764 Budynas-Nisbett:Shigley's Ill Design of Mechanical 15.Bevel and Worm Gears The McGraw-Hill Mechanical Engineering Elements Companies,2008 Design,Eighth Edition Bevel and Worm Gears 767 Figure 15-2 Circular pitch Cutting spiral-gear teeth on the Face advance basic crown rock. Mean radius of crown rack Spira angle Basic crown rack Figure 15-3 Hypoid gears.(Courtesy of Gleason Works,Rochester, N.YJ It is frequently desirable,as in the case of automotive differential applications,to have gearing similar to bevel gears but with the shafts offset.Such gears are called hypoid gears, because their pitch surfaces are hyperboloids of revolution.The tooth action between such gears is a combination of rolling and sliding along a straight line and has much in common with that of worm gears.Figure 15-3 shows a pair of hypoid gears in mesh. Figure 15-4 is included to assist in the classification of spiral bevel gearing.It is seen that the hypoid gear has a relatively small shaft offset.For larger offsets,the pinion begins to resemble a tapered worm and the set is then called spiroid gearing.Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 15. Bevel and Worm Gears 764 © The McGraw−Hill Companies, 2008 Bevel and Worm Gears 767 Basic crown rack Cutter radius Spiral angle Mean radius of crown rack Circular pitch Face advance Figure 15–2 Cutting spiral-gear teeth on the basic crown rack. Figure 15–3 Hypoid gears. (Courtesy of Gleason Works, Rochester, N.Y.) It is frequently desirable, as in the case of automotive differential applications, to have gearing similar to bevel gears but with the shafts offset. Such gears are called hypoid gears, because their pitch surfaces are hyperboloids of revolution. The tooth action between such gears is a combination of rolling and sliding along a straight line and has much in common with that of worm gears. Figure 15–3 shows a pair of hypoid gears in mesh. Figure 15–4 is included to assist in the classification of spiral bevel gearing. It is seen that the hypoid gear has a relatively small shaft offset. For larger offsets, the pinion begins to resemble a tapered worm and the set is then called spiroid gearing.