This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 Excerpt: …better, the more teeth they have; hence, as the arc of action of bevel teeth, at their outer extremities, for example, is in the plane Y 5t, (perpendicular to the paper) and virtually with radii V 5 and v o, the action of the bevel wheels, with nominal radii ab and db, is equivalent to that of spur wheels with radii V 5 and v b. c–Warped Communicators. Example XXXVII. The complete Projections of a Screw and Nut. Description.–If a square, Ao–A'a'r’s’, Pl. XXIII., Fig. 1, revolve uniformly around an axis, O–O'O, and at the same time move parallel to the axis, and uniformly, it will describe the winding or spiral rail, thread, or solid ADG gda–A'a'r’s, G'G g g’, M’M m m’. This surface is bounded as follows: Its outer surface, generated by A–AV, during the movement of the square, is cylindrical and vertical in this case. Its inner surface, generated by a–a'r’, is also cylindrical and vertical. Its upper and lower surfaces generated by Aa–s'r’, find Aa–Afa’, respectively, are called right helicoids: called helicoida from the form of the bounding curves, as ADG–A’D'G’, which is a helix; and called right helicoids, because A.a–AV and Aa–r’s’ are perpendicular to the axis O–O'O. Now let equidistant threads, like that just described, be formed, solid with an interior cylinder or core, adg–a'TU'V, and the result will be a square threaded screw. The height, AM’, to which the point A ascends, in one revolution around the axis, O–O'O, is the pitch of the screw. As the spaces, as t'G, between the threads must be equal to the threads, in order to receive the corresponding threads of the internal screw, Fig. 2, it follows that A’M’ must be some even number of times AY, the height of a thr…