Since most coil springs and all screw threads depend upon a curve known as a helix, it will be necessary to know what a helix is, and how it can be drawn, before taking up the construction of springs and screws.
Suppose we take a cylindrical piece of wood, such as is shown in Fig. 51, and a rectangular piece of paper ABFE, with the side AB equal to the circumference of the cylinder, and the side AE equal to the length of the cylinder. If we lay off along AE any convenient distance AD, and draw the line DC parallel to AB, we have the rectangle ABCD. Now draw the diagonal AC of this rectangle and wrap the paper around the cylinder, keeping the side AE on an element of the cylinder; the paper will just cover the cylinder, the edge BF meeting the edge AE. The point C coincides with the point D, and is on the same element of the cylinder as A; therefore the line AC has made one complete turn around the cylinder, advancing the distance AD in this turn. The curve which the line AC now takes is called a helix, and the distance AD is called the pitch of the helix.
Fig. 51. Diagram of Simple Helix Construction.
If on the piece of paper we also choose a point H, half way between A and D, and draw from this point a line HJ parallel to line AC, this line HJ will form another helix parallel to the helix formed by the line AC, when the paper is wrapped around the cylinder. The pitch of both helices is the same.
The helix is often incorrectly called a spiral, but there is a marked difference between the two. The spiral is a curve which lies in one plane and winds around a point, constantly receding from the point, according to some law. The mainspring and hairspring of a watch are in the form of spirals.
To draw the projections of a helix we must know the diameter of the cylinder upon which the helix is formed, and the pitch of the helix. Fig. 52 shows the construction.
Fig. 52. Diagram Showing Construction of Right-Hand Helix Curve.
Draw two projections of the cylinder ABDC; along any element, preferably one of the contour elements AB or CD, lay off the pitch AE. Divide the circumference of the circle, which is the end view of the cylinder, into any number of equal parts, and number the points of division 1,2,8, etc. Divide the pitch AE into the same number of equal parts, and number these points of division in the same way that the points on the circle are numbered, calling A point 1. From point 2 on the circle, draw a line parallel to A B; and from point 2 on AB, draw a perpendicular to AB. The point L, where the parallel line meets the perpendicular line, is one point on the projection of the helix. The points M, N, etc., are found in the same manner. A smooth curve starting from A, going through all the points and ending at E, will be the projection of one turn of the helix. The half from A to R is on the front, and is, therefore, a full line, while the half from R to E is on the back and is a dotted line. It should be observed that the point R is on the perpendicular from 7, which is just half-way between A and E; that is, the distance CR is just one-half the pitch. The curve from E to B is the projection of the next turn of the helix and is exactly like the first one.
Fig. 53. Diagram of Left-Hand Helix Curve.
The helix shown in Fig. 52 is called a right-hand helix. If the curve starts at C and is drawn as in Fig. 53, we have a left-hand helix. Notice that the visible part (from C to R) slants in the same direction as the invisible part of the right-hand helix, which is shown dotted in Fig. 52.
Since the helix is a line drawn on the surface of a cylinder, the other projection of the helix must be the circumference of the circle, which is the end view of the cylinder. Fig. 54 shows a right-hand double helix, and Fig. 55 is a right-hand triple helix.
The construction of these curves should be studied carefully in order that springs and screw threads may be better understood.
Fig. 54. Diagram of Right-Hand Double Helix.