TA 101: Technical Arts 2015-16 II Dr. Prishati Raychowdhury Department of Civil Engineering IIT Kanpur Office: FB 336; Phone: 6692 E-mail: prishati@iitk.ac.in

Lecture 6 Isometric Projection

Review: Dimensioning Dimensioning is done to describe various features of an object Show dimensions in the view that shows the most relevant features Do not repeat a dimension Place dimensions outside the view, as far as possible Take dimensions out from visible outlines than from hidden lines Give dimensions from Baseline /finished surface /centerline of a hole (as far as possible) Depending on available space, chose wisely among full arrows, half arrows, lines or dots Depending on available space, choose wisely among parallel, chain or combined dimension style

Axonometric Projection Greek: axon = axis, metric = measure Axonometric = To measure along axes

Axonometric Projection Axonometric projection is theoretically an orthographic projection in which only one plane is used and the object being turned so that its three faces are visible Plane of Projection Plane of Projection Plane of Projection Orthographic Projection Axonometric Projection

Axonometric Projection: Overview In orthographic projection, projections are taken on two or more mutually perpendicular planes In Axonometric projection, the object is oriented (rotated TWICE) a priori and appropriately, so that all its 3D features are clearly visible on the vertical plane of projection Axonometric view is one kind of pictorial view

Axonometric/Pictorial View: Example 100 80 20 25 60 50 40 12 x z Y

Advantages and Limitations Easier to visualize the design Relative proportioning of overall size Relative positioning & sizing of constituent parts Good for marketing, showing assembly, conceptual ideas Disadvantage: Does not show true shapes (shapes distorted) Does not show details Not good for dimensioning/manufacturing

Axonometric vs. Orthographic Views

Axonometric Projection: Basic Concept One may get several pictorial views depending on the angle of each rotation Some sort of uniformity and standardization is required

Foreshortening When does a line appears in its true length? The Projection plane is parallel to the object face Rotate object about vertical axis Result: Two sides are “foreshortened” Rotate object about both vertical and profile axes Result: Three sides are “foreshortened”

Foreshortening for a Cube Top view No object rotation Front, Top and Side views (no foreshortening) Object rotated about vertical axis (Two sides are foreshortened) Object rotated about vertical and profile axis (3 sides are foreshortened) Square face becomes what?

Axonometric Projection: Classification Axonometric drawings are classified based on how many axes are foreshortened All three axes are unequally foreshortened: Trimetric projection. [Supposedly the most pleasing to the eye and the most difficult to produce] Two of the sides equally foreshortened: Dimetric projection. [Supposedly less pleasing to the eye but easier to produce than trimetric drawings] All three sides equally foreshortened: Isometric projection. [Supposedly least pleasing to the eye but easiest to draw]

Axonometric Projection: Classification

Isometric Projection Equal foreshortening of all 3 sides To obtain an isometric view of an object: Step 1: Start with the front principal face of the object (cube) parallel to the projection plane

Isometric Projection Step 2: Rotate the object by 45° about its vertical axis

Isometric Projection Step 3: Tilt the object forward by 35°16' (35.27°) For a cube, this corresponds to a forward tilt till the body diagonal AB appears as a point in the front view The three axes that meet at A on the projection plane form equal angles of 120°. They are called the isometric axes.

Isometric Projection The forward tilt of the object causes the edges and planes to become foreshortened as they are projected on the projection plane. The lengths of the projected lines are equal to the cosine of 35o16’ (0.81647) times the true lengths. The projected lengths are approximately 81% of the true lengths.

Concept of Isometric Projection EH Concept of Isometric Projection GH FH HH BH DH H AH CH E F AF EF BF FF BP AP FP EP P F A B HP GP CF GF DF HF DP CP H G FH HH C D EH GH BH DH HP 450 DF H AH CH GF FF AF AP BP EP FP FF EF BF P F EF BF AF GF CF HF DF CP DP GP HP FF FP BP EP EF BF AF AP HP Isometric Projection GF DP GP DF 350 15’ 52’’ CP CF

Isometric Axes Isometric Axis 120 Isometric Box 30 30

Important points • Each edge of the cube is parallel to one of the isometric axes. • Any line that is parallel to an isometric axis is called an isometric line. • The planes of the cube faces and all planes parallel to them are called isometric planes.

Isometric Projection/Isometric View A drawing produced using a scale of 0.816 {1:1.225} is called an Isometric Projection and is a true representation of the object If everything else is kept same, but we produce the drawing using full scale {1:1}, it is called an Isometric Drawing /View An isometric drawing has the same proportions as an isometric projection, but is larger by a factor of 1.225 to 1

Remember! Isometric Projections: Isometric lines drawn using isometric scale Foreshortened Isometric Drawing/View: Isometric lines drawn using 1:1 scale No foreshortening, take actual lengths

Isometric Scale It is fastest to create an isometric scale for drawing isometric drawings Position a regular scale at 45° to the horizontal Project lines vertically to a 30° line as shown This foreshortens the true distances and creates an isometric scale along the 30° line This isometric scale can now be used conveniently to mark off appropriate distances in the isometric projection

Construction of an Isometric Scale 45o line 10 TRUE SCALE 9 8 30o line 7 ISOMETRIC SCALE 6 5 4 3 2 1 ISOMETRIC PROJECTIONS: Use ISOMETRIC SCALE ISOMETRIC DRAWING/VIEW/SKETCH: Use REGULAR/TRUE SCALE

Isometric Projection Vs Drawing/View/Sketch Isometric projections are foreshortened because the object is tipped with respect to the viewing plane. Isometric sketches, or drawings, are usually NOT foreshortened because they still appear proportionate when showing the dimensions full size along isometric axes/lines. It is easier just to sketch the full dimension.

Isometric Views Isometric Projection (A): Foreshortened (81/100) B Isometric Projection (A): Foreshortened (81/100) Isometric Drawing (B): No foreshortening (100/100) No difference in shape - Isometric drawing larger in linear proportion by about 1.23:1 Most common form is to use isometric drawing

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