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| Drafting Fundamentals The aim of this article is to describe drafting so that a student, after they have become familiar with the following, will understand the principles that are applied to mechanical and architectural drawings. This article is written with the hope that it would be helpful to drafting students who have not had the time to take our more involved courses here at the Drafting Course Access Board. Though we try to present most of the principles of drafting, it's not a graded course, all though if you want, a more advanced course can be found here at our school. Instrumental drawing is the art of representing the different parts of any model or machine as seen completed using a drafting board or a CAD program. In looking at any model or part of any machine, all the visual rays have to be considered as perpendicular to the paper that the drawing is placed on. So, the common expression that the projection of any point in space upon any plane is always at the foot of a perpendicular drawn from the point to the plane (which plane is the drawing paper or computer screen). It's customary to draw a line separating the top view or plan from the front view or elevation. (See Figure 1.) That line is called the "intersecting line."
(Plate 1, Figure 1.) Figure 1 represents the paper bent at right angles, to represent the two planes that the drawings are supposed to be made, and which the perpendicular projecting lines are illustrated, by projecting the planes of a rectangular solid, seen first in end view on Figure 1. The horizontal plane is then rotated around the top of the vertical plane until the two coincide, as shown, and also the projection already made on the horizontal plane has to rotate with it. Figure 2 shows the length of the imaginary planes upon which are to be shown the length of the solid. The two views, top and front, may be placed anywhere to the right or left, upon the planes, but they must be placed directly over or under each other. Here we may make another positive statement — that the two views or projections of the same point must be in one perpendicular to the intersecting line. Figure 3 is a pictorial diagram whereon the three dimensions of the solid are shown, as well as its two projections — top view and front view — and the three figures. Figures 1, 2 and 3, when looking in the direction of the arrows, show exactly the location of the object projected upon them, i. e., the distance down from the top plane and the distance back of the front plane. These planes may be considered transparent, because they are interposed between the draftsman and the object. Having introduced the subject from a simple standpoint, we may consider the planes as unlimited in dimensions, and for all future drawings draw a single line only on the paper merely to separate the top view from the front view, already referred to as the intersecting line.
It needs tot be understood that this kind of drawing is a science of factual representation, and not a science of appearance, Therefore it will readily be seen that more than one view of an object will have to be given. On page 9 a number of elevations or front views are given which all appear exactly alike, altho the top views or plans of those objects show they are widely different from each other.
Plate 2 shows the two top views and two front views of a triangular block or prism. Figure S shows two views of the prism when its long edges are parallel to both the horizontal and the vertical planes. Figures 6 and 7 show an end view of the prism when the long edges are at right angles to the plane upon which the end views are shown. ( Dotted lines represent invisible edges that cannot be seen from the position of the draftsman, i. e.% the lower edge in the top view is shown dotted, hence invisible in that view.) A flat tint of lines is shown upon the prism to call attention to that particular part of the prism. Figure 8 shows a front view or elevation, also the top view of a similar solid, when its long edges are still parallel to the vertical plane; hence the two elevations, Figures 5 and 8 are exactly the same shape, the top view or plan in Figure 8 only changing in appearance. Why? Because its long edges are no longer parallel to the horizontal planes. Its short edges are projected on the horizontal plane the same length in both the top views. Figures 5 and 8. Why? Because they still remain parallel to the horizontal plane.
Plate 3. Figure 9 shows the top and front views of a similar block or prism, differing only in position, the long edges still being parallel to the horizontal plane, but making 30 degrees with the vertical plane. In the front view or elevation of this solid the altitude of the triangle still remains parallel to the vertical plane, and is seen its true length. Figure 10 shows the front view and the top view of a similar prism as that of Figure 9 with this difference, that its long edges are no longer parallel to the horizontal plane but make angles of 30 degrees (in projection) with the horizontal plane, hence to show the top view in that position move the elevation e to / and by drawing vertical projecting lines from / to intersect the horizontal projecting lines drawn from the top view of Figure 9 we shall obtain the new top view J' The flat tint of lines are drawn upon the same ends of the prism in its various positions merely to call particular attention to that end. (They are not section lines.) Having completed the top view /' all its edges now make angles with both the horizontal and the vertical plane. ( Note.—All lines or edges making angles with the vertical plane, must first be shown upon the horizontal.) (Also all lines or edges making angles with the horizontal plane must first be shown upon the vertical.)
Plate 4. Figures 11, 12 and 13 show the top and front views of three square pyramids. In the preceding figures we have dealt only with the exterior part of those figures; now we are to deal with the interior parts, or sections of the figures. In Figure 11 a horizontal section has been cut — one that is parallel to the base. In Figure 12 a vertical section has been cut — one that is at right angles to the base. In Figure 13 an oblique section has been cut — one that makes an angle with the base. (Note.— All sections or parts of a figure that are cut, are represented by cross or section lines, or it may be represented by a dot and dash line which bounds the section.)
Plate 5. Figure 14 shows the top and front views of a cylinder; also two views of a single line (a b) drawn across the cylinder at random. By the application of sections we are to find how much of the line (a' V) is contained within the cylinder. If we imagine the cylinder cut by a vertical plane, lying in the same plane as the line, the elevation of this vertical plane will be a rectangle (a, b, c, d) and will show where the line enters one side of the rectangle in point x, and where the line leaves it in point y. Figure 15 shows the front and top views of a cone, also two views of a line {a b) passing through the cone parallel to the base, hence parallel to the horizontal plane, and making an angle with the vertical plane, as shown. By taking a horizontal section in the same plane as the line, the top view of the section is a circle, and the line cuts the circle at x and_y, showing how much of the line is contained in the cone.
Plate 6. Figure 16 shows the top and front views of a sphere, that is intersected by a horizontal plane (a, b, c, d) of given dimensions, as shown. The top view shows that the edge (d, c,) cuts the sphere in front of the center; the edge (a, b) extends in front of and outside of the sphere. Problem: To find the line of intersection between this plane and the sphere: Cut a horizontal section through the sphere, which contains the plane (a, b, c, d). The plan or top view is represented by a circle, which necessarily is in the same plane as the plane (a, b, c, d) and shows the line of intersection, which is a curved line marked (x, y, s). Figure 17 shows two views of a square pyramid intersected by a vertical plane, whose angles or corners are marked 1, 2, 3, 4. To find the lines of intersection between the pyramid and this plane, cut a vertical section through the pyramid, that will contain the plane 1, 2, 3, 4. The front view of this vertical section is marked by points a, b, c, d. The edges of the vertical plane a, b, c, d intersect the plane 1, 2, 3 and 4 in points 1', 2', 3' and 4'. (Note.—A straight line is projected upon a plane by projecting its two ends. A curved line is projected upon a plane by projecting a series of points assumed in the curved line. The view first called for in the text must be drawn first.)
Plate 7. Figure 18 shows the front and top views of a cone, when the base of the cone makes an angle of 45 degrees with h, and its axis is parallel to v (its base is necessarily at right angles to v, and is marked by points 1 and 7). In order to complete the top view of the cone, it is necessary to assume other points in its circular base. Locate a point (x^) in the centre between points 1 and 7, using this point as a centre, describe a semi-circle, which represents half of the base parallel to v. Upon this semi-circle assume other points equidistant apart and marked 2, 3, 4, 5 and 6, as shown. Project these points into the line 1 and 7, which represents the edge view of the base of the cone, and mark them 2', 3', 4', 5' and 6'. It is now necessary to locate these points in the horizontal projection. To do this locate the axis x, x", as shown; using x' as a centre, describe a semi-circle parallel to h, whose diameter equals line 1-7. Upon this semi-circle locate points 1, 2, 3, 4, 5 and 6, as in vertical projection. To complete the elliptical view of the base, draw horizontal projection lines from these points in the semi-circle to intersect vertical projection lines from the same points in the edge view of the base. By drawing tangents from x to the elliptical base the top view of the cone is completed. In the next view, Figure 19, the same cone is shown when its axis is not parallel to either plane. Hence we must change the position of the top view (which shows that the axis is parallel to v) and place it in the desired position, say 45 degrees. Draw a line at 45 degrees with the intersecting line and mark a part of this line x and x'. Pick up by tracing paper, or any other method, the top view, T, and place it so that its axis coincides with x and x1 in the new position. We may refer to the first elevation as E, and the plan on top view as T. We have changed T to V in the second position and now by drawing vertical projection lines from the points in T to intersect horizontal projection lines from the same points in E we obtain the new elevation E', in which the axis and the base make angles with both planes.
Plate 8. Figure 20 shows the development of the cone. If a cylinder made of paper be taken and cut lengthwise on some line parallel to its axis and then unfolded, the surface will form a rectangle whose height equals the height of the cylinder, and whose length equals the circumference of the cylinder. Assume any point x as a centre, and with a radius equal to one side of the cone, describe an arc whose length is equal to the circumference of the base. In the previous figure we have divided the base into twelve equal divisions. If we lay off these twelve divisions upon this arc, and join the two end ones to point x, we have the developed surface of the cone. The base, which is a circular plane, may be made tangent to the curve at any point. Review. The importance of the preceding elementary work can hardly be overestimated, as it takes in all the principles in the drawing and projecting of different models, their exterior and interior, straight and curved lines, and some development. No more difficult problem can be given than to draw a model whose edges and surfaces make angles with both the planes. Figures 24, 25, 26 and 27 show a further application of these principles in the intersection of solids, and apply especially to machine and architectural drawing.
Plate 9. Figure 21 shows a front and top view of one end of a connecting rod. The shape of the end, or butt as it is usually called, is found by placing a piece of rectangular stock in a lathe and turning one end of it cylindrical. The line of connection between the cylindrical and the rectangular parts will be curved, and it is called the line of intersection. In the top view this line appears to be straight and it is emphasized by a heavy line. The problem is to find the front view of this curved line, which is done by making imaginary horizontal sections intersecting both the circular and the rectangular parts, which necessarily gives points and lines upon the exterior surfaces of both (and applies the principles employed in Figures 16 and 17 ). If a horizontal section were taken on the line a am front view its true shape would be a circle. If another similar section were taken on line x x its true shape would be rectangular. If other horizontal sections were taken through the front view and marked b, c, and d and the top view of those were drawn, their true shapes would be partially circular and partially rectangular. Suppose we draw the top view of circle b first, with a radius tangential to the emphasized line, then in the edge view of circle b will be found b', which will be the highest point in the curve in front view. The top view of circle c, c", <f" may now be drawn, passing through the four corners of the rectangle and marked c, <?, c", <f". Now by locating those points in the edge view of the same circle we shall have the four lowest points in the curve in the front view. The section d may now be taken anywhere between the highest point b and the lowest points c, <f, c", c"', thus locating the two points d' and d". If a smooth curve now be drawn through the points V, d' and <f we shall have the front view of the curve. Figure 22 shows two more views of the same butt end and is marked in a similar manner. The flat tint of lines shown upon the front view merely call attention to the flat surface. (They are not section lines.) Figure 23 is a similar rod end with this difference, that it is composed of square and circular stock. The method of finding the curve of intersection would be similar to that of Figures 21 and 22. The dimensions of the cylindrical part and the radius of the curve in the neck would be given to the machinist.
Plate 10. Figure 24 shows the application of the principles of projection by a complete drawing of one end of a connecting rod and consists of two views (partially in section). It would be great bit of practice to make a drawing of the rod to a larger scale and make drawings of its parts in detail.
Plate 11. Figures 25, 26 and 27. Figure 25 shows the section of a house on lines A, B seen upon Figure 27. Figure 26 is another view of Figure 25. Figures 25 and 26 are drawn to a scale of half inch to a foot. Figure 27 is drawn to a scale of one-eighth inch to one foot. |
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