Righthand cylindrical helix

The helix is a curve generated on the surface of the cylinder by a point which revolves uniformly around n D

Cylindrical Helix

Fig. 10.9 Archimedean spiral

Fig. 10.9 Archimedean spiral the cylinder and at the same time either up or down its surface. The method of construction is shown in Fig.

1 Draw the front elevation and plan views of the cylinder, and divide the plan view into a convenient number of parts (say 12) and number them as shown.

2 Project the points from the circumference of the base up to the front elevation.

3 Divide the lead into the same number of parts as the base, and number them as shown.

4 Draw lines of intersection from the lead to correspond with the projected lines from the base.

5 Join the points of intersection, to give the required cylindrical helix.

6 If a development of the cylinder is drawn, the helix n D

Surface Development Cylinder

Fig. 10.10 Right-hand cylindrical helix

Fig. 10.10 Right-hand cylindrical helix will be projected as a straight line. The angle between the helix and a line drawn parallel with the base is known as the helix angle.

Note. If the numbering in the plan view is taken in the clockwise direction from point 1, then the projection in the front elevation will give a left-hand helix.

The construction for a helix is shown applied to a right-hand helical spring in Fig. 10.11. The spring is of square cross-section, and the four helices are drawn from the two outside corners and the two corners at the inside diameter. The pitch of the spring is divided into 12 equal parts, to correspond with the 12 equal divisions of the circle in the end elevation, although only half of the circle need be drawn. Points are plotted as previously shown.

A single-start square thread is illustrated in Fig. 10.12. The construction is similar to the previous problem, except that the centre is solid metal. Four helices are plotted, spaced as shown, since the threadwidth is half the pitch.

Cylindrical HelixConical Spiral

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