Transcript of "Isometric projections for engineering students"
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ISOMETRICPROJECTIONS AND ISOMETRIC DRAWING
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IntroductionOrthographic view shows only two dimensions inany particular view. This makes it difficult tointerpret them and only technically trained personcan interpret the meaning of these orthographicviews.A non-technical person Can not imagine the shapeof the object from orthographic projections.Whereas, pictorial projections can be easilyunderstood even by persons Without any technicaltraining because such views show all the threeDimensions Of an object in the same view.
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But pictorial view does not show the true shapeand size of any principal surface of An object andit does not show the hidden portions.Pictorial projections are easy to imagine so theseare used in sales literature.
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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.
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Types of Projection:I) Orthographic ProjectionII) Pictorial ProjectionPictorial Projection :The projection in which the length , heightAnd depth are shown in one view iscalled Pictorial Projection.Types of Pictorial Projection:I) AxonometricII) ObliqueIII) Perspective
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Axonometric Projection:When projection is obtained on plane inclined toall the three principal planes, then It is calledAxonometric projection.Types of Axonometric projection:sometricDimetricTrimetric
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Isometric Projection :The projection is obtained on a plane which isequally inclined to all the three principal planes.Isometric Projections and Isometric drawings arerepresented on the plane paper or sheet by drawingisometric axes, isometric lines and isometric planes.
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When a cube is kept in particular position then itgives isometric axes, isometric lines and isometricplanes.Particular position : When cube is resting on H.P.on corner G and diagonal EC is Perpendicular to AV.P. B D E C F H 30o 30o M G N Base Line
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Isometric Axes :The three lines CB,CD and CG meeting at the pointC and making angle of 120 degree with each otherare called isometric axes.Isometric lines:The lines parallel to isometric axes are calledisometric lines.Isometric planes:The planes represented by faces of cube are calledisometric planes.Similarly any planes parallel to these planes are alsocalled isometric planes.
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Isometric drawing or isometric view:The pictorial view drawn with true scale is calledIsometric drawing or isometric view.Isometric projection:The pictorial view drawn with the use of isometricscale is called Isometric projection.
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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
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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. forFig.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 CM N Figure-1(a) P
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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. forFig.1(b) at 30º with base line MN. Q BNote:- The diagonal linea’c’ in ortho. View Sdecreases in its iso. View A(Fig. 1-b), as AC (known Cas, non isometric line) H L D X M Figure-1(b) N P
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Figure shows the Top View of a rectangular plane of100 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.
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A 70 10 0D B X C 30° 30°ISOMETRIC VIEW OF THE HORIZONTALRECTANGULAR PLANE (100 X 70) for itsR.H.S.V.
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B 100 C A 70 D X 30° 30°ISOMETRIC VIEW OF THE HORIZONTALRECTANGULAR PLANE (100 X 70) for itsL.H.S.V.
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c’d’ c’ M1 C2 C3 d’ N2a’ b’ M2 b’ C1 C4 N1 Xa b a’
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ISOMETRIC VIEW OF SIMPLE PLANESAim:-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.
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? 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=RH 30° R 2 C Now, only the R Quadrant of a circleG D R 1 C2 (L.H.S. upward), is to F C3 be drawn using FourX E center method. C1 C4 (i) 30°
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? b’ c’a’ 30° d’ H Rg’ L f’ e’ L C ? B D A 30° E H F G X 30° (ii)
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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 fD 30° j i D1 45° 45° a L1 k h L2 g L T.V.
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? b c d e BC=bc= ? ED=EF=R R AK=ak=L1 GH=gh=L2D 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 2X G (i) 30°
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? b c d e BC=bc= ? R AK=ak=L1D 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 L2B H isometric. J M D1 D 30° K L 45° 1 L A X 30° (ii)
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Draw the Iso.View of a regular Pentagonal planeX 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 g40 c R a D p b q C 2D S G Q E 40 B A X P 3D
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O’ Draw the Iso.View of a Pentagonal Pyramid, having 60 base sides 40mm, axis 60mmX 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 c40 R a D C b G 2D S Q E 40 B A X 3D
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Aim:- Figure shows the orthographicprojections of a cut simple block. Draw itsappropriate 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).
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A a 55 15 20 B b c d 55 60 R.H.S.V. F.V.Normally, dotted lines 30are not drawn in Iso. 20View, unless 1 2specifically required 55to reveal the object 3 T.V.perfectly. Figure 15 15
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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 XNOTE:- IN R.H.S.MISSED VIEW, THE AREAS, A & B ARE SEEN AND IS DRAWN IN ITS CORROSPONDING SPACE
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Figure shows Front Viewand Top View of a machineparts. Sketch its isometricview & dimension it.
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SQ.HOLE OF 20R25 C B 30° A D 2070 30 20 F.V. b2 20 10 20 a c b110 70 20 T.V.
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ISOMETRIC VIEWSQ.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
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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.
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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.
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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
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III. AThe Front View of the Top Face of a Cube havingedges “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 facea’ 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
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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 3/2a’ 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)
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Aim:- Sketch shows the Orthographicviews of a machine component. Drawits appropriate Isometric view, using“splitting the object into pieces”techniques. Give the dimensions onthe ISOMETRIC VIEW drawn.
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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.
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Dimensions 20must be C 10given on theIsometric 25 50 30view, which 30are not 20 50 40shown here. B 20 80 20 Ø3070 R4 0 R15 25 20 90 80x80 20 25 A square D
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ExerciseFigure shows the Orthographicviews of a machine component.Draw its Isometric view.Give the dimensions as peraligned system.
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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.
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Solution ø30 R30 20 B 60 25 c 15 20 35 15 40 20 b 10 a 40 A 120 80ISOMETRIC X VIEW