Isometric projections for engineering students
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The document discusses isometric projections and isometric drawing. It begins by explaining the limitations of orthographic views and how isometric projections show all three dimensions of an object in a single view. It then defines the principles and types of projection, including orthographic, pictorial, axonometric, isometric, dimetric and trimetric. The remainder of the document focuses specifically on isometric projection, defining isometric axes, lines, planes and drawings. It provides examples of how to construct isometric views of various objects from their orthographic projections.
Isometric projections for engineering students
- 1. ISOMETRIC PROJECTIONS AND ISOMETRIC DRAWING
- 2. Introduction Orthographic view shows only two dimensions in any particular view. This makes it difficult to interpret them and only technically trained person can interpret the meaning of these orthographic views. A non-technical person Can not imagine the shape of the object from orthographic projections. Whereas, pictorial projections can be easily understood even by persons Without any technical training because such views show all the three Dimensions Of an object in the same view.
- 3. But pictorial view does not show the true shape and size of any principal surface of An object and it does not show the hidden portions. Pictorial projections are easy to imagine so these are used in sales literature.
- 4. Principle of Projection : If straight lines are drawn from various points of an object to meet a plane then it is said that object is Projected on that plane. These straight lines from the object to the plane are called projectors. The figure formed by joining the points at which the projectors meet the plane is called Projection of that object.
- 5. Types of Projection: I) Orthographic Projection II) Pictorial Projection Pictorial Projection : The projection in which the length , height And depth are shown in one view is called Pictorial Projection. Types of Pictorial Projection: I) Axonometric II) Oblique III) Perspective
- 6. Axonometric Projection: When projection is obtained on plane inclined to all the three principal planes, then It is called Axonometric projection. Types of Axonometric projection: sometric Dimetric Trimetric
- 7. Isometric Projection : The projection is obtained on a plane which is equally inclined to all the three principal planes. Isometric Projections and Isometric drawings are represented on the plane paper or sheet by drawing isometric axes, isometric lines and isometric planes.
- 8. When a cube is kept in particular position then it gives isometric axes, isometric lines and isometric planes. Particular position : When cube is resting on H.P. on corner G and diagonal EC is Perpendicular to A V.P. B D E C F H 30o 30o M G N Base Line
- 9. Isometric Axes : The three lines CB,CD and CG meeting at the point C and making angle of 120 degree with each other are called isometric axes. Isometric lines: The lines parallel to isometric axes are called isometric lines. Isometric planes: The planes represented by faces of cube are called isometric planes. Similarly any planes parallel to these planes are also called isometric planes.
- 10. Isometric drawing or isometric view: The pictorial view drawn with true scale is called Isometric drawing or isometric view. Isometric projection: The pictorial view drawn with the use of isometric scale is called Isometric projection.
- 11. F.V. L.H.S.V. X T.V.
- 12. Aim:- Figure-1, shows the F.V. & T.V. of a simple vertical rectangular plane of size LH. Draw its isometric view, for (a) R.H.S.V. & (b) L.H.S.V. a’ b’ H d’ L c’ F.V. a b d T.V. c Figure-1
- 13. MN, is the base line for isometric axes. PQ, is the isometric axis (vertical) for Fig.1(a) PR, is the isometric axis ( horizontal),for R.H.S.V. for Fig.1(a) at 30º with base line MN. Q A Note:- The diagonal line R a’c’ in ortho. View B increases in its iso. View D (Fig.1-a), as AC (known H L as, non isometric line) X C M N Figure-1(a) P
- 14. MN, is the base line for isometric axes. PQ, is the isometric axis (vertical) for Fig.1(b) PS, is the isometric axis ( horizontal),for L.H.S.V. for Fig.1(b) at 30º with base line MN. Q B Note:- The diagonal line a’c’ in ortho. View S decreases in its iso. View A (Fig. 1-b), as AC (known C as, non isometric line) H L D X M Figure-1(b) N P
- 15. Figure shows the Top View of a rectangular plane of 100 x 70. Draw its isometric view i) for R.H.S.V & ii) for L.H.S.V. a b 70 d c 100 T.V.
- 16. A 70 10 0 D B X C 30° 30° ISOMETRIC VIEW OF THE HORIZONTAL RECTANGULAR PLANE (100 X 70) for its R.H.S.V.
- 17. B 100 C A 70 D X 30° 30° ISOMETRIC VIEW OF THE HORIZONTAL RECTANGULAR PLANE (100 X 70) for its L.H.S.V.
- 18. c’ d’ c’ M1 C2 C3 d’ N2 a’ b’ M2 b’ C1 C4 N1 X a b a’
- 19. ISOMETRIC VIEW OF SIMPLE PLANES Aim:-Figure shows the F.V.of a cut geometric plane.Draw its Isometric view . (i)For R.H.S.V. & (ii)For L.H.S.V. ? b’ c’ a’ 30° d’ H R g’ L f’ e’ F.V.
- 20. ? b’ c’ Darken the required arc FD a’ with center C2 d’ 30° H R g’ L f’ e’ A L ? -: Solution :- B AB=a’ b’ ED=EF=R H 30° R 2 C Now, only the R Quadrant of a circle G D R 1 C2 (L.H.S. upward), is to F C3 be drawn using Four X E center method. C1 C4 (i) 30°
- 21. ? b’ c’ a’ 30° d’ H R g’ L f’ e’ L C ? B D A 30° E H F G X 30° (ii)
- 22. Aim:-Figure shows the T.V. of a cut geometric plane. Draw its Isometric, (i)For R.H.S.V. & (ii) For L.H.S.V. b ? c d e R f D 30° j i D1 45° 45° a L1 k h L2 g L T.V.
- 23. ? b c d e BC=bc= ? ED=EF=R R AK=ak=L1 GH=gh=L2 D f 30° j i Draw, J I // AG ( at a distance of D1 ) D1 45° 45° a L1 k L h L2 g Note :- (1) MJ=KM=D1, as T.V. B angle jka=45 ? (2) Angle JKA & D C Angle IHG are not 30° D 45 in isometric. A 45° J M L 1 D1 R E K N L H I L 45° F 2 X G (i) 30°
- 24. ? b c d e BC=bc= ? R AK=ak=L1 D f 30° j i Draw, J I // AG ( at a distance of D1 ) D1 45° 45° a L1 k L h L2 g Note :- (1) MJ=KM=D1, as E T.V. angle jka=45 D F (2) Angle JKA & ? C I 45° G R Angle IHG are N not 45 in L2 B H isometric. J M D1 D 30° K L 45° 1 L A X 30° (ii)
- 25. C2’ F.V. C2 C1’ C1 T.V.
- 26. d 4 3 e c 3’ d’ 1 a c’ b 2 4’ e’ 3 2’ b’ d a’ c 4 1’ e 2 b a 1
- 27. C2’ C3’ c’ M1 C4’ C2 d’ N2 C3 T.V. M2 b’ C4 C1 N1 X a’ F.V.
- 38. Draw the Iso.View of a regular Pentagonal plane X a’ b’ c’ Y of 40mm sides, with one e’ d’ 90° side normal to V.P. & the s d r plane is in H.P. e g 40 c R a D p b q C 2D S G Q E 40 B A X P 3D
- 39. O’ Draw the Iso.View of a Pentagonal Pyramid, having 60 base sides 40mm, axis 60mm X a’ g’ b’ c’ Y long,when its base is in e’ d’ H.P.with a side of it normal d to V.P. e O 60 O g c 40 R a D C b G 2D S Q E 40 B A X 3D
- 40. Aim:- Figure shows the orthographic projections of a cut simple block. Draw its appropriate Pictorial ( Isometric ) view, giving the dimensions. NOTE: The appropriate Isometric will be,considering its R.H.S.V. ( which is not given & is to be added as a missed view).
- 41. A a 55 15 20 B b c d 55 60 R.H.S.V. F.V. Normally, dotted lines 30 are not drawn in Iso. 20 View, unless 1 2 specifically required 55 to reveal the object 3 T.V. perfectly. Figure 15 15
- 42. 20 30 ISOMETRIC VIEW 1 20 55 a 15 20 40 A b c d a 2 60 F.V. 30 35 20 1 2 15 3 b c B 55 3 15 30 15 T.V. 15 d 55 15 X NOTE:- IN R.H.S.MISSED VIEW, THE AREAS, A & B ARE SEEN AND IS DRAWN IN ITS CORROSPONDING SPACE
- 43. Figure shows Front View and Top View of a machine parts. Sketch its isometric view & dimension it.
- 44. SQ.HOLE OF 20 R25 C B 30° A D 20 70 30 20 F.V. b2 20 10 20 a c b1 10 70 20 T.V.
- 45. ISOMETRIC VIEW SQ.HOLE OF 20 a 25 10 C 95 c B A 20 30° b2 b1 20 30 25 D 20 11 5 20 50 X
- 46. Aim:- Figure shows the F.V. & T.V. of a machine component. Figure 20 Draw its R3 0 15 pictorial F.V. (ISOMETRIC) 20 view, giving 15 30 30 the dimensions. R10 15 20 120 40 T.V.
- 47. Note 1:- The machine component is splitted into four different parts, for its iso. sketching, with bottom base part as first drawn. Note 2:-The circularity or part of that of Ortho.View, is to be drawn in Iso view as an ellipse or part of that using “four center method”,as explained earlier. Note 3:- Such components may be drawn in iso., by area (plane)wise w.r.t F.V, T.V & S.V directions. Never prefer “box method” for such components.
- 48. 20 Split-II Solution 60 See, Note 2 20 20 Split-III 15 R3 0 20 Split-IV 65 15 ISOMETRIC R1 0 VIEW 30 30 120 Split-I See, Note 2 15
- 49. ISOMETRIC SCALE 70 (To be used for isometric projections) ) e 60 in ° l 50 45 ( on 40 TH G 30 e) EN lin L 20 0° A L (o n3 TU 10 60 TH √3) A C P N G √2 / 0 40 C LE BY -5 R I ED -10 20 ET C OM EDU IS (R Q B 45° 30° 90° A BASE LINE
- 50. III. A The Front View of the Top Face of a Cube having edges “e” (with one of the body diagonal line, normal D to V.P. ) is to be treated as ISOMETRIC of the Top Face of the Cube d’ (with a side parallel to V.P.) A 30° 45° m’ C All the edges Top face a’ M c’ edges, base face edges and 4 vertical edges of b’ the cube are reduced in its isometric view, in a’d’= f (AD) the stated condition. B
- 51. Cos 30º = a’m’/a’d’ ----- (1) Cos 45º = a’m’/AD ----- (2) From (1) & (2) a’m’ = a’d’ cos30º = AD cos45º D i.e. a’d’ = AD cos45º/cos 30 d’ e x 1/ 2 = A 30° 45° m’ C 3/2 a’ M c’ i.e. a’d’ = AD x 2/3 b’ i.e. ISOMETRIC LENGTH = a’d’= f (AD) B (0.815 x ACTUAL LENGTH)
- 52. Aim:- Sketch shows the Orthographic views of a machine component. Draw its appropriate Isometric view, using “splitting the object into pieces” techniques. Give the dimensions on the ISOMETRIC VIEW drawn.
- 53. 90 20 50 R40 Sketch 40 20 30 20 φ40 T.V. 10 30 R.H.S.V. 80 (missed view) may be added here in height 20 & depth range F.V.
- 54. Dimensions 20 must be C 10 given on the Isometric 25 50 30 view, which 30 are not 20 50 40 shown here. B 20 80 20 Ø30 70 R4 0 R15 25 20 90 80x80 20 25 A square D
- 55. Exercise Figure shows the Orthographic views of a machine component. Draw its Isometric view. Give the dimensions as per aligned system.
- 56. Ø30 R30 c 25 60 B 15 35 40 15 60 b a 20 A 10 40 120 80 L.H.S.V. FRONT VIEW FIGURE NOTE:- The front view areas are A & B, while the side view areas are a, b & c.
- 57. Solution ø30 R30 20 B 60 25 c 15 20 35 15 40 20 b 10 a 40 A 120 80 ISOMETRIC X VIEW
- 58. F.V. L.H.S.V.
- 59. c1’
- 61. 34 60 25 L= 60 mm H= 25 mm D= 34 mm X