In Chapter 11, the kinematic relationships and factors that must be considered in designing straight-toothed or spur gears were presented. Several specialized forms of gears exist. We now deal with the three principal types of nonspur gearing: helical, worm, and bevel gears.* The geometry of these different types of gearing is considerably more complicated than for spur gears (see Figure 11.1). However, much of the discussion of the previous chapter applies equally well to the present chapter. Therefore, the treatment here of nonspur gears is relatively brief. As noted in Section11.9, the reader should consult the American Gear Manufacturing Association (AGMA) standards for more information when faced with a real design problem involving gearing.

Helical, bevel, and worm gears can meet specific geometric or strength requirements that cannot be obtained from spur gears. Helical gears are very similar to spur gears. They have teeth that lie in helical paths on the cylinders instead of teeth parallel to the shaft axis. Bevel gears, with straight or spiral teeth cut on cones, can be employed to transmit motion between intersecting shafts. A worm gearset, consisting of screw meshing with a gear, can be used to obtain a large reduction in speed. The analysis of power screw force components, to be discussed in Section 15.3, also applies to worm gears. By noting that the thread angle of a screw corresponds to the pressure angle of the worm, expressions of the basic definitions and efficiency of power screws are directly used for a wormset in Sections 12.9 and 12.11.