plane (top and bottom views) and in the views onthe profile plane (right and left side views), theline appears foreshortened. Note, however, thatyou don’t need to calculate the amount of theforeshortening, since it works itself out as youproject the various views.CIRCLES IN MULTI-VIEW ORTHO-GRAPHIC PROJECTION.— A circle on asurface that is parallel to the plane of projectionwill project as a circle. A circle on a surface thatis oblique to the plane of projection, however, willproject as an ellipse, as shown in figure 5-21. Theupper view in this figure is a top view of a wedge,the wedge having a hole bored through itperpendicular to the inclined face. The outline ofthis hole on the front face of the wedge projectsas an ellipse in the front view. You get the minoraxis of the ellipse by projecting downward asshown. The length of the major axis is equal tothe diameter of the hole.Another ellipse is shown in the front view.This is the partly hidden and partly visible outlineof the hole as it emerges through the back of thewedge. The back of the wedge is parallel to thefront view plane of projection; therefore, thisellipse is the true outline of the hole on the backof the wedge. The outline is elliptical because thehole, though it is circular, is bored obliquely tothe back face of the wedge.To draw these ellipses, you could use anyof the methods of drawing an accurate ellipseexplained in the previous chapter on geometricconstruction,or you could use an ellipsetemplate.AUXILIARY VIEWS.— In theory, thereare only three regular planes of projection:the vertical, the horizonal, and the profile.Actually, it is presumed that each of these is, asit were, double; there is, for example, onevertical plane for a front view and another fora back view.We assume, then, a total of six regular planesof projection. A projection on any one of the sixis a regular view. A projection NOT on one ofthe regular six is an AUXILIARY VIEW.The basic rule of dimensioning requires thata line be dimensioned only in the view in whichits true length is projected and that a plane withits details be dimensioned only in the view inwhich its true shape is represented. To satisfy thisrule, we have to create an imaginary plane thatis parallel with the line or surface we want toproject in its true shape. A plane of this kindthat is not one of the regular planes is called anAUXILIARY PLANE.In the upper left of figure 5-22, there is asingle-view projection of a triangular block,the base of which is a rectangle. This block ispresumed to be placed for multi-view projectionFigure 5-22.-A line oblique to all planes of projection is foreshortened in all views.5-13
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