In constructing the elevation of a four-piece elbow, first draw the profile A B C, from which project one of the arms of the elbow, as shown by the lines A F and C G, Fig. 321, At right angles to this lay off the other arm of the elbow. M L X T. continuing the lines of each until they intersect. Through the points of intersection draw the diagonal line a d. Establish the point a on this diagonal line at convenience, and bom it draw the lines a b and a e at right angles to the two arms of the elbow respectively. From a as center, and with a b as radios, describe the arc b f e c, as shown, which divide into three equal parts, thus obtaining the points-f and e. Through f and e, to the center a, draw the lines f a and e a, which will represent the centers of the middle sections of the elbow, at right angles to which the sides of the same are to be drawn. Through f, and at right angles to f a, draw L K, meeting M L in the point L, and stopping on the line a d at the point K. Through e, and at right angles to e a, draw a line, commencing in the point K and terminating in G where it-meets the line E G. In like manner draw the lines of the inner side of the elbow, as shown by F H and H I. Draw the miter or joint lines F G, H K and L I, as shown. For the patterns proceed as follows: Divide the profile into any convenient number of equal parts. Place the T-square parallel to E G, and, bringing the blade against the points in the profile, drop corresponding points upon the miter line F G. Change the T-square so that its blade shall be parallel to the lines of the second section of the elbow, and, bringing it against the points in F G, cut corresponding points on HK. Opposite the end of and at right angles to the lower arm of the elbow, lay off the stretchout line O P, as shown, through the divisions in which draw the usual measuring lines. Place the T-square at right angles to the arm of the elbow, and, bringing it successively against the points in the miter line F G, cut the corresponding measuring lines. Then a line traced through the points thus obtained, as shown from R to T, will with O P constitute the pattern of one of the arms. Produce a e, representing the middle of the second section in the elbow, as shown by V W, upon which lay off a stretchout, and through the points in the same draw measuring lines. Placing the T-square parallel to a e, or, what is the same, at right angles to the second section of the elbow, bring it against the several points in the miter lines H K and F G, and cut the corresponding measuring lines. Then lines traced through the points thus obtained, as shown from X to Z and Y to S, will give the pattern.

Fig. 321. - A Four-Piece Elbow.

PROBLEM 42. The Patterns for a Five-Piece Elbow.

To construct the elevation of a five-piece elbow, first draw the profile, as ABC, Fig. 322, from which project one of the arms of the elbow, as shown at the left by E S R D, continuing its lines indefinitely. At right angles to this lay off the other arm, continuing its lines till they intersect those of the horizontal arm, or till their outer lines intersect, as at g. Draw g a at an angle of 45 degrees to either arm, upon which establish the point a with reference to the curve which it is desired the elbow shall have, and from it, at right angles to the two arms of the elbow respectively, draw a b and a c. From a as center, with a b as radius, describe the arc b f e d c, which divide into four equal parts, thus obtaining the points d, e and f, and draw d a, e a and f a. Then these lines represent center lines of the several sections of which the elbow is composed, at right angles to which their sides are to be drawn.

It may be here remarked that the number of center lines made use of in dividing the quarter circle b c represents the number of pieces in the elbow. Therefore, to draw an elevation of an elbow in any number of pieces, construct the quadrant abc as above described, then divide b c into such a number of parts that the number of lines drawn to a (including a b and a c) shall equal the number of pieces required. Thus the five lines a b, a f, a e, a d and a c are the center lines of the five pieces of which the elbow shown in Fig. 322 is constructed. Although the two extreme lines a b and a c are not, strictly speaking, center lines, their relation to the adjacent miter lines is the same as that of the other lines radiating from a. Through f, and at right angles to f a, draw V S, joining the side of the arm E S in the point S, and joining a corresponding line drawn through e in the point V. In like manner draw the line T R, representing the inner side of the same section. The remaining sections are to be obtained in the same way. As but one section is necessary for use in cutting the patterns, the others may or may not be drawn, all at the option of the pattern cutter. Draw the miter or joint lines S R, V T, etc. Divide the profile (or one-half of it) in the usual manner. Place the T-square parallel to the lines of the arm, and, bringing the blade against the several points in the profile, drop corresponding points upon the miter line S R. Shift the T-square so that the blade shall be parallel to the part V S R T, and transfer the points in S R to V T, as shown. For the pattern of the arm, at right angles to it lay off a stretchout of A B C, as shown by F G, through the points in which draw the usual measuring lines. Place the T-square at right angles to the arm, and, bringing it against the points in R S, cut the corresponding measuring lines, as shown. Then a line traced through these points, as shown from H to I, will be the pattern. For the pattern of the piece S V T R prolong the line a f, as shown by L K, upon which lay off a stretchout, through the points in which draw the measuring lines in the usual manner. Placing the T-square at right angles to S V, or, what is the same, parallel to the stretchout line, bring it against the several points in the lines R S and T V, and cut the corresponding measuring lines. Then lines traced through the points thus obtained, all as shown by N P O M, will be the pattern sought.

Fig. Sit - A Five-Piece Elbow.