CHAPTER 6 Multiviews and Auxiliary ViewsINTRODUCTION 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 (LOS), and plane of projection.
6.1Projection methods are developed along two lines: perspective and parallel. Projection theory comprises the principles used to represent graphically 3-D objects and structures on 2-D media. |
6.3Drawing 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. |
6.4In 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. |
6.5-6In 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. |
MULTIVIEW PROJECTION PLANES |
6.7Orthographic 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. 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. |
6.8The 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. |
6.9The top view of an object shows the width and depth dimensions. The top view is projected onto the horizontal plane of projection. |
6.10The side or profile 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. |
6.11The 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. |
ADVANTAGES OF MULTIVIEW DRAWINGS |
6.12-15The advantage of multiview drawings over pictorial drawings is that multiview drawings shows the true size and shape of the various features of the object, whereas pictorials distort true dimensions which are critical in manufacturing and construction. |
6.163-D graphical data base used in CNC machining. |
6.17-18There are six principal mutually perpendicular views projected onto three mutually perpendicular projection planes. these views are the top, front, right, left, bottom and back. |
6.19The 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. |
6.20The arrangement of views may vary as long as the dimension alignment is correct. |
6.21AThird angle projection is the standard projection for the United States and Canada. The ANSI third angle icon is shown. |
6.21BFirst angle projection is the standard in Europe and Asia. The ANSI first angle icon is shown. |
6.22-24The difference between first and third angle projection is the placement of the object and the projection plane. |
6.25Adjacent 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. |
6.26-27Hidden features are represented by dashed lines. Some examples include: Holes - to locate the limiting elements. Surfaces - to locate the edge view of the surface. Change of planes - to locate the position of the change of plane or corner. |
6.28Center lines are alternate long and short thin dashes and are used for the axes of symmetrical parts and features, such as cylinders and drilled holes. |
6.29Center line usage follows standard drawing practices: Center lines for holes and slots locate limiting elements and any changes in planes. Center lines should not terminate at another line or extend between views. Very short, unbroken center lines may be used to represent the axes of very small holes. Center lines can indicate radial symmetry. Center lines do not break when they cross another line at or near 90 degrees. Center lines can be used as paths of motion. |
CREATING MULTIVIEW SKETCHES |
6.30Some objects can be adequately described with only one view. |
6.31Cylindrical, and conical objects can often be described with two views |
6.32-3Two-view sketches are created by blocking in details, then adding centerlines, circles, arcs, and hidden lines. |
6.34Creating three view drawings by traditional methods. |
6.35-8Creating a three view drawing using CAD methods. |
VIEW SELECTIONBefore a multiview drawing can be created four basic decisions must be made: |
6.39-40Determine the best position of the object and select the views that will show the least amount of hidden features. |
6.41Determine the front view which should show the object in its natural view or assembled state, such as the front view of a car. |
6.42Determine the minimum number of views needed to describe the object. |
6.43Once the front view is selected, determine the other views needed to describe the object with the fewest number of lines. |
6.44An edge, or corner, is the intersection of two planes, and is represented as a line on a multiview drawing. A normal edge, 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. |
6.45An oblique edge or line, is not parallel to any principal plane of projection; therefore it never appears as a point or in true length in any of the six principal views. |
6.46A normal or principal plane is parallel to one of the principal planes of projection, and therefore is perpendicular to the line of sight. 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) 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) 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) A 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) 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. |
MULTIVIEW REPRESENTATIONS |
6.47Multiview 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. The intersection of two lines. A specific position in space. |
6.48A plane surface will always be represented by as 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). |
6.49Angles are true size when they are in a normal plane. |
6.50Curved 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. |
6.51-52Rounded 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. |
6.53-54An ellipse is used to represent a hole or circular feature that is viewed at an angle other than perpendicular or parallel. |
6.55Holes follow standards and conventions of representation: 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. A blind hole is a hole that is not drilled all the way through the object. Counterbored holes are used to allow the heads of bolts to be flush or below the surface of the part. Countersunk holes are commonly used for flathead screws, and are represented by 45 degree lines. A spotface hole provides a place for heads of fasteners to rest by creating a smooth surface on cast parts. 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. |
FILLETS, ROUNDS, FINISHED SURFACES AND CHAMFERS |
6.56-7A fillet is a rounded interior corner and a round is a rounded exterior corner normally found on a cast or forged part. 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. |
6.58Conventional practices used to represent fillets and rounds on multiview drawings. |
6.59Finish mark symbols differ according to the drawing standards being followed. |
6.60A chamfer is a beveled corner used on the openings of holes and the ends of cylindrical parts, to eliminate sharp corners. |
6.61-62A runout is a special method of representing filleted surfaces that are tangent to cylinders. Notice that the end of the curve terminates at the point of tangency. |
ELLIPTICAL, IRREGULAR CURVES, AND INTERSECTING CYLINDERS |
6.63-64If a right cylinder is cut at an acute angle to the axis, an ellipse is created. |
6.65Irregular 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. |
6.66When two cylinders intersect a line of intersection is formed. This line can be straight, curved, or form a ‘V’ depending on the ratio of diameters of the two cylinders When cylinders intersect prisms, the point of intersection is represented by a line except when the width of the prism is equal to the diameter of the cylinder. When cylinders intersect cylinders, large holes or slots are represented using true projection, while small holes and slots are not. |
MULTIVIEW DRAWINGS VISUALIZATION |
6.67Styrofoam or clay can be used to make real models of objects you've drawn multiviews of. One technique that will improve multiview drawing visualization skills is the study of completed multiview drawings of various simple objects. |
6.68Visualization of multiview drawings by decomposing the object into its basic geometric forms that create the object. |
6.69-70Adjacent 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.
Inclined surfaces.
Cylindrical surfaces
A combination of the above. |
6.71Similar-shaped surfaces retain their basic configuration or shape an all planer views. |
6.72When multiview drawings are created from a given pictorial view, surfaces can be labeled to check the accuracy of the solution. |
6.73Missing line problems can be used to develop visualization. |
6.74Vertices labeling can also be used to check the accuracy of multiview drawings. |
6.75Example of using the analysis by solids for the advancement of spatial abilities. |
6.76-8Example of using the analysis by surfaces for the advancement of spatial abilities. |
6.79No two contiguous areas can lie in the same plane. |
ANSI STANDARDS FOR MULTIVIEW DRAWINGSANSI standards of multiview drawings form the common language used by engineers and technologists for communication information. |
6.80A 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. |
6.81Partial views can be used to clarify a drawing by removing unnecesary features (usually shown with hidden lines). |
6.82ANSI revolution conventions allow geometry to be revolved into positions that allow an object to be viewed true size and shape. |
6.83Objects can be revolved on bolt circles. |
6.84Inclined arms can also be revolved perpendicular to the line of sight to allow for better visualization of the object. |
6.85A removed view may have to be created that is at a different scale and thus cannot be aligned with the existing views. |
AUXILIARY VIEW PROJECTIONSThere are times when one of the six principal views will not completely describe an object. This is especially true when there are inclined or oblique planes or features on an object. For these cases, a special orthographic view called an auxiliary view can be created. |
6.86An auxiliary view is an orthographic view which is projected onto any plane other than the frontal, horizontal, or profile plane. An auxiliary view is not one of the six principal views. To show the true size and shape of surface ABCD an auxiliary view can be created by positioning a line of sight perpendicular to the inclined plane, then constructing the new view. In fold-line method, the object is suspended in a glass box to show the six principal views, created by projecting the object onto the planes of the box. The box is then unfolded, resulting in the six principal views. However, when the six views are created, surface ABCD never appears true size and shape; it always appears either foreshortened or on edge. |
6.87-8The object suspended inside a glass box, which has a special or auxiliary plane that is parallel to inclined surface ABCD. The line of sight required to create the auxiliary view is perpendicular to the new projection plane and to surface ABCD. |
6.89The auxiliary glass box is unfolded with the fold lines between the views shown as phantom lines. In the auxiliary view, surface ABCD is shown true size and shape and is located at distance M from the fold line. The line AB in the top view is also located at distance M from its fold line. |
6.90Changing the position of the object, such as moving it closer to the frontal plane, changes distance M, the distance from the nearest edge of the object to the fold line. |
6.91The reference plane method is a technique that locates a plane relative to the object instead of suspending the object in a glass box. When using reference planes or fold lines always remember the following: Reference or fold lines are always drawn perpendicular to the projection lines between the views. Transfer measurements are always taken parallel to the projection lines and perpendicular to the reference or fold lines. Reference planes always appear on edge as a line in the views adjacent to the central view but never in two adjacent views. Distances from the object to the reference or fold lines in the auxiliary view and the measuring view are the same. |
AUXILIARY VIEW CLASSIFICATIONS |
6.92Auxiliary views are created by positioning a new line of sight relative to the object. It is possible to create any number of auxiliary views, including a new auxiliary view from an existing auxiliary view. Therefore, auxiliary views are first classified as: primary, secondary, or tertiary. A primary auxiliary view is a single view projected from one of the six principal views. A secondary auxiliary view is a single view projected from a primary auxiliary view. A tertiary auxiliary view is a single view projected from a secondary or another tertiary auxiliary view. |
|
2002 McGraw-Hill Higher Education