Alternative titles: draughting; engineering drawing; engineering graphics








Types of drawings


Dimensions and tolerances

The sizes of parts and overall sizes of assemblies are conveyed by dimensions placed on the drawing. The basic objective in dimensioning a drawing is to give the manufacturing or construction personnel the dimensions they need to do their work without requiring them to add, subtract, or estimate distances. If mass production is to be undertaken, special attention must be given to the dimensions of interchangeable parts that fit together. To dimension a distance as, say, two inches cannot require that it be exactly two (2.000 . . . ) inches, because no one can machine material with such precision. Particularly for parts of machinery, the designer must specify the acceptable range for the size of a hole, a shaft, or other feature requiring proper fit—perhaps 1.995 to 2.005 inches. The difference between the acceptable maximum and minimum dimensions given for a hole, shaft, or other feature is known as the tolerance. In the example above the tolerance is 0.010 (that is, 2.005 − 1.995) inch. Unsatisfactory tolerancy of mating parts ordinarily results in a machine with improper function or greatly reduced useful life. On the other hand, the cost of production increases greatly as tolerances are made stricter. It is an important design decision to require the correct level of tolerance for the functioning of any particular product. Additional information on a set of drawings indicates the materials to be used and the types of finish required on the surfaces.

Systems of representation


The shapes of all the parts and their interrelation are exactly described by the representation of that information in the set of drawings. Such description can be a lesser or greater challenge, depending on the complexity of the design. In the 15th century some of the leading artists and architects developed geometric schemes of perspective. Geometric perspective is a drawing method by which it is possible to depict a three-dimensional form as a two-dimensional image that closely resembles the scene as visualized by the human eye. The camera produces photographs with such resemblance. Images produced by the eye, the camera, and systems of perspective can all be interpreted in terms of what is known as central projection. Lines of sight may be thought of as extending from the points of the object under observation to a central point of convergence—the lens of the eye or the camera, or the reference point of the perspective construction. In the case of the eye these lines of sight are focused by the lens into an image on the curved retina. In the camera they pass through the lens to form an image on a flat piece of film. In systems of geometric perspective the converging lines of sight form an image on an imaginary picture plane located between the object and the central point of the construction.

Perspective drawings and photographs are easily interpreted because they closely resemble visual images. This resemblance includes the diminution of the relative size of the representations of portions of the object that recede from the viewer and the distortion of the angular relations of the lines of the object. The object shown in perspective in Figure 1A may be interpreted as a cube. The same object is represented in Figure 1B according to the projectional system ordinarily used for engineering and architectural drawings; there it is evident that the object is not a cube. Such projections are used because they convey accurate information about the shape of the object.

Orthographic projection

The projection used for engineering and architectural drawings is called orthogonal (“right-angled”) or orthographic because the lines of sight from points on the object to the picture plane of the image are perpendicular to that plane. Thus, the lines of sight, called projectors, are parallel rather than convergent (as they are in the central projection of the eye, the camera, and geometric perspective).

Descriptive geometry







Hidden lines

It is standard practice to use dashes to represent any line of an object that is hidden from view. A drafter—in deciding whether a line in a view should be represented as hidden or as visible—relies on the fact that in third-angle projection the near side of the object is near the adjacent view, but in first-angle projection the near side of the object is remote from the adjacent view. In Figure 4B (third-angle projection) the top of the front view is near the top view; the front of the top view is near the front view; and the front of the side view is near the front view. In first-angle projection, however, the top of the front view is remote from the top view; the front of the top view is remote from the front view, and the front of the side view is remote from the front view. In a third-angle projection, what is remote in an adjacent view cannot hide what is near in that view.

Figure 5 shows a pictorial representation of an object and the third-angle projections of that object. The arrangement of the three views gives intuitive reinforcement to the correct selection of the line shown as hidden in each view because it is blocked by portions of the object that are nearer in the adjacent views. The number of hidden lines in a view of a complicated object may be very great. For purposes of studying visibility, the direction of projection may be thought of as always vertically downward for a top view, always horizontally from front to back for a front view, and always horizontally right-to-left for a right-side view.

In Figure 5 the hidden lines in the views could be identified by visualizing the object, a process that can be quite difficult for complicated objects. The following basic principle of descriptive geometry is useful in analyzing such a problem:


Figure 6 demonstrates this statement. Although the ground line, or line of intersection of H and V, is seldom drawn in the representations of front and top or of front, top, and side views of objects, it is understood to be horizontal. Thus for any point P, PH and PV lie on a vertical line of the drawing.

A tetrahedron (triangular pyramid) with vertices A, B, C, and D is shown in third-angle projection in Figure 7 . The edges AC and BD do not intersect, although their projections do. To determine which of these two edges is visible in the top view, the drafter considers location M, where the H projection of a point on AC and the H projection of a point on BD coincide. By principle I the V projections of these two points will lie on a vertical line from the crossing of AHCH and BHDH. A vertical construction line in Figure 7 indicates that the point on BD is nearer to the top of the tetrahedron than the point on AC. This means that BD crosses above AC, so that BD must be visible in the top view and AC hidden. Similarly, to study the visibility of these lines in the front view, the vertical construction line is drawn through Q, the crossing of AVCV and BVDV; this procedure indicates that the point on BD is nearer to the front of the tetrahedron than the point on AC. Thus BD crosses in front of AC, so that BD is visible in the front view and AC is hidden.

Auxiliary views

Figure 8 illustrates another basic principle of descriptive geometry that facilitates the discussion of auxiliary views:

II. Given two planes (A and C) perpendicular to a third plane (B), a point P projected orthogonally onto the three planes, and the rotation of A and C into B about their respective lines of intersection with B (LA and LC), then PA is the same distance from LA as PC is from LC.

To convey complete and correct information many views may be necessary to show every plane surface bounding the object in its true size and shape at least once. In choosing the principal views, the drafter positions the object with reference to H and V so as to have the maximum number of its surfaces parallel to H or V or R, a third plane perpendicular to both H and V. Orthographic projection yields the true size and shape of every such surface in the front, the top, or the side view. A surface parallel to H or V or R, the three principal planes, is perpendicular to the other two. Additional or auxiliary views are necessary to represent the true size and shape of other plane surfaces. A plane perpendicular to only one of the three principal planes is said to be in an inclined position; a plane not perpendicular to any of the principal planes is said to be in an oblique position.

Figure 9 illustrates the application of principle II to represent the true size and shape of an inclined surface. The groove in surface ABCD makes an angle of 30° with a line (not shown) parallel to the edge DC. An auxiliary view in which A, B, C, and D are labeled with primes, obtained by projection onto a plane P, parallel to the surface ABCD, is the only one in which the true shape of ABCD and the true size of the 30° angle are correctly shown. The dimension indicated by the double-headed arrow is the same in the H (top) and auxiliary views, as required by principle II. The plane of the auxiliary view and the plane of the H view are perpendicular to the plane of the V view.

The true shape of an oblique surface can be shown correctly only on a second auxiliary view prepared by an extension of the procedure used for a first auxiliary view.


Pictorial views

Although the emphasis on true descriptions of sizes and shapes requires orthographic projection for working and construction drawings, pictorial representations may be useful. In architecture, for example, the designer of the exterior of a building or the interior of an important space may be guided by perspective drawings and other pictorial representations. The construction of major projects may be preceded by the building of three-dimensional models, although these are expensive and seldom used in the early stages of design. Pictorial representations often are used for attracting investors or for advertising of new buildings and other products. Although a specialist in marketing might be intimidated by working drawings, he might grasp a pictorial representation easily enough to make useful suggestions about a design before production or construction was under way.

The execution of a perspective drawing may require more time than is justified in the design of a small item. In many cases orthographic projection, coupled with the rotation of the object with respect to the reference planes, produces an adequate pictorial representation.

Figures 2A, 2C, 3 , 4A , and 5 illustrate the pictorial representation achieved by oblique projection, in which the principal surface of the object is considered to be in the plane of the paper and thus is represented in true size and shape. The angle the receding axis makes with the horizontal lines of the drawing is chosen arbitrarily but with care in terms of the clarity of the particular representation. True lengths are set off along the receding axis as an arbitrary choice. This is a convenient method for constructing a pictorial representation. Unacceptable distortion results when oblique projection is used to represent large objects or those with large dimensions or important details along the receding axis.

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