Page:The Kinematics of Machinery.djvu/175

 whole procedure may therefore be there repeated, a second auxiliary centroid, similar or dissimilar to the first, being employed to give the two new profiles c and d Fig. 108.

If the describing points are points upon the auxiliary centroids, all the roulettes must extend to the primary centroids, we can therefore join the profiles a and c, and also the profiles b and d, into one piece. Then by repeating the process for a number of positions on each of the centroids we can obtain profiles which may serve as those of tooth-formed projections upon the element to which they belong. A regular series of such projections with

. 107. FIG. 108.

corresponding hollows between them gives us the familiar spur- wheel. The portion of the centroid lying between homologous points of two consecutive teeth is there called the pitch, and the centroid itself is the pitch-line, or if circular the pitch-circle. Circles (" describing " circles) are used as the auxiliary centroids. The teeth must carry such portions of the roulette profiles that the restraint is never interrupted; such portions must be at least so large that the restraint by each tooth lasts while the centroids roll through a distance equal to the pitch; the contact between each pair of teeth, in other words, must continue for at least this period.

With spur-wheels or toothed-wheels having cylindric axoids it may be further required that all wheels of the same pitch should gear with each other, that is that their tooth-profiles should com- municate a motion to which the corresponding centroids (pitch lines) are circular.* Wheels so arranged we may call Set-


 * If wrongly formed profiles be set to work with each other the motion of the