Isometric Projections
It is easy to draw the two principal views (plan and elevation) of an object from its pictorial representation. The reverse is not always easy to visualize the object from two of its principal views. A third view on the profile plane aids to visualize the
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Isometric Projections
It is easy to draw the two principal views (plan and elevation) of an object from its pictorial representation. The reverse is not always easy to visualize the object from two of its principal views. A third view on the profile plane aids to visualize the exact shape of the object. Isometric projection is an orthographic projection of an object on the vertical plane showing its three dimensions in one view (elevation). To understand the principles of isometric projection, let us consider the auxiliary projection of a cube. The problem is one of drawing the projections of a cube when one of its solid diagonals is perpendicular to the vertical plane. The solution for this problem, which is self-explanatory, is given in Fig. 14.1. The special features on the final elevation are summarized as follows: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
The 12 edges of the cube are distinct. Three edges d0 h0 , e0 h0 and g0 h0 are invisible. The 12 edges are equal in length and hence they are equally inclined to the VP. The edges a0 b0 , c0 d0 , e0 f0 and g0 h0 , which are parallel, are also parallel in the final elevation. The edges a0 d0 , b0 c0 , f0 g0 and e0 h0 , which are parallel, are also parallel in the final elevation. The vertical edges a0 e0 , b0 f0 , c0 g0 and d0 h0 are also vertical in the final elevation. The faces of the cube are equally inclined to the vertical plane. The diagonal a0 c0 on the face a0 b0 c0 d0 is not foreshortened and is perpendicular to the edge b0 f0 . The diagonal a0 f0 on the face a0 b0 f0 e0 is not foreshortened and is perpendicular to the edge b0 c0 . The diagonal c0 f0 on the face b0 c0 g0 f0 is not foreshortened and is perpendicular to the edge b0 a0 . The edges b0 f0 , b0 c0 and b0 a0 make equal inclination of each 120 .
The final elevation is the isometric projection of the cube. Another special feature of the projection is given below:
© Springer Nature Singapore Pte Ltd. 2018 K. Rathnam, A First Course in Engineering Drawing, DOI 10.1007/978-981-10-5358-0_14
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Isometric Projections
Fig. 14.1 Auxiliary projections of a cube
Fig. 14.2 Isometric projection of a square
The foreshortened length c0 -d0 is called the isometric length of the edge CD (refer to Fig. 14.2). Consider the triangles CDP and c0 -d0 -P which are the right angled triangles and have the common adjacent edge c0 P, pffiffiffi 3 c0 P ¼ cos 30 ¼ c 0 d0 2 c0 P 1 ¼ cos 45 ¼ pffiffiffi CD 2 p ffiffi 0 0 d Hence, cCD ¼ p2ffiffi3 ¼ 0:816 isometric length ¼ 0:816 actual length
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Isometric Projections
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Fig. 14.3 Projections of a cube and its isometric projection
The final elevation of the cube is redrawn together with the projections of the cube in its simple position as shown in Fig. 14.3. The three mutually perpendicular co-ordinate axes OX, OY and OZ are introduced in the plan and elevation of the cube as shown in the figure. These axes which appear inclined to each other at 120 in the isometric projection are called as the isometric axes. Any plane parallel to two of the isometric axes is
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