The essentials of descriptive geometry . end will follow a path in space which is a curveof double curvature called a helix. It must be apparent that allpoints between these extreme points of the generatrix will alsodescribe helices of sizes which will vary according to the positionof the point on the generatrix. The surface of the helicoid, then,may be said to be made up of a series of concentric hehces, andin order to study such a surface properly the nature of the heUxmust first be considered. 128. The helix is a space curve generated by moving a pointaround and along an axis at a uniform r
The essentials of descriptive geometry . end will follow a path in space which is a curveof double curvature called a helix. It must be apparent that allpoints between these extreme points of the generatrix will alsodescribe helices of sizes which will vary according to the positionof the point on the generatrix. The surface of the helicoid, then,may be said to be made up of a series of concentric hehces, andin order to study such a surface properly the nature of the heUxmust first be considered. 128. The helix is a space curve generated by moving a pointaround and along an axis at a uniform rate. The distance fromthe axis may be constant giving a cylindrical helix (Fig. 125), orit may vary uniformly giving a conical helix (Fig. 126). In i6o ESSENTIALS OF DESCRIPTIVE GEOMETRY either of these cases the distance the generating point moves inthe direction of the axis during one revolution is called the examples of such curves may be found in the centerlines of cylindrical and conical springs (Figs. 127 and 128).. 129. To construct a cylindrical helix it is necessary to knowthe pitch and diameter of the cylinder on which the helix may bewrapped. In Fig. 129 the pitch and diameter of the cylinder aregiven. The plan view of the curve will be, of course, a circle and WARPED SURFACES l6l may be drawn at once. To find the elevation, divide the pitchdistance into any number of convenient parts, say 24, and dividethe circle of the H projection into the same number of the generating point start in H at point o. In moving fromo to I the point makes one twenty-fourth of a complete turn
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