This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
A shows the part elevation of the panel; a b and c d, the miter-lines drawn at angles of 45o. In its proper position with the lines of the mould-ing, draw the profile B, the curve or mould of which divide into equal spaces, as shown by the figures 1 to 7; and from the points thus obtained, parallel to 1 b, draw lines intersecting the miter-line a b as shown. From these intersections, parallel to b d, draw lines intersecting also c d. At right angles to b d draw the stretchout line 1' 7', upon which place the stretchout of the profile B. At right angles to 1' 7', and through the numbered points of division, draw lines, which intersect by lines drawn at right angles to b d from similarly numbered intersections on the miterlines a b and c d. Trace lines through the various points of intersecting in the pattern as shown. Then will C D E F be the required cut for the ends of the panel.
Fig. 281, it being necessary only to make D E in Fig. 282 that length when laying out the pattern on the sheet metal.
Where the miter-cut is required for a panel whose angles are other than right angles, as, for example, a triangular panel as shown in Fig. 283, then proceed as shown in Fig. 284. First draw the elevation of the triangular panel as shown by A B C, the three sides in the case being equal. Bisect each of the angles A, B, and C, thus obtaining the miter-lines A c, B b, and C a. In line with the elevation, place in its proper position the profile E, which divide into equal spaces as shown; and from the numbered division points, parallel to A C, draw lines cutting the miter-line C a. From these intersections, parallel to C B, draw lines intersecting the miter-line, b B. At right angles to C B draw the stretchout line 1' 7', upon which place the stretchout of the profile E. Through the numbered points of division and at right angles to 1' 7', draw lines as shown, which intersect by lines drawn at right angles to C B from intersections of similar numbers on the miter-lines a C and b B. Through the points thus obtained, trace the pattern F G H I.
It makes no difference what shape or angle the panel may have; the principles above explained are applicable to any case.
By referring to the plan, it will be seen that the four parts b a, a b', b' a', and a' b are symmetrical; therefore, in practice, it is necessary only to draw the one-quarter plan, as shown in Fig. 286, and omit the elevation, since the height d e (Fig. 285) is known. Thus, in Fig. 286, draw the quarter-plan of the panel, no matter what is its shape, as shown by a 1 5 6 9 Divide the curves from 1 5 and 6 9 into equaspaces, indicated respectively by 1. 2, 3, 4 and 5, and 6, 7. 8, and 9. From these points, draw lines to the apex a. As the pattern will be developed by triangulation, a set of triangles will be required, as shown in Fig. 287, for which proceed as follows: Draw any horizontal line, as a 1; and from a erect the perpendicular a a' equal to the height the panel is to have. Now take the lengths of the various lines in Fig. 286 from a to 1, a to 2, a to 3, etc., to a to 9, and place them on the line at a 1 in Fig. 287, as shown by similar numbers. Then using as radii the various lengths a' 1, a' 2, a' 3, etc., to a' 9, and with any point, as a' in Fig, 288 as center, describe the various arcs shown from 1 to 9. From any point on the arc 1 draw a line to a'. Set the dividers equal to the spaces contained in the curve 1 5 in Fig. 286; and, starting from 1 in Fig. 288 step from one arc to another having similar numbers, as shown from 1 to 5. In similar manner, take the distance from 5 to 6 and the spaces in the curve 6 9 in Fig. 286, and place them on corresponding arcs in Fig. 288, stepping from one arc to the other, resulting in the points 5 to 9. Trace a line through the points thus obtained. Then will a' 1 5 6 9 a' be the quarter-pattern, which can be joined in one-half or whole pattern as desired.
The rule given in Fig. 290 is applicable to any angle or profile. First draw a section or an elevation of the moulding as shown by A B 14 1. Directly below the moulding, from its extreme point, as 2 3, draw a plan of the desired angle as shown by C 2 D. Bisect this angle by using 2 as center and, with any radius, describing an arc meeting the sides of the angle at C and E. With the same or any other radius, and with C and E as centers, describe arcs intersecting each other in F. From the corner 2, draw a line through F. Then will 2 H be the miter-line, or the line bisecting the angle C 2 D. Now divide the profile 1 14 into equal spaces as shown by the figures, and from the points thus obtained drop vertical lines intersecting the miter-line 2
H in plan from 1 to 14 as shown.