The essentials of descriptive geometry . an and elevation of the helixdescribed by the end of the generating line. Construction. In Fig. 130 let AB be the generating Hne in itsfirst position. Let the axis be the line through A perpendicularto H, and let the distance that the point B rises during onerevolution of AB about the axis be equal to twice the distancefrom 12 to the G. L. Draw the hehx described by point Baccording to the directions in Article 129. As the point B takesup the position on this helix indicated by the points i, 2, 3, etc.,the point A will remain in contact with the axis an
The essentials of descriptive geometry . an and elevation of the helixdescribed by the end of the generating line. Construction. In Fig. 130 let AB be the generating Hne in itsfirst position. Let the axis be the line through A perpendicularto H, and let the distance that the point B rises during onerevolution of AB about the axis be equal to twice the distancefrom 12 to the G. L. Draw the hehx described by point Baccording to the directions in Article 129. As the point B takesup the position on this helix indicated by the points i, 2, 3, etc.,the point A will remain in contact with the axis and will rise equaldistances, as shown by al, a2, a3, etc. By joining the successivepositions of A and B the positions of the generating line as itmoves about the axis may be shown. If the points where theseseveral positions of the generating hne pierce H be found, as atb, bi, b2, bs, etc., the curve of the base may be located. From aninspection of the drawing it will be seen that the intersection of 164 ESSENTIALS OF DESCRIPTIVE GEOMETRY. Fig. 130. WARPED SURFACES 165 the surface with H gives a curve called the Spiral of the drawing only a little over one-half of one revolution of theline AB about the axis has been shown. 132. There are two general kinds of helicoidal surfaces bothof which have many practical uses. When the generatrix is in-clined to the axis, as in , the resulting helicoid iscalled an oblique helicoid; andwhen the generatrix is per-pendicular to the axis, as inFig. 134, the surface is calleda right helicoid. In its prac-tical applications the heli-coidal surface is not indefinitein extent but is limited usuallyby cylinders. Fig. 131 showsa plan and elevation of anoblique helicoidal surface inthe form of a screw 132 shows a right heli-coidal surface such as is usedin cams. Practical examplesof helicoids may be found inso-called spiral stairways,screw conveyors, propellers,screw threads, twist drills, etc. 133. Propo&ition 42. Giv
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