Chapter OutlineINTRODUCTION Pictorial sketches are a type of technical illustration that shows several faces of an object at once. Such sketches are used by any industry that designs, sells, manufactures repairs, installs or maintains a product. Axonometric and oblique pictorial sketches use a parallel projection technique and are frequently used in technical documents, sales literature, maintenance manuals, and documentation supplements in engineering drawings. Perspective sketches are the most realistic types of drawings used in engineering and technology. A perspective drawing creates a pictorial view of an object that resembles what you see. It is the best method for representing an object in three dimensions. This chapter goes into the details necessary for creating perspective sketches.
7.1The Greek word axon means axis and metric means to measure. Axonometric projection is a parallel projection technique used to create pictorial drawings of objects by rotating the object on an axis relative to a projection plane to create a pictorial view. |
7.2One of four principle projection techniques is used in technical drawing: Multiview Axonometric Oblique Perspective In multiview, axonometric, and oblique projection the observer is theoretically infinitely far away from the projection plane. Only in perspective projection is the viewer at some finite distance to the object. The differences between a multiview drawing and an axonometric drawing are that, in a multiview, only two dimensions of an object are visible in each view and more than one view is required to define the object; whereas, in an axonometric drawing, the object is rotated about an axis to display all three dimensions, and only one view is required. |
7.3Axonometric drawings are classified by the angles between the lines comprising the axonometric axes. When all three angles are unequal the drawing is classified as a trimetric. When two of the three angles are equal the drawing is classified as a dimetric. When all three angles are equal the drawing is classified as a isometric. |
7.4Although there are an infinite number of positions that can be used to create such a drawing only are few are used. |
ISOMETRIC AXONOMETRIC PROJECTIONS |
7.5An isometric view of an object is created by rotating it 45 degrees about a vertical axis, then tilted forward until the body diagonal of the cube (A-B) appears as a point in the front view. The angle the cube is titled forward is 35 degrees 16 minutes. The three corners meet to form equal angles of 120 degrees and is called the isometric axis. All the edges of the cube are parallel to the edges that make up the isometric axis since projections of parallel lines are parallel. Any line that is parallel to one of the legs of the isometric axis is called an isometric line. The planes of the faces of the cube and all planes parallel to them are called isometric planes. |
7.6The forward tilt of the cube causes the edges and planes of the cube to become foreshortened as it is projected onto the picture plane. Thus the projected lengths are approximately 80% of the true lengths and an isometric projection ruler must be used. If the drawing is drawn at full scale it is called an isometric drawing. Isometric drawings are almost always preferred over isometric projection for engineering drawings, because they are easier to produce. |
7.7The development of an isometric scale produced on paper using a regular scale. |
7.8Size comparison of isometric drawing and true isometric projection. |
ISOMETRIC AXONOMETRIC DRAWINGS |
7.9Isometric axes can be positioned in a number of different ways to create different views of the same object. Regular isometric is developed looking down on the top of the object. Reversed axis isometric is developed by looking up on the bottom of the object. Long axis isometric is developed by looking from the right with one axis drawn at 60 degrees to the horizontal. |
7.10Any line that runs parallel to any of the isometric axes is called an isometric line. Any line that does not run parallel to an isometric axes is called a non-isometric line. Non-isometric lines are inclined and oblique object lines that cannot be measured directly when creating an isometric drawing but are must be created by locating two endpoints. |
7.11A cube represented in an isometric drawing. The three faces on the isometric cube are called isometric planes. Isometric planes are surfaces which are parallel to the isometric surfaces formed by any two adjacent isometric axes. |
7.12Planes which are not parallel to any isometric plane are called non-isometric planes. |
7.13In isometric drawings hidden lines are omitted unless absolutely necessary to completely describe the object. Normally, most isometric drawings will not have any hidden lines. You can avoid using hidden lines if the most descriptive viewpoint is chosen. However, there are times when the object has some features which cannot be described no matter which isometric viewpoint is taken. |
7.14In isometric drawings center lines are drawn if symmetry must be shown or for dimensioning. Normally, center lines are not used on isometric drawings. |
7.15Dimensioned isometric drawings used for production purposes must be ANSI standard, with dimension and extension lines and lines to be dimensioned lying in the same plane. |
7.16Dimensioned drawings used for illustration purposes may use the aligned method. |
7.17Creating a isometric drawing. |
7.18Circles that lie on any face of an isometric cube will appear as ellipses. |
7.19Sketching an isometric ellipse. |
7.20Sketching an isometric cylinder. |
7.21Since arcs are partial circles, they appear in isometric drawings as partial isometric ellipses. |
7.22Isometric sketches of common objects. |
7.23Constructing an isometric sketch having an oblique surface. |
7.24To draw an angle in an isometric drawing, locate the endpoints of the lines that form the angle and draw the lines between the endpoints. |
7.25Irregular curves are drawn in isometric by constructing points along the curve in the multiview drawing which are then located in the isometric view. These points are then connected with an irregular curve drawing instrument. |
7.26-7Drawing isometric ellipses using an isometric ellipse template. Make sure that the template is a true isometric template. That is, it has an exposure angle of 35 degrees 16 minutes. |
7.28-30Section views in isometric sketches. |
7.313-D models projected as an isometric drawing. |
7.32Isometric assembly drawings used for production purposes normally have circles, called balloons, that contain numbers and are attached to leader lines, point to the various parts. |
OBLIQUE PROJECTION AND SKETCHINGOblique drawings are a form of pictorial drawings in which the most descriptive or natural front view is placed parallel to the plane of projection. |
7.33Oblique projection is used as the basis for both oblique drawing and oblique sketching. However, oblique projection and to a large extent oblique drawing, is not as commonly used as other types of pictorials because of the excessive distortion that occurs. Because of its simplicity, many times oblique sketches are used to communicate ideas. Oblique projection is a unique form of parallel projection. As the name indicates, oblique projection results when the projectors are parallel to each other but at some angle other than perpendicular to the projection plane. If the principal view of the object is placed such that its surfaces are parallel to the projection plane, the resulting projection is an oblique pictorial. Historically, the most descriptive face of an object in oblique projection has been placed parallel to the frontal plane. |
7.34The actual angles that the projectors make with the plane of projection in oblique projection is not significant, thus different angles can be used. However, angles for receding edges of between 30° and 60° are preferable because they offer minimum distortion of the object. |
7.35-6A comparison of orthographic projection and oblique projection. |
7.37Types of oblique drawings: The cavalier oblique is drawn true length along the receding axis. The cabinet oblique is drawn half the true length along the receding axis. The general oblique can be drawn anywhere from full to half length along the receding axis. |
7.38The half-size receding axis on the cabinet oblique reduces the amount of distortion. |
7.39The various angles for a cavalier oblique drawing. |
7.40Any face of an object that is placed parallel to the frontal plane in oblique projection will be drawn true size and shape. Thus, the first rule in creating an oblique drawing is to develop the drawing so that cylinders or irregular surfaces are placed parallel to the frontal plane. This allows these features to be drawn quicker and without distortion. |
7.41A second rule in developing oblique drawings is that the longest dimension of an object should be located parallel to the frontal plane. |
7.42If there is conflict between these two rules always draw the cylindrical or irregular surfaces parallel with the frontal plane because representing this geometry without distortion is more advantageous. |
7.43-4Constructing an oblique sketch using the box technique. |
7.45Perspective drawing techniques are used primarily because they come the closest to representing objects and scenes as we would view them in the real world. One of the most important features of perspective drawings is the convergence of parallel edges as they recede from the viewer. |
7.46-7Note that perspective drawing techniques were not developed until the 14th and 15th centuries in Europe. The earliest techniques, developed by artists such as Albrecht Durer, used projection frames to assist in the accurate recreation of what they saw with their eyes. Exercise 7.1 gives an example of how you can use clear plastic as a plane of projection and capture a perspective view. |
PERSPECTIVE PROJECTION TERMINOLOGY |
7.48Terminology will be important for both explaining perspective drawing techniques and laying them out. Important terms include: The horizon line is the position that represents the eye level of the observer. The station point in the perspective drawing is the eye of the observer. The picture plane is the plane upon which the object is projected. A vanishing point is the position on the horizon where lines of projection converge. The ground line represents the plane on which the object rests. |
7.49Changing the object's position relative to the picture plane determines the size of the object. |
7.50Changing the vertical alignment of the alignment of the vanishing point an the object controls the direction of the lines of convergence. |
7.51Tracing the line of convergence in a photograph or rendered image can be used to find the vanishing point. |
7.52The figure demonstrates how the relationship between the horizon line (HL) and ground line (GL) determines the type of perspective view: Bird's eye view: ground line below the horizon line. Human's eye view: ground line six feet below the horizon line. Ground's eye view: ground line at the same level as the horizon line. Worm's eye view: ground line above the horizon line. |
PERSPECTIVE PROJECTION CLASSIFICATIONS |
7.53Perspective views are classified according to the number of vanishing points. Increasing the number of vanishing points increases the realism of the drawing but also increases the drawing difficulty. The vanishing points for a one- and two-point perspective drawings both go to the horizon line. The third vanishing point in a three-point perspective drawing is located perpendicular to the horizon line. |
PERSPECTIVE PROJECTION VARIABLES SELECTION |
7.54Emphasize the importance of planning ahead for a drawing by deciding on a number of key variables. Since the primary purpose of a perspective drawing is to convey a sense of realism, it is important to define the relationship of the observer to the object. The important variables are: Distance of the object from the picture plane Position for the station point Position of the ground line relative to the horizon line Number of vanishing points For example, the depiction of a toaster would probably have the object fairly close to the picture plane with the observer looking either straight ahead or slightly down at it (i.e. human's eye or bird's eye view). On the other hand, a large building would be farther away using either a worm's eye or ground's eye view, depending on how far the building is from the observer. |
7.55-7As 3-D CAD becomes more popular, perspective pictorials drawn by hand will largely be replaced by ones created from the model on computer. Where hand - constructed perspective pictorials will still be applicable is when a pictorial sketch needs to depict some convergence - usually a larger object such as a building. Just as with a hand-drawn perspective, defining the relationship between the viewer and the object is critical to a the creation of a successful pictorial. With most 3-D CAD systems, a viewpoint can be established anywhere with any cone of vision. The key is to set these variables so that the necessary geometric information is most clearly communicated to the viewer. |
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2002 McGraw-Hill Higher Education