An isometric view of a rectangular block is shown in Fig. 11.1. The corners of the block are used to position a line DF in space. Three orthographic views in firstangle projection are given in Fig. 11.2, and it will be apparent that the projected length of the line DF in each of the views will be equal in length to the diagonals across each of the rectangular faces. A cross check with the isometric view will clearly show that the true length of line DF must be greater than any of the diagonals in the three orthographic views. The corners nearest to the viewing position are shown as ABCD etc.; the corners on the remote side are indicated in rings. To find the true length of DF, an auxiliary projection must be drawn, and the viewing position must be square with line DF. The first auxiliary projection in Fig. 11.2 gives the true length required, which forms part of the right-angled triangle DFG. Note that auxiliary views are drawn on planes other than the principal projection planes. A plan is projected from an elevation and an elevation from a plan. Since this is the first auxiliary view projected, and from a true plan, it is known as a first auxiliary elevation. Other auxiliary views could be projected from this auxiliary elevation if so required.
The true length of DF could also have been obtained by projection from the front or end elevations by viewing at 90° to the line, and Fig. 11.3 shows these two alternatives. The first auxiliary plan from the front
Plan
Plan
End elevation
Front elevation
End elevation
Front elevation
First auxiliary elevation
First auxiliary elevation
elevation gives triangle FDH, and the first auxiliary plan from the end elevation gives triangle FCD, both right-angled triangles.
Figure 11.4 shows the front elevation and plan view of a box. A first auxiliary plan is drawn in the direction of arrow X. Now PQ is an imaginary datum plane at right angles to the direction of viewing; the perpendicular distance from corner A to the plane is shown as dimension 1. When the first auxiliary plan view is drawn, the box is in effect turned through 90° in the direction of arrow X, and the corner A will be situated above the plane at a perpendicular distance equal to dimension 1. The auxiliary plan view is a true view on the tilted box. If a view is now taken in the direction of arrow Y, the tilted box will be turned through 90° in the direction of the arrow, and dimension 1 to the corner will lie parallel with the plane of the paper. The other seven corners of the box are projected as indicated, and are positioned by the dimensions to the plane PQ in the front elevation. A match-box can be used here as a model to appreciate the position in space for each projection.
Second auxiliary elevation
First auxiliary plan
Second auxiliary elevation
First auxiliary plan
The same box has been redrawn in Fig. 11.5, but the first auxiliary elevation has been taken from the plan view in a manner similar to that described in the previous example. The second auxiliary plan projected in line with arrow Y requires dimensions from plane P1Q1, which are taken as before from plane PQ. Again, check the projections shown with a match-box. All of the following examples use the principles demonstrated in these two problems.
Part of a square pyramid is shown in Fig. 11.6; the constructions for the eight corners in both auxiliary views are identical with those described for the box in Fig. 11.4.
Auxiliary projections from a cylinder are shown in Fig. 11.7; note that chordal widths in the first auxiliary plan are taken from the true plan. Each of twelve points around the circle is plotted in this way and then projected up to the auxiliary elevation. Distances from plane PQ
Second auxiliary elevation
Second auxiliary elevation
First auxiliary plan
First auxiliary plan are used from plane P1Q1. Auxiliary projections of any irregular curve can be made by plotting the positions of a succession of points from the true view and rejoining them with a curve in the auxiliary view.
Figure 11.8 shows a front elevation and plan view of a thin lamina in the shape of the letter L. The lamina lies inclined above the datum plane PQ, and the front elevation appears as a straight line. The true shape is projected above as a first auxiliary view. From the given plan view, an auxiliary elevation has been projected in line with the arrow F, and the positions of the corners above the datum plane P1Q1 will be the same as those above the original plane PQ. A typical dimension to the corner A has been added as dimension 1. To assist in comprehension, the true shape given could be cut from a piece of paper and positioned above the book to appreciate how the lamina is situated in space; it will then be seen that the height above the book of corner A will be dimension 2.
Now a view in the direction of arrow G parallel with the surface of the book will give the lamina shown projected above datum P2Q2. The object of this exercise is to show that if only two auxiliary projections are given in isolation, it is possible to draw projections to find the true shape of the component and also get the component back, parallel to the plane of the paper. The view in direction of arrow H has been drawn and taken at 90° to the bottom edge containing corner A; the resulting view is the straight line of true length positioned below the datum plane P3Q3. The lamina is situated in this view in the perpendicular position above
the paper, with the lower edge parallel to the paper and at a distance equal to dimension 4 from the surface. View J is now drawn square to this projected view and positioned above the datum P4Q4 to give the true shape of the given lamina.
In Fig. 11.9, a lamina has been made from the polygon ACBD in the development and bent along the axis AB; again, a piece of paper cut to this shape and bent to the angle ^ may be of some assistance. The given front elevation and plan position the bent lamina in space, and this exercise is given here since every line used to form the lamina in these two views is not a true length. It will be seen that, if a view is now drawn in the direction of arrow X, which is at right angles to the bend line AB, the resulting projection will give the true length of AB, and this line will also lie parallel with the plane of the paper. By looking along the fold in the direction of arrow Y, the two corners A and B will appear coincident; also, AD and BC will appear as the true lengths of the altitudes DE and FC. The development can now be drawn, since the positions of points E and F are known along the true length of AB. The lengths of the sides AD, DB, BC and AC are obtained from the pattern development.
Development
Development
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