Isometric projection
In isometric projection, the projection plane forms three equal angles with the coordinate axis. Thus, considering the isometric cube in Figure 2.4, the three cube axes are foreshortened to the same amount, i.e. AB = AC = AD. Two things result from this, firstly, the angles a = b = 30° and secondly, the rear (hidden) corner of the cube is coincident with the upper corner (corner D). Thus, if the hidden edges of the cube had been shown, there would be dotted lines going from D to F, D to C and D to B. The foreshortening in the three axes is such that AB = AC = AD = (2/3)°6 = 0.816. Since isometric projections are pictorial projections and dimensions are not normally taken from them, size is not really important. Hence, it is easier to ignore the foreshortening and just draw the object full size. This makes the drawing less complicated but it does have the effect of apparently enlarging the object by a factor 1.22 (1 50.816). Bearing this in mind and the fact that both angles are 30°, it is not surprising that isometric projection is the most commonly used of the three types of axonometric projection.
The method of constructing isometric projections is shown in the diagrams in Figures 2.5 and 2.6. An object is translated into isometric projection by employing enclosing shapes (typically squares and rectangles) around important features and along the three axes. Considering the isometric cube in Figure 2.4, the three sides are three squares that are 'distorted' into parallelograms, aligned with the three isometric axes. Internal features can be projected from these three parallelograms.
The method of constructing an isometric projection of a flanged bearing block is shown in Figure 2.5. The lefthand drawing shows the construction details and the righthand side shows the 'cleaned up' final isometric projection. An enclosing rectangular cube could be placed around the whole bearing block but this enclosing rectangular cube is not shown on the construction details diagram because of the complexity. Rather, the back face rectangle CDEF and the bottom face ABCF are shown. Based on these two rectangles, the construction method is as follows. Two shapes are drawn on the isometric back plane CDEF. These are the base plate rectangle CPQF and the isometric circles within the enclosing square LMNO. Two circles are placed within this enclosing square. They represent the outer and inner diameters of the bearing at the back face.
The method of constructing an isometric circle is shown in the example in Figure 2.6. Here a circle of diameter ab is enclosed by the square abed. This isometric square is then translated onto each face of the isometric cube. The square abed thus becomes a parallelogram abed. The method of constructing the isometric circles within these squares is as follows. The isometric square is broken down further into a series of convenient shapes, in this case five small longthin rectangles in each quadrant. These small rectangles are then translated on to the isometric cube. The intersection heights ef, gh, ij and kl are then projected onto the equivalent rectangles on the isometric projection. The dots corresponding to the points fhjl are the points on the isometric circles. These points can be then joined to produce isometric circles. The isometric
Figure 2.5 Example of the method of drawing an isometric projection bearing bracket
Figure 2.5 Example of the method of drawing an isometric projection bearing bracket
circles can either be produced freehand or by using matching ellipses. Returning to the isometric bearing plate in Figure 2.5, the isometric circles representing the bearing outside and inside diameters are constructed within the isometric square LMNO. Two angled lines PR are drawn connecting the isometric circles to the base CPQF. The rear shape of the bearing bracket is now complete within the enclosing rectangle CDEF.
Returning to the isometric projection drawing of the flanged bearing block in Figure 2.5. The inside and outside bearing diameters in the isometric form are now projected forward and parallel to the axis BC such that two new sets of isometric circles are constructed as shown. The isometric rectangle CPQF is then projected forward, parallel to BC that produces rectangle ABST, thus completing the bottom plate of the bracket. Finally, the web front face UVWX is constructed. This completes the various constructions of the isometric bearing bracket and the final isometric drawing on the righthand side can be constructed and hidden detail removed.
Any object can be constructed as an isometric drawing provided the above rules of enclosing rectangles and squares are followed which are then projected onto the three isometric planes.
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