Projection.
The word projection means to throw forward, and in ordinary machine drawing it is the projecting or throwing forward of one view from another view.
In drawings the lines in one view or plan may be availed of to find those of others of the same object, and also to find their shape or curvature as they would appear in the other representations; this is called projection-drawing.
Fig. 222is the illustration as shown infig. 212on page 143, with the addition of dotted projection line, which illustrates the method of throwing forward the section and the end view of the object; these two views are procured from the plan or first figure, as shown infig. 222.
Fig. 224represents the square bolt and nut shown infig. 216, and the mode of projecting is similarly shown by dotted lines.
Fig. 223shows file handle shown infig. 215and the mode of projecting.
Fig. 222.
Fig. 222.
Fig. 223.
Fig. 223.
Fig. 224.
Fig. 224.
The principles upon which “projection” in drawing is based, are illustrated in the following examplesand text: As a real object can be scaled with a foot rule, so a drawing must permit of scaling and measuring. This measuring may take place as with the real object in full size or the drawing may, for the sake of convenience, be reproduced and measured in a reduced scale, as half, or in still smaller sizes. Sometimes itmay prove convenient to enlarge the drawing to twice the natural size of the object, as a means of making it stand out more clearly than the real size would accomplish.
For practical purposes, it is productive of economy of time to mark the dimensions of height and width or depth on the drawing in figures, to avoid the scaling. This marking of the dimensions is best done at the time of making the drawing, while the conception of the object is clear.
To convey a correct impression of the object, all lines that are marked to be of equal length should appear equally long on the drawing and be capable of being scaled to such equal length; for this, it must be assumed that the eye of the observer is equally distant from all points of a plane through the nearest point, or one of the axes of the object, and that the lines of sight are all parallel to each other and square to this plane.
Infig. 225these lines of sight are seen as directed toward one side of a cube or block; it will be readily understood, however, that in this way nothing is visible and accessible for scaling and dimensioning except this front face of the block, thus, a determination of the dimensions of only height and width would be possible, while the dimension of depth is entirely undetermined.
Sight linesFig. 225.
Fig. 225.
It is thus necessary to get a view of the block from another side; the direction in which it will be most instructive to obtain additional views is in the direction of the breadth and of the length and square to the lines of sight of the first view.
Fig. 226shows how the lines of sight would strike the object in the three directions. If these lines should be rays of light, some of them would pass by the bodyuntil they squarely strike the large plane surfaces,I,II,III; naturally the rays of light on the faces of the object will be retained, and cannot strike the plane surfaces, thus leaving dark shadows of exactly the same outlines as the block; these would be exact drawings of the faces, and if by some means they can be fixed and retained on the plane they can be completely measured and dimensioned.
This throwing forward of the outline of the object in different views on the planes is called projection of the object, and furnishes a highly important means of fixing the outlines and dimensions in the three main directions of height, width and depth; evidently, the light rays passing by the front face may not all reach the plane of projection, but they may be retained by protruding parts of the object behind the front face. These protruding parts naturally would also be projected on the plane in the same manner as the main body of the block.
These projections of the protruding part are plainly visible in planeIIand planeIII, while the part would not be drawn in outline in planeI. It may be imagined, however, that the greater thickness of the body in the direction of the protruding part would intensify also the shadow, thus outlining the face of the protruding part in planeI.
It is apparent that these three projections are all needed, but as drawing is all done in one single plane, the three projections will for the sake of convenience have to be brought into a single plane. This can be realized if planeIIis swung around axisO Zand planeIIIaround axisO Y, until all three surfaces are in one single plane, which would then appear as shown infig. 227.
It is also possible to assume transparent planes in front of the body and extend the parallel lines of sight forward instead of backward. Thus an outline picture will be created on each of the three planesI,II,IIIinfig. 228, in a manner similar tofig. 226. For drawing purposes, all three views again have to be brought into a single plane, which is done by swingingIIaroundO Z, andIIIaroundO Yin the same manner asfig. 227was evolved fromfig. 226.
It will be noted that infig. 229planeIIIis now aboveIand planeIIon the left-hand side ofI, while infig. 227they were below and at the right-hand side of planeI. As the swinging of the top and side planes takes place around the edges of the front planeItwo systems may thus be distinguished, according to the position of planeIin regard to the object.Fig. 226thus represents the system of backward projection, whilefig. 228represents the system of forward projection.
Either system can have, however, the planeIIat the right- or left-hand side edge, while planeIIImay be attached to the top or bottom edge of planeI; it is readily understood that a number of combinations are possible for each system, as it is not necessary to adhere absolutely to one rule. The system of forward projection is the one generally practiced and further examples are all executed by this system, meaning that the planes are always between the observer and the object.
ProjectionsFig. 226.
Fig. 226.
ProjectionsFig. 227.
Fig. 227.
ProjectionsFig. 228.
Fig. 228.
For the clearness of the drawing, it is desirable to have all corners, edges and outlines appear in such solid lines as they appear to the eye. If, therefore, certain sharply defined outlines occur on one side more than on the opposite one, it is most desirable to take the view against the side that has the most definitely marked outlines.
If the opposite side should show a number of wholly different features, it may prove even desirable to show this side also, thus gaining four views instead of the usual three, and so obtain a more complete understanding of the shape of the object, besides giving increased facilities for dimensioning each part of the body.
This additional view may be taken from the sides, as well as up or down, thus making a maximum of five views possible by which the outside of the object may be delineated.
Fig. 230shows why it may be desirable to take five views of a block that has a receding space of different outlines in each of the side and top and bottom faces.
It is not necessary, however, to resort to five views in such a case as is represented infig. 230, as the only differing feature, the circular space inIIIbottom, might be shown inIIItop by dotted lines, and the difference ofIIright might be shown inIIleft, also by dotted lines. It is desirable to show four or five views only where great complication and consequent lack of clearness through numerous dotted lines would result from having a less number of views.
ProjectionsFig. 229.
Fig. 229.
So far the projections and views have only represented the outlines of the object; it may often be desirable, however, to show central holes or other perforationsor variations of sections; in this case it is possible to imagine the object cut in slices, by planes, through certain well defined axes, or other lines of distinctive importance, and then take a view of this sectional plane with its newly created intersections or sharply marked outlines; thus, a section may often take the place of the third, fourth or fifth view to great advantage.
ProjectionsFig. 230.
Fig. 230.
It is not always possible to get a view against a face or side of the object, but, with irregularly shaped bodies or under special conditions, it may be necessary to take a view of corners, sloping planes, curved or irregularly shaped surfaces.
Fig. 231shows a hexagonal nut in the three normal projections; from the top view it is readily seen that the front view shows the side of the hexagon in a contracted scale, and that therefore the scaling and dimensioning for the horizontal direction have all to be done in the top or plan view; the front and side views convey, however, the dimension of height correctly, and these are therefore the right places for scaling and dimensioning in the vertical direction.
Fig. 231shows how a cylindrical outline appears in the three views; the hole in the nut presents itself as circular in the top view, while it appears in the front and side views as a rectangle. For simple objects, it is unnecessary to show the edges of the planes, and the three views are grouped, as regards distances and positions, as most convenient for the execution of the drawing.
Where sloping surfaces are of irregular form, it may be necessary to employ help lines for their full determination in the three views.Fig. 232shows how the surface that is produced by a slanting cut through a cylinder would appear in the three views. The help lines are placed in the top view in eight equal divisions around the circumference of the cylinder. These division lines are shown by dotted lines on the cylinder inthe front and side views. Their intersections, with the sloping cut in the front view, furnish also the height of the corresponding points for the side view.
ProjectionsFig. 231.
Fig. 231.
By progressive determination of points, lines and surfaces, even the most complicated bodies can be completely represented for their reproduction in any application to mechanical or industrial purposes.
ProjectionsFig. 232.
Fig. 232.
The spur wheel shown onpage 163is an example of projection drawing.
The wheel is illustrated in three views:fig. 235is a side view, or elevation;fig. 234is a front elevation;fig. 233is a section view onC D. The section is projected from the front elevation by drawing parallel lines from the points in front elevation where the lines are intersected by the center lineC D, cutting the plane of view and showing the interior shape atC D.
The side elevation,fig. 235, is projected from the front elevation,fig. 234, by drawing parallel lines from the edges in the front view across its face.
In actual drawing practice the figures should be made about three times larger than the example, and as follows:
For the front elevation draw the center linesA B,C D, and from their point of intersection as a center, with the compasses draw the inner circle or hole, also the pitch lineE E. With the dividers space this line into nineteen equal divisions; each point on this line will be the center of a tooth, and the distance from one point to the next one is the pitch of the tooth.
Now, with the dividers mark off the thickness of tooth at each side of these points on pitch line; with the compasses draw the outer circle for points of teeth, the inner circle for the root of teeth, and circles for thickness of rim and hub; also circles representing the fillets at rim and hub. For clearness and to prevent confusion these lines are shown on one-half the wheel only, terminating in center lineC D; all the lines of the front elevation are now complete excepting the teeth.
In the drawing office it is unusual to delineate all the teeth in a gear wheel, the lines without the teeth as now completed being deemed sufficient, giving all particulars; however, to prevent the error of mistaking the circles it is well to represent one or two teeth on the drawing.
GearFig. 233.—Fig. 234.—Fig. 235.
Fig. 233.—Fig. 234.—Fig. 235.
In the example, proceed and complete the entirewheel, taking on the compasses a radius equal to the pitch of the tooth; set them on the pitch line at the pointG, already spaced for thickness of tooth, draw lineHfrom pitch line to root of tooth; proceed similarly all around the circle, completing one side. Next, reverse the operation and draw the corresponding side of the root of tooth. Now take a radius equal to half the space between teeth and the thickness of tooth on pitch line, and, with center in pitch line, as shown atI, draw the outside or addendum of tooth,J; it will be apparent that the reverse addendum of the tooth next adjoining can be formed at the same time, with one setting of the compasses; finish all the teeth similarly; the front elevation will thus be completed.
Fig. 233is an excellent example of sectional drawing, to be executed as follows:
First draw the center lineL Moffig. 233, lay off at each side of it half the breadth of face and of the hub; now project, from center lineC D, in the front elevation,fig. 234, with the T-square the upper and lower teeth, the fillets, the chamfers, the hub and center hole, also dot in the pitch lineF F, take the radii and draw the fillets and chamfers; draw section lines and the view will appear as shown infig. 233.
Fig. 235is a side elevation offig. 234, and is a fine sample of projection, to be executed as follows:
Proceed similarly as forfig. 233, projecting the lines from the outside edges of the front elevation, instead of from the center lineC Das in last figure, and the end elevation will be as shown infig. 235.
The student will be assisted in understanding this working drawing by consulting thepagesunder the heading of “Gearing.”
LETTERING, INKING, SECTION LINING
Fig. 236.
Fig. 236.