Plan Length in Engineering Drawing
True lengths and auxiliary views
An isometric view of a rectangular block is shown in Fig. eleven.ane. 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 exist apparent that the projected length of the line DF in each of the views will exist equal in length to the diagonals across each of the rectangular faces. A cantankerous check with the isometric view will clearly show that the true length of line DF must exist greater than any of the diagonals in the iii orthographic views. The corners nearest to the viewing position are shown every bit 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 foursquare with line DF. The showtime auxiliary projection in Fig. 11.two gives the truthful length required, which forms part of the right-angled triangle DFG. Notation that auxiliary views are drawn on planes other than the principal projection planes. A plan is projected from an height and an elevation from a program. Since this is the offset 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 and so required.
The truthful 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
Terminate elevation
Front elevation
Cease elevation
Front elevation
Starting time auxiliary elevation
Beginning auxiliary superlative
height gives triangle FDH, and the offset auxiliary program from the end height gives triangle FCD, both correct-angled triangles.
Effigy eleven.4 shows the front end elevation and plan view of a box. A starting time auxiliary plan is drawn in the direction of pointer X. Now PQ is an imaginary datum airplane at correct angles to the direction of viewing; the perpendicular distance from corner A to the plane is shown every bit dimension one. When the outset auxiliary plan view is drawn, the box is in effect turned through 90° in the direction of pointer 10, and the corner A will exist situated above the plane at a perpendicular distance equal to dimension 1. The auxiliary programme view is a true view on the tilted box. If a view is at present taken in the direction of pointer Y, the tilted box will be turned through xc° in the direction of the arrow, and dimension i to the corner will lie parallel with the plane of the newspaper. The other seven corners of the box are projected as indicated, and are positioned by the dimensions to the plane PQ in the front end elevation. A lucifer-box can be used here as a model to appreciate the position in space for each projection.
2nd auxiliary elevation
Outset auxiliary plan
2nd auxiliary meridian
Start auxiliary plan
The aforementioned box has been redrawn in Fig. 11.5, but the first auxiliary pinnacle has been taken from the plan view in a mode similar to that described in the previous case. The second auxiliary plan projected in line with pointer Y requires dimensions from airplane 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 issues.
Function 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. eleven.4.
Auxiliary projections from a cylinder are shown in Fig. xi.vii; annotation that chordal widths in the showtime auxiliary plan are taken from the true program. Each of twelve points around the circle is plotted in this way and so projected up to the auxiliary elevation. Distances from aeroplane PQ
Second auxiliary elevation
2nd auxiliary elevation
First auxiliary plan
Commencement auxiliary plan are used from plane P1Q1. Auxiliary projections of any irregular bend can be made past plotting the positions of a succession of points from the truthful view and rejoining them with a bend in the auxiliary view.
Effigy 11.8 shows a front end elevation and program view of a thin lamina in the shape of the letter of the alphabet 50. The lamina lies inclined above the datum plane PQ, and the front end summit appears as a straight line. The truthful shape is projected above as a first auxiliary view. From the given plan view, an auxiliary peak has been projected in line with the arrow F, and the positions of the corners to a higher place the datum airplane 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 higher up the volume to appreciate how the lamina is situated in space; it will then be seen that the superlative above the volume of corner A will exist dimension 2.
Now a view in the direction of pointer G parallel with the surface of the volume will give the lamina shown projected above datum P2Q2. The object of this practice is to show that if just two auxiliary projections are given in isolation, information technology is possible to describe projections to observe the truthful 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 xc° to the bottom border 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 newspaper, with the lower edge parallel to the paper and at a distance equal to dimension iv from the surface. View J is now drawn square to this projected view and positioned above the datum P4Q4 to give the truthful shape of the given lamina.
In Fig. 11.nine, a lamina has been made from the polygon ACBD in the development and bent along the axis AB; again, a piece of paper cutting to this shape and bent to the angle ^ may be of some assistance. The given front elevation and plan position the aptitude 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. Information technology will exist seen that, if a view is now drawn in the management of arrow 10, 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 ii corners A and B will appear coincident; also, Advertising and BC will appear as the true lengths of the altitudes DE and FC. The development can at present be fatigued, since the positions of points Eastward and F are known forth the true length of AB. The lengths of the sides AD, DB, BC and AC are obtained from the pattern development.
Evolution
Development
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