are given. Draw it’s isometric view. 10 20 40 40 X Y 50 D 30 D 16 FV TV Hareesha N G, DSCE, Bengaluru

  21. STUDY ILLUSTRATIONS Z Iso-Direction 450 R 300 r Adopt same procedure. Draw lower semicircle only. Then around ‘C’ construct Rhombus of Sides equal to Isometric Diameter. For this use iso-scale. Then construct ellipse in this Rhombus as usual And Complete Isometric-Projection of Hemi-sphere. TO DRAW ISOMETRIC PROJECTION OF A SPHERE 1. FIRST DRAW ISOMETRIC OF SQUARE PLATE. 2. LOCATE IT’S CENTER. NAME IT P. 3. FROM PDRAW VERTICAL LINE UPWARD, LENGTH ‘ r mm’ AND LOCATE CENTER OF SPHERE “C” 4. ‘C’ AS CENTER, WITH RADIUS ‘R’ DRAW CIRCLE. THIS IS ISOMETRIC PROJECTION OF A SPHERE. 17 ISOMETRIC PROJECTIONS OF SPHERE & HEMISPHERE r r R r Isom. Scale P C r r C R R TO DRAW ISOMETRIC PROJECTION OF A HEMISPHERE R r P P C = Center of Sphere. P = Point of contact R = True Radius of Sphere r = Isometric Radius. Hareesha N G, DSCE, Bengaluru

  22. 18 Z STUDY ILLUSTRATIONS 450 R 300 r 50 D 30 D 50 50 D PROBLEM: A HEMI-SPHERE IS CENTRALLY PLACED ON THE TOP OF A FRUSTOM OF CONE. DRAW ISOMETRIC PROJECTIONS OF THE ASSEMBLY. r r R r P FIRST CONSTRUCT ISOMETRIC SCALE. USE THIS SCALE FOR ALL DIMENSIONS IN THIS PROBLEM. Hareesha N G, DSCE, Bengaluru

  23. Z STUDY ILLUSTRATIONS X Y 19 A SQUARE PYRAMID OF 40 MM BASE SIDES AND 60 MM AXIS IS CUT BY AN INCLINED SECTION PLANE THROUGH THE MID POINT OF AXIS AS SHOWN.DRAW ISOMETRIC VIEW OF SECTION OF PYRAMID. 3’ 4’ 4 1’ 2’ 3 a 1 d 1 4 2 o 3 2 b c Hareesha N G, DSCE, Bengaluru

  24. Z STUDY ILLUSTRATIONS F.V. & T.V. of an object are given. Draw it’s isometric view. 50 X Y 20 25 25 20 20 O O Hareesha N G, DSCE, Bengaluru

  25. Z STUDY ILLUSTRATIONS F.V. & T.V. of an object are given. Draw it’s isometric view. 35 FV 35 10 y x 20 30 10 40 70 TV 21 O O Hareesha N G, DSCE, Bengaluru

  26. Z STUDY ILLUSTRATIONS F.V. & T.V. and S.V.of an object are given. Draw it’s isometric view. y x 24 ALL VIEWS IDENTICAL FV SV 10 40 60 40 TV 60 Hareesha N G, DSCE, Bengaluru

  27. Z STUDY ILLUSTRATIONS F.V. & T.V. and S.V.of an object are given. Draw it’s isometric view. ALL VIEWS IDENTICAL FV SV 10 y x 40 60 TV 40 60 25 Hareesha N G, DSCE, Bengaluru

  28. 26 Z STUDY ILLUSTRATIONS F.V. & T.V. and S.V.of an object are given. Draw it’s isometric view. FRONT VIEW L.H.SIDE VIEW 20 20 20 50 x y 20 30 20 20 20 TOP VIEW ORTHOGRAPHIC PROJECTIONS O O Hareesha N G, DSCE, Bengaluru

  29. Z F.V. and S.V.of an object are given. Draw it’s isometric view. STUDY ILLUSTRATIONS 30 SQUARE 40 20 50 20 10 30 60 F.V. S.V. 27 O O Hareesha N G, DSCE, Bengaluru

  30. Z STUDY ILLUSTRATIONS F.V. & T.V. of an object are given. Draw it’s isometric view. FV 40 10 O 45 30 D 10 50 80 TV 28 O Hareesha N G, DSCE, Bengaluru

  31. Z STUDY ILLUSTRATIONS F.V. & T.V. of an object are given. Draw it’s isometric view. 40 FV O 10 X Y 100 10 25 TV 10 10 30 25 30 R 20 D 29 O Hareesha N G, DSCE, Bengaluru

  32. Z STUDY ILLUSTRATIONS 30 FV RECT. SLOT 10 50 35 10 Y X O 20 D TV 60 D 30 D 30 F.V. & T.V. of an object are given. Draw it’s isometric view. O Hareesha N G, DSCE, Bengaluru

  33. Z STUDY ILLUSTRATIONS F.V. and S.V.of an object are given. Draw it’s isometric view. 25 15 25 40 10 25 25 O 80 25 S.V. F.V. 31 10 O Hareesha N G, DSCE, Bengaluru

  34. Z STUDY ILLUSTRATIONS F.V. & T.V. of an object are given. Draw it’s isometric view. 450 30 FV 40 X Y O 30 D TV 40 15 40 32 O Hareesha N G, DSCE, Bengaluru

  35. Z F.V. and S.V.of an object are given. Draw it’s isometric view. STUDY ILLUSTRATIONS HEX PART 30 20 20 40 20 50 20 15 O 30 60 100 33 O Hareesha N G, DSCE, Bengaluru

  36. Z STUDY ILLUSTRATIONS F.V. & T.V. of an object are given. Draw it’s isometric view. 40 20 F.V. 30 10 X Y O 10 30 10 30 80 T.V. 34 O Hareesha N G, DSCE, Bengaluru

  37. Z F.V. and S.V.of an object are given. Draw it’s isometric view. STUDY ILLUSTRATIONS 10 10 15 25 25 X Y O 10 50 FV LSV 10 X Y O FV LSV 35 36 NOTE THE SMALL CHZNGE IN 2ND FV & SV. DRAW ISOMETRIC ACCORDINGLY. Hareesha N G, DSCE, Bengaluru

  38. Z F.V. and S.V.of an object are given. Draw it’s isometric view. STUDY ILLUSTRATIONS 10 20 20 30 15 10 15 15 30 15 Y X 50 LEFT S.V. F.V. O 37 O Hareesha N G, DSCE, Bengaluru

  39. Z F.V. and S.V.of an object are given. Draw it’s isometric view. STUDY ILLUSTRATIONS 30 10 60 30 O 40 40 F.V. S.V. 38 O Hareesha N G, DSCE, Bengaluru

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