This section is from the book "Modern Shop Practice", by Howard Monroe Raymond. Also available from Amazon: Modern Shop Practice.
Very often a belt has to pass through a floor or partition. The holes through which the belt runs should be large enough to be sure that the belt shall never strike the sides, but it is desirable that they should be no larger than is necessary to accomplish that result. Accordingly) the boles should be laid out so that they may be cut in the right place and at the proper angle. Figs. 108 to 110 show the method of locating the position of the floor holes for the various kinds of belts, the top only of the floor being shown.
In Fig. 108 we have a common open belt. The circles representing the pulleys are drawn, and the belt drawn around them. A short pitch line should be also drawn in each part of the belt where it passes through the floor. These parts of the pitch line are simply lines parallel to, and halfway between, the lines which represent the outer and inner faces of the belt. Next draw the two rectangles which represent the plan view of the pulleys, and draw through them the center line RS. From the points E and H, where the pitch line intersects the line representing the top of the floor, draw perpendiculars to RS, meeting it in points F and G. F and G are the center points of the rectangles 1 2 3 4 and 5 6 7 8y which form the outline of the belt holes on the surface of the floor. The long dimension of the rectangles will be parallel to the shafts on which the pulleys are located. After the belt holes are so found, the distances of their center lines to the right or left of the lines T and X, respectively (which are the center lines of the shafts), can be measured on the drawing, and the workman can mark them out on the floor by plumbing down (or up) from the shafts, getting the lines T and X on the floor directly under or over the center of the shafts, and thus locating on the floor the points F and G, and consequently the belt holes, from the dimensions taken from the drawing. Fig. 109 shows how to draw the holes for a crossed belt. Draw the two views of the pulleys and the center lines AC and DB of the belt in the elevation; also the center line RS in the plan. It is well, also, to draw the belt complete in the elevation, as it makes it easier to determine which way the belt holes will slant. From points E and H, where the center lines of the belt intersect the floor line, draw EL and HK perpendicular to RS, and meeting RS in F and G. The points F and G are the center points of the belt holes, and it only remains to determine the angles which the center lines of the holes make with T and X, respectively. These will be the same as the angles made with HK and EL. When the belt is leaving the pulley at A, a line drawn perpendicularly across to its inner face would occupy the position indicated by the dotted line aa' in plan; and the belt, in passing from A to C, twists through an angle of 180°, and the line which was at aa' will occupy the position cc'. Therefore, when the belt has passed from A to H, it will have twisted through an angle which will bear the same relation to 180° that the distance A H bears to the distance AC. That is, if A H = ¼ of AC. the angle JGK is ¼ of 180°, or 45°. Whether the angle JGK shall be laid off to the right or to the left of line HK, must be reasoned out by considering which way the belt twists in passing A to C. The angle of the other belt hole (LFM) is determined in the same way.
Fig. 107. Diagrammtic Layout for Cone Pulleys.
Fig. 108. Diagram Showing Method of Locating Belt Holes.
Fig. 109. Diagram Showing Location of Holes for Crossed Belt.
Fig. 110 shows the method of finding the belt holes of a plain quarter-twist belt, similar to Fig. 98. The centers G and F in plan are found by projecting from the elevation, as shown by the construction lines. The angle which the center line of hole at G makes with the center line of the shaft, is found by dividing 90° in the ratio of the distances P and N. The angle of the center line of the belt hole at F with the center line of the shaft, is found in a similar manner, by dividing 90° in the ratio of the distance A E to EC. It is usually sufficiently accurate, however, after having found the angle at G, to draw the center line of the other hole parallel to it.
 
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