This section is from the book "A Practical Workshop Companion For Tin, Sheet Iron, And Copper Plate Workers", by Leroy J. Blinn. Also available from Amazon: A Practical Workshop Companion For Tin, Sheet Iron, And Copper Plate Workers.
Fig. 61. To describe an Elbow at Right Angles.

Let ABCD, fig. 61, be the given elbow; draw the line AB at right angles to BC; draw the line FC; describe the semicircle AGB; divide the semicircle into any number of equal parts; from the points draw lines parallel to BC, as 1, 2, 3, etc.
Fig. 62.

Set off the line ABC, fig. 62, equal in length to the circumference of the elbow AB; erect the perpendicular lines AD, BE and CF; set off on each side of BE the same number of equal distances, as in the semicircle AGB; from the points draw lines parallel to BE; make BE equal to BC; make AD and CF equal to AF; also, each of the parallel lines bearing the same figures as 11, 22, 38, etc.; then a line traced through the points will form the pattern.
Edges to be allowed.
Patterns for Elbows may be described at any angle, by any of the Rules for cutting Elbow patterns; in laying out Elbow patterns let AB equal diameter of the Elbow, and BCD the angle.
Elbows.
2b describe an Elbow Pattern at any angle.
Fig. 63.

Let ABCD, fig. 63, be the given Elbow;. draw the line AB at right angle to BF; draw the line EF; describe the semicircle AGB; divide the semicircle AGB into any number of equal parts; from the points draw lines parallel to BF, as 1, 2, 3, etc.
Fig. 64.

Set off the line ABC, fig. 64, equal in length to the circumference of the Elbow AB; erect the perpendicular lines AF, BE and CD; set off on each side of BE the same number of equal distances, as in the semicircle AGB; from the points draw lines parallel to BE, as 1, 1, 2, 2, 3, 3, etc.; make BE equal to BF; make AF and CD equal to AE; also, each of the parallel lines bearing the same figures as 1, 1, 2, 2, 3, 3, etc.
Then a line traced through the point will form the pattern. Edges to be allowed.
Elbows.
Fig. 65. To describe a Pattern for an Elbow in Three Sections.

Let ABED, fig. 65, be the given elbow; draw the line FC; make FK equal to one-half the diameter of the elbow, with F as a centre; describe the arcs GL; divide the arc GL into four equal parts; draw the lines FH and FJ; also, the line JH; draw the line AB at right angles to BC; describe the semicircle AMB; divide the semicircle into any number of equal parts; from the points draw lines parallel to BH, as 1, 2, 3, etc.
Fig. 66.

Set off the line ABC, fig. 66, equal in length to the circumference of the elbow AB; erect the perpendicular lines AD, BH and CE; set off on each side of BH the same number of equal distances as in the semicircle AMB; from the points draw lines parallel to BH; make BH equal to BH; make AD and CE equal to AN; also, each of the parallel lines bearing the same number as 1,1, 2, 2, 3,3, etc.; then a line traced through the points will form one of the sections; make DF and EG equal to HJ; then reverse section No. 1, and place D at G and E at F, and trace a line fron G to F, this will form section No. 2 and 3.
Edges to be allowed.
 
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