AUXILIARY VIEWS C H A P T E R E I G H T

OBJECTIVES 1. Create an auxiliary view from orthographic views. 2. Draw folding lines or reference-plane lines between any two adjacent views. 3. Construct depth, height, or width auxiliary views. 4. Plot curves in auxiliary views. 5. Construct partial auxiliary views. 6. Create auxiliary section views. 7. Produce views to show the true length of a line, point view of a line, edge view of a surface, and true-size view of a surface. 8. Show the true size of the angle between two planes (dihedral angle). 9. Construct the development of prisms, pyramids, cylinders, and cones. 10. Use triangulation to transfer surface shapes to a development. 11. Create the development of transition pieces. 12. Graphically solve for the intersection of solids. 13. Apply revolution to show true-length edges and true-size surfaces.

UNDERSTANDING AUXILIARY VIEWS Auxiliary views are useful for both design and documentation. Many objects are shaped so that their principal faces are not parallel to the standard planes of projection. To show the true circular shapes, use a direction of sight perpendicular to the plane of the curve, to produce an Auxiliary View.

The Auxiliary Plane To show the inclined surface (P) true size, the direction of sight must be perpendicular to the inclined plane. The auxiliary plane in this case is perpendicular to the frontal plane of projection and hinged to it. It is angled to the horizontal (top) and profile (side) viewing planes.

Primary Auxiliary Views A primary auxiliary view is projected onto a plane that is perpendicular to one of the principal planes of projection and is inclined to the other two.

Depth Auxiliary Views All these views show the object’s depth and therefore are all depth auxiliary views.

Height Auxiliary Views The front view and all these auxiliary views show the height of the object. Therefore, all these auxiliary views are height auxiliary views.

Width Auxiliary Views The front view and all these auxiliary views are width auxiliary views.

Successive Auxiliary Views From a primary auxiliary view , a secondary auxiliary view can be drawn, then from it a third auxiliary view, and so on. Successive Auxiliary Views

Secondary Auxiliary Views A secondary auxiliary view is projected from a primary auxiliary view onto a plane that is inclined to all three principal projection planes. Second Auxiliary View, showing the True Size of the Top Oblique Surface

Reference Planes Instead of using one of the planes of projection, you can use a reference plane parallel to the plane of projection that touches or cuts through the object. If you are using 2D CAD, you can draw half of the view and then mirror the object.

USING TRIANGLES TO SKETCH AUXILIARY VIEWS You can use two triangles to quickly draw parallel and perpendicular lines for “accurate” sketches. • Place two triangles together so that the 90° corners are on the outside. • Slide them on your drawing until the outer edge of one triangle is along the line to which you want to sketch parallel. • Hold down the triangle and slide the other along it. • Draw parallel lines along one edge of the triangle. Draw perpendicular lines along the other edge.

USING GRID PAPER TO SKETCH AUXILIARY VIEWS You can use grid paper to help sketch auxiliary views by orienting the lines of the grid paper underneath your vellum or other semitransparent drawing sheet so that the grid is parallel to the inclined edge in the drawing…

USING CAD TO CREATE AUXILIARY VIEWS Most CAD systems allow you to rotate the grid or to create a new coordinate system (often called the user coordinate system) so that it aligns with the inclined surface. If you are using 3D CAD, you can create true-size auxiliary views by viewing the object perpendicular to the surface you want to show true size.

CIRCLES AND ELLIPSES IN AUXILIARY VIEWS Circular shapes appear elliptical when viewed at an angle other than 90° (straight on to the circular shape). This is frequently the case when constructing auxiliary views.

HIDDEN LINES IN AUXILIARY VIEWS Generally, hidden lines should be omitted in auxiliary views, unless they are needed to clearly communicate the drawing’s intent. Your instructor may ask you to show all hidden lines for visualization practice, especially if the auxiliary view of the entire object is shown. Later, when you are familiar with drawing auxiliary views, omit hidden lines when they do not add needed information to the drawing.

REVERSE CONSTRUCTION To complete the regular views, it is often necessary to first construct an auxiliary view where critical dimensions will be shown true size.

PARTIAL AUXILIARY VIEWS Using an auxiliary view often makes it possible to omit one or more regular views, but auxiliary drawings are time consuming to create and may even be confusing because of the clutter of lines. Partial views are often sufficient and easier to read.

AUXILIARY SECTIONS An auxiliary section is simply an auxiliary view in section. Note the cutting-plane line and the terminating arrows that indicate the direction of sight for the auxiliary section. In an auxiliary section drawing, the entire portion of the object behind the cutting plane may be shown, or the cut surface alone may be shown.

VIEWING-PLANE LINES AND ARROWS When the drawing sheet is too crowded to show the auxiliary view in direction projection you can use a viewing-plane line or a viewing direction arrow to indicate the direction of sight for the auxiliary view.

TRUE LENGTH OF A LINE To show a line true length, make the fold line parallel to the line you want to show true length in the auxiliary view. Whenever a line is parallel to the fold line between two views, it will be true length in the adjacent view.

POINT VIEW OF A LINE To show the point view of a line, choose the direction of sight parallel to the line where it is true length. 1. Choose the direction of sight to be parallel to line 1–2. 2. Draw folding line H/F between the top and front views, as shown. 3. Draw folding line F/1 perpendicular to line 1–2 where it is true length, and any convenient distance from line 1–2 (front view). 4. Draw projection lines from points 1 and 2 to begin creating the auxiliary view. 5. Transfer points 1 and 2 to the auxiliary view at the same distance from the folding line as they are in the top view and along their respective projection lines. They will line up exactly with each other to form a point view of the line.

EDGE VIEW OF A PLANE To show the edge view of a plane, choose the direction of sight parallel to a true-length line lying in the plane. 1. Choose the direction of sight to be parallel to line 1–2 in the front view where it is already shown true length. 2. Draw folding line H/F between the top and front views, as shown. 3. Draw folding line F/1 perpendicular to true-length line 1–2 and any convenient distance. 4. Draw projection lines from points 1, 2, 3, and 4 to begin creating the auxiliary view. 5. Transfer points 1, 2, 3, and 4 to the auxiliary view at the same distance from the folding line as they are in the top view and along their respective projection lines. Plane 1–2–3–4 will appear on edge in the finished drawing.

TRUE SIZE OF AN OBLIQUE SURFACE Showing the true size of a surface continues from the method presented for showing inclined surfaces true size, where the edge view is already given. But to show an oblique surface true size, you need first to show the oblique surface on edge and then construct a second auxiliary view to show it true size.

DIHEDRAL ANGLES The angle between two planes is called a dihedral angle. Auxiliary views often need to be drawn to show dihedral angles true size, mainly for dimensioning purposes.

DEVELOPMENTS AND INTERSECTIONS A development is a flat representation or pattern that when folded together creates a 3D object.

Revolved and Extruded Solids A solid generated by revolving a plane figure about an axis in the plane of the figure is a revolved solid.

Developable Surfaces A developable surface may be unfolded or unrolled to lie flat. Surfaces composed of single-curved surfaces, of planes, or of combinations of these types are developable.

DEVELOPMENTS The development of a surface is that surface laid out on a plane. Practical applications of developments occur in sheet metal work, stone cutting, pattern making, packaging, and package design. (Courtesy of Kessler Brewing Co.)

HEMS AND JOINTS FOR SHEET METAL AND OTHER MATERIALS Hems are used to eliminate the raw edge as well as to stiffen the material. You must add material for hems and joints to the layout or development. The amount you add depends on the thickness of the material and the production equipment.

TRIANGULATION Triangulation is simply a method of dividing a surface into a number of triangles and transferring them to the development. To find the development of an oblique cone by triangulation, divide the base of the cone in the top view into any number of equal parts and draw an element at each division point. Development of an Oblique Cone by Triangulation

DEVELOPING A SPHERE The surface of a sphere is double curved and is not developable, but it may be developed approximately by dividing it into a series of zones and substituting a portion of a right circular cone for each zone.

AXIS OF REVOLUTION Revolution, like auxiliary view projection, is a method of determining the true length and true size of inclined and oblique lines and planes. The axis of revolution appears as a point in this view. The object revolves but does not change shape in this view. In the adjacent views in which the axis of revolution, if it were drawn, would show as a line in true length, the dimensions of the object that are parallel to the axis of revolution do not change.