Cyclopedia of mechanical engineering; a general reference work Editor-in-chief Howard Monroe Raymond Assisted by a corps of mechanical engineers, technical experts, and designers of the highest professional standing . ese surfaces, we attain the desired result of positively drivingwithout excessive side pressure. These artificial projections, or t(?eth, must fit into one another;hence the surfaces of the original cylinders, having been brokenup into alternate projections and hollows, have entirely disap- 321 ik; machine design peared to the eye; they nevertheless exist as ideal or imaginarysur
Cyclopedia of mechanical engineering; a general reference work Editor-in-chief Howard Monroe Raymond Assisted by a corps of mechanical engineers, technical experts, and designers of the highest professional standing . ese surfaces, we attain the desired result of positively drivingwithout excessive side pressure. These artificial projections, or t(?eth, must fit into one another;hence the surfaces of the original cylinders, having been brokenup into alternate projections and hollows, have entirely disap- 321 ik; machine design peared to the eye; they nevertheless exist as ideal or imaginarysurfaces, which roll together with the same surface velocities aa ifin bodily form, provided that the curves of the teeth are correctlyformed. Several mathematical curves are available for use astooth outlines, but in practice the involute and cycloidal curvesare the only ones used for this purpose. The ideal surfaces are known as pitch cylinders or pitchcircles. In Fig. 32 is shown an end view of .such a p;iir of cylin-ders in contact at their pitch point P. In gear calculations weassume that there is no slip between the pitch circles, acting asdriving cylinders; hence the speeds of tlie two pitch circles at the. Fig. .32. pitch point are equal. If M and M, be the revolutions per minuteof the cylinders respectively, r and i\ their radii, then 2ir»M = 2 7rr,Mi; That is, the number of revolutions varies inversely as the radii. The simple calculation as above is the key to all calculationsinvolving gear trains in reference to their speed ratio. Fig. 33 represents cycloidal teeth in the two extreme positionsof beginning and ending contact. The normal pressure Q or Q|between the teeth in each position acts through tlae pitch point 0,as it must always do in order to insure the condition of ideal roll- MACIIIIsE DESIGN 117 ing of the pitch circles, and the velocity ratio proportional to —^ As the surfaces of the teeth slide together, frictional resistance isproduced at their point of
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