Computer Aided Engineering Design
TRANSFORMATIONS AND PROJECTIONS 43 Rfyz= –1000 0100 0010 0001 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ The transformations are A B* C* D* E* F* A ...
44 COMPUTER AIDED ENGINEERING DESIGN 2.6 Computer Aided Assembly of Rigid Bodies Transformations can be used to position CAD pri ...
TRANSFORMATIONS AND PROJECTIONS 45 can be determined aspp 12 ′× ′. The angle β between the planes PP P 123 ′′ ′ and Q 1 Q 2 Q 3 ...
46 COMPUTER AIDED ENGINEERING DESIGN RRxy= TQ 10 00 0–1 0 0 00–10 00 01 , = 0.707 0 – 0.707 0 01 0 0 0.707 0 0.707 0 00 0 1 , = ...
TRANSFORMATIONS AND PROJECTIONS 47 (iv) For α = (90° + β), S 1 * and S 2 are hinged about Q 1 Q 3 and are perpendicular to each ...
48 COMPUTER AIDED ENGINEERING DESIGN ′ ′ ′ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ P ...
TRANSFORMATIONS AND PROJECTIONS 49 computer. Though recent developments in computer graphics facilitate better appreciation of a ...
50 COMPUTER AIDED ENGINEERING DESIGN Figure 2.21 Perspective projection of P on the x-y plane Figure 2.20 Classification of proj ...
TRANSFORMATIONS AND PROJECTIONS 51 OP* = OE + EP* = x*i + y*j + z*k = –w + * = – + ( – *) + ( – *) + ( – *) w z w w z xx w z yy ...
52 COMPUTER AIDED ENGINEERING DESIGN Example 2.10. A unit cube is placed in the first octant, as shown in Figure 2.23, such that ...
TRANSFORMATIONS AND PROJECTIONS 53 = 2 1 0 1.2 2 2 0 1.2 1 2 0 1.2 1 1 0 1.2 2 1 0 1.1 2 2 0 1.1 1 2 0 1.1 1 1 0 1.1 1.67 .833 0 ...
54 COMPUTER AIDED ENGINEERING DESIGN The vertices of the square ABCD are now transformed to get the perspective image ABCD in Fi ...
TRANSFORMATIONS AND PROJECTIONS 55 We may observe that for projection on the x-y plane, the entire third row of Prxy is 0. Simil ...
56 COMPUTER AIDED ENGINEERING DESIGN a single view. However, true dimensions are not shown as there is a foreshortening of the d ...
TRANSFORMATIONS AND PROJECTIONS 57 If all three foreshortening factors are equal, we get an isometric projection. For shy = shz ...
58 COMPUTER AIDED ENGINEERING DESIGN Draw (a) An isometric projection of the block. (b) A dimetric projection of the block for s ...
TRANSFORMATIONS AND PROJECTIONS 59 Figure 2.27 Four possible dimetric projections of the block Figure 2.28 A trimetric projectio ...
60 COMPUTER AIDED ENGINEERING DESIGN 2.9 Oblique Projections In axonometric projections, the parallel rays or projectors are per ...
TRANSFORMATIONS AND PROJECTIONS 61 For a parallel ray passing through any general point P(x,y,z), we can obtain the image Q(qx,q ...
62 COMPUTER AIDED ENGINEERING DESIGN Figure 2.32 Cavalier projections –6–4–20246 3 2.5 2 1.5 1 0.5 0 ψ = 0° –6 –4 –2 0 2 4 6 3 2 ...
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