In Fig. 304, let E A B F be the front elevation of a keystone, as for a window cap, of which K L M P S R is a sectional view, giving the profile of the molding M N O P, over which it is required to fit. The sink in the face extends throughout its entire length, and is shown by G H D C, its depth being shown by the line K T of the section. EFHG and ABDC thus become moldings, of which E A and F B are the parallel lines, E F, G H, C D and A B the miter lines, and K R the profile. Likewise C G H D becomes a molding, of which G H and C D are the miter lines and K T the profile. Therefore, to obtain the pattern of the face pieces, divide the profile of the face K R into any convenient number of spaces, and from the points thus obtained carry lines across the face of the keystone, as shown. At right angles to the top of the keystone lay off a stretchout of K R, as shown by K2 R1, through which draw the usual measuring lines. Placing the T-square parallel to the stretchout line, and bringing it successively against the points in the lines C D and A B bounding the face strip, cut the corresponding measuring lines. Then a line traced through these points, as shown by C2 A2 B2 D1, will be the pattern for this part.

In developing the pattern for the sink the usual method would be to divide K T into equal spares, carrying lines across the face, and thence into the stretchout; but since this would result in confusion of lines, the same points as were established in K R have been used, which are quite as convenient as the others mentioned, save that the points in K T must be obtained from the points in K R, by carrying lines back to K T, as shown, and in laying off the stretchout each individual space must be measured by the dividers.

Fig. 304.   The Patterns for a Keystone Having a Molded Face with Sink.

Fig. 304. - The Patterns for a Keystone Having a Molded Face with Sink.

At right angles to the line H D of the keystone lay off a stretchout of K T, as shown by K1 T1, through the points in which draw the usual measuring lines. Place the T-square at right angles to the lines across the face of the keystone, and, bringing it successively against the points in the lines G H and C D, forming the sides of the sink, cut the corresponding measuring lines drawn through K1 T1 Then lines traced through these points, as indicated by G1 H1 and C1 D1, will form the pattern of the required sink piece. For the pattern of the piece forming the sides of the sink in the face of the keystone, K R T becomes the elevation of a molding running in the direction of R T, of which K R and K Tare the miter lines and C D the profile. Hence, at any convenient place above or below the sectional view, lay off the stretchout of the line C D, as determined by the lines drawn across it in the first operation, all as indicated by C2 D12. Through the points in C2 D2 draw measuring lines in the usual manner. The next operation, in course, would be to drop lines from the points in the profile to the miter lines; but as this has already been done by the lines of the first operation, it is only necessary to place the T-square at right angles to the measuring lines, and bring it successively against the several points in the lines K R and K T, and cut the corresponding measuring lines, as shown. Then a line traced through these points, as indicated by K3 R2 and K3 T2, will be the pattern of the piece required.

For the side of the keystone, K L S R becomes the face of a molding, of which A B is the profile and K R the miter line at one side, and L M and P S the miter lines at the other. From this point forward the problem is, in principle, the same as Problem 10. For convenience, and to avoid confusion, it is best to again make use of the same set of lines instituted in the first part of the demonstration. Therefore, lay off the stretchout A1 B1 equal to A B, putting into it all the points occurring in A B, through which draw measuring lines in the usual manner. Place the T-square at right angles to these measuring lines, and, bringing it successively against the points in the line K R, and likewise against L M and P S of the back, cut corresponding measuring lines, as shown. Then a line traced through these points of intersection, as shown by N1 M1 L1 K4 R2 S1 P1 O1, will be the outline of the required pattern, with the exception of that part lying between N' and O1, which make a duplicate of N O. By examination of the points in A1 B1 and the lines drawn through the same and making comparison with the points in A B, it will be seen that in order to locate accurately the position of the profile of the window cap molding MNOP, two additional points, as shown by x1 and y1, have been introduced, corresponding to x and y, the points of intersection between the extreme lines of the cap molding itself and the side of the keystone A B, as shown in the elevation by the curved lines of that molding. In practice it is frequently necessary to introduce extra points in operations of this character.

PROBLEM 27. The Pattern of a Square Shaft to Fit Against a Sphere.

In Fig. 305, let H A A1 K be the elevation of a square shaft, one end of which is required to fit against the ball D F E. Draw the center line FL, upon which locate the center of the ball G. Continue the sides of the shaft across the line of the circumference of the ball indefinitely. From the points of intersection between the sides of the shaft and the circumference of the ball, A or A1, draw a line at right angles to the sides of the shaft, across the ball, cutting the center line, as shown at B. Set the dividers to G B as radius, and from G as center, describe the arc C C1, cutting the sides in the points C and C1 Then H C C1 K will be the pattern of one side of a square shaft to fit against the given ball.

Fig. 305.   The Pattern of a Square Shaft to Fit Against a Sphere.

Fig. 305. - The Pattern of a Square Shaft to Fit Against a Sphere.