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Engineering and technical graphics are dependent on projection methods. The two projection methods primarily used in engineering graphics are perspective and parallel. Projection theory comprises the principles used to represent graphically 3-D objects and structures on 2-D media. All projection theory is based on two variables, line of sight and plane of projection.
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PROJECTION THEORY |
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| 8.1 Two projection methods used in projection theory: perspective and parallel. |
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| 8.2 Projection theory comprises the principles used to represent graphically 3-D objects and structures on 2-D media. |
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| 8.3 Drawing more than one face of an object by moving your line of sight relative to the object helps in understanding the 3-D form. A line of sight is an imaginary ray of light between an observer's eye and the object. |
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| 8.4 In perspective projection, all lines of sight start at a single point. and the object is positioned at a finite distance and viewed from a single point. |
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| 8.5-6 In parallel projection, all lines of sight are parallel, the object is positioned at infinity and viewed from multiple points on an imaginary line parallel to the object. The 3-D object is transformed into a 2-D representation or a plane of projection that is an imaginary flat plane upon which the image created by the lines of sight is projected. The paper or computer screen on which the graphic is created is a plane of projection. |
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| 8.6 Orthographic projection is a parallel projection technique in which the plane of projection is positioned between the observer and the object, and is perpendicular to the parallel lines of sight. Orthographic projection techniques can be used to produce both pictorial and multiview drawings. |
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MULTIVIEW PROJECTION PLANES |
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| 8.7 Multiview projection is an orthographic projection for which the object is behind the plane of projection, and is oriented so only two of its dimensions are shown. Generally three views of an object are drawn, and the features and dimensions in each view accurately represent those of the object. |
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| 8.8 The front view of an object shows the width and height dimensions. The frontal plane of projection is the plane onto which the front view of a multiview drawing is projected. |
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| 8.10 The side view of an object shows the height and depth dimensions. The side view is projected onto the profile plane of projection. The right side view is the standard side view normally used. |
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| 8.11 The top view is always positioned above and aligned with the front view, and the right side view is always positioned to the right of and also aligned with the front view. |
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ADVANTAGES OF MULTIVIEW DRAWINGS |
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| 8.12-15 The advantage of multiview drawings over pictorial drawings is that multiview drawings show the true size and shape of the various features of the object, whereas pictorials distort true dimensions which are critical in manufacturing and construction. |
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| 8.16 3-D graphical data base used in CNC manufacturing. |
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THE SIX PRINCIPAL VIEWS |
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| 8.17-18 There are six principal mutually perpendicular views projected onto three mutually perpendicular projection planes. These views are the top, front, right, left, bottom and back. |
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| 8.19-20 The width dimension is common to the front and top views. The height dimension is common to the front and side views. The depth dimension is common to the top and side views. |
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| 8.21 The arrangement of views may vary as long as the dimension alignment is correct. |
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| 8.22A Third angle projection is the standard projection for the United States and Canada. The ANSI third angle icon is shown. |
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| 8.22B First angle projection is the standard in Europe and Asia. The ANSI first angle icon is shown. |
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| 8.23-25 The difference between first and third angle projection is the placement of the object and the projection plane. |
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| 8.26 Adjacent views are two orthographic views placed next to each other such that the dimension they share in common is aligned. Every point or feature in one view must be aligned on a parallel projector in any adjacent view. Related views are two views that share the same adjacent views. Distances between any two points of a feature in related views must be equal. The view from which adjacent views are aligned is the central view. |
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| 8.27 The alphabet of lines specifies the line type and thickness for the allowable types of lines to be used on a technical drawing. These linetypes are standardized and specified by ANSI. |
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| 8.28 Hidden features are represented by dashed lines. Some examples include: Holes - to locate the limiting elements. |
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| 8.29-30 CAD software contains a variety of linetype specifications which can be assigned to lines in drawings. |
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| 8.31 Some objects can be adequately described with only one view. |
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| 8.32 Cylindrical, conical, and pyramidal objects can be described with two views. |
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| 8.33-38 Creating three view drawings by traditional and CAD methods. |
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VIEW SELECTION |
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| 8.39 Before a multiview drawing can be created, four basic decisions must be made. Determine the best position of the object. |
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| 8.40 Select the views that will show the least amount of hidden features. |
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| 8.41 Determine the front view which should show the object in its natural view or assembled state, such as the front view of a car. |
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| 8.42 Determine the minimum number of views needed to describe the object. |
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| 8.43 Once the front view is selected, determine the other views needed to describe the object with the fewest number of lines. |
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FUNDAMENTAL VIEWS OF EDGES AND PLANES |
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| 8.44 An edge, or corner, is the intersection of two planes, and is represented as a line on a multiview drawing. A normal edge or line, or true-length line, is an edge that is parallel to a plane of projection and thus perpendicular to the line of sight. An inclined edge, or line, is parallel to a plane of projection, but inclined to the adjacent planes and appears foreshortened in the adjacent views. Features are foreshortened when the lines of sight are not perpendicular to the feature. |
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| 8.45 An oblique line is not parallel to any principal plane of projection, therefore, never appears in its true length or point in any of the six principal views. |
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| 8.46 A normal or principal plane is parallel to one of the principal planes of projection, and therefore is perpendicular to the line of sight. |
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A frontal plane is parallel to the front plane of projection and is true shape and size in the front and back views. (plane A) |
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A horizontal plane is parallel to the horizontal plane of projection and is true shape and size in the top and bottom views. (plane B) |
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A profile plane is parallel to the profile plane of projection and is true shape and size in the right and left views. (plane C) |
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An inclined plane is perpendicular to one plane of projection (edge) and inclined to adjacent planes (foreshortened), and cannot be viewed in true size and shape in any of the principal views. (plane D) |
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An oblique plane is oblique to all principal planes of projection. An oblique surface does not appear in its true shape or size, or as a line in any of the principal views; instead, an oblique plane always appears foreshortened in any principal view. |
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MULTIVIEW REPRESENTATIONS |
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| 8.47 Multiview representations of common geometric shapes. A point represents a specific position in space and has no width, height, or depth. A point can represent: The end view of a line. |
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| 8.48 A plane surface will always be represented by an edge (line) or an area (surface). Areas that are the same feature will always be similar in configuration from one view to the next, unless viewed on edge. Parallel features will be parallel in all views. Surfaces that are parallel to the lines of sight will appear as edges (lines). |
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| 8.49 Angles are true size when they are in a normal plane. |
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| 8.50 Curved surfaces are used to round the ends of parts and to show drilled holes and cylindrical features. Only the far outside boundary, or limiting element, of a curved surface is represented in multiview drawings. |
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| 8.51-52 Rounded ends or partial cylinders are represented in the circular view by arcs and by rectangles in the adjacent views. If the cylinder is tangent no change of plane is shown, but if tangency does not exist then a line is used to represent the change of plane between the partial cylinder and the prism. |
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| 8.53-54 An ellipse is used to represent a hole or circular feature that is viewed at an angle other than perpendicular or parallel. |
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| 8.55A A through hole is a hole that goes all the way through an object, is represented in one view as two parallel hidden lines for the limiting elements, and is shown as a circle in the adjacent view. |
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| 8.55B A blind hole is a hole that is not drilled all the way through the object. |
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| 8.55C Counterbored holes are used to allow the heads of bolts to be flush or below the surface of the part. |
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| 8.55D Countersunk holes are commonly used for flathead screws, and are represented by 45 degree lines. |
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| 8.55E A spotface hole provides a place for heads of fasteners to rest by creating a smooth surface on cast parts. |
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| 8.55F The representation of a threaded hole is shown. In all hole representations a line must be drawn to represent the change that occurs between the large and small diameter. |
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| 8.56 A fillet is a rounded interior corner and a round is a rounded exterior corner normally found on a cast or forged part. |
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| 8.57 When a surface is to machined to a finish, a finish mark in the form of a v is drawn on the edge view of the surface to be machined. |
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| 8.58-59 Conventional practices used to represent fillets and rounds on multiview drawings. |
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| 8.60 A chamfer is a beveled corner used on the openings of holes and the ends of cylindrical parts, to eliminate sharp corners. |
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| 8.61-62 A runout is a special method of representing filleted surfaces that are tangent to cylinders. |
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| 8.63-64 If a right cylinder is cut at an acute angle to the axis, an ellipse is created. |
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| 8.65 Irregular or space curves are created by plotting points along the curve in one view, and then transferring or projecting the points into the adjacent views. |
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| 8.66 When two cylinders intersect, a line of intersection is formed. |
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| 8.67 When cylinders intersect prisms, large prisms are represented using true projection, while small prisms are not. |
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| 8.68 When cylinders intersect cylinders, large holes or slots are represented using true projection, while small holes and slots are not. |
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MULTIVIEW DRAWING VISUALIZATION |
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| 8.69 Visualization of multiview drawings by projection. |
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| 8.70 Visualization of multiview drawings by physical model construction. |
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| 8.71 Visualization of multiview drawings by decomposing the object into its basic geometric forms that create the object. |
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| 8.72-73 Adjacent areas are surfaces which reside next to each other. The boundary between the surfaces is represented as a line indicating a change in planes. No two adjacent areas can lie in the same plane and adjacent surfaces represent: Surfaces at different levels. |
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| 8.74 Similar-shaped surfaces retain their basic configuration or shape an all planer views. |
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| 8.75 When multiview drawings are created from a given pictorial view, surfaces can be labeled to check the accuracy of the solution. |
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| 8.76 Missing line problems can be used to develop visualization. |
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| 8.77 Vertices labeling can also be used to check the accuracy of multiview drawings. |
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| 8.78 Example of using the analysis by solids for the advancement of spatial abilities. |
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| 8.79-81 Example of using the analysis by surfaces for the advancement of spatial abilities. |
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| 8.82 No two contiguous areas can lie in the same plane. |
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ANSI STANDARDS FOR MULTIVIEW DRAWINGS |
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ANSI standards of multiview drawings form the common language used by engineers and technologists for communication information. |
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| 8.83 A partial view shows only what is necessary to completely describe the object. A conventional break line is placed in a location where it does not coincide with a visible or hidden line. |
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| 8.84 Partial views can be used to unnecessary geometry in a projection, including features which will primarily be shown in hidden lines and better seen in another view. |
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| 8.85 ANSI revolution conventions allow geometry to be revolved into positions that allow an object to be viewed true size and shape. |
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| 8.86 Objects can be revolved on bolt circles to eliminate hidden lines and improve visualization. |
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| 8.87 Inclined arms can also be revolved perpendicular to the line of sight to allow for better visualization of the object. |
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| 8.88 A removed view may have to be created that is at a different scale and thus cannot be aligned with the existing views. |
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SUMMARY |
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Multiview drawings are an important part of engineering and technical graphics. To create multiview drawings takes a high degree of visualization skill and much practice. Multiview drawings are created by closely following orthographic projection techniques and ANSI standards. |