Does technical lingo confuse you? If so, welcome to the bevel gear sector and its special kind of hell. The same “system” that benefited from standard geometry books for “straight” and “spiral” configurations can veer off into any number of other shaft arrangements to suit machine designers’ wildest ideas.
The initial high-volume use of straight bevel gears was in automotive rear axle assemblies. The Model T Ford was manufactured in — until then — unheard of numbers; it used a straight bevel gear “final drive” with straight bevel differential gears. A simple, yet compact and efficient right-angle system with intersecting shafts. Noise was not an issue and neither was compactness or ground clearance; cars were expected to be loud and roads looked like something a modern four-wheel drive truck would avoid. With a whopping 25 horsepower on tap, the gears were not severely loaded. It is doubtful that lengthwise crowning of the tooth flanks — “Coniflex” in Gleason-speak — was ever specified.
Customer expectations had changed by the late 1920s and Ford responded with the Model A. The more powerful 40 horsepower motor was faster and the final drive was upgraded to a spiral bevel gear set; the differential gears remained straight bevels. Still on intersecting shaft because ground clearance could not be reduced. Outside of major metropolitan areas, the spring mud had not gone away and the ruts remained deep.
It was not long before road conditions improved and reduced ground clearance and lower centers of gravity became topics of discussion amongst enthusiasts. Expensive cars started to move to hypoid final drives — “Gleason speak” for non-intersecting shafts where the pinion shaft axis is below the output gear centerline.
Industrial, construction, and off-road vehicle designers were very creative in their use of bevel gears. Angular (non-90 degree) shaft angles permitted all sorts of innovations, especially when combined with a non-intersecting arrangement. Large machines that originally made straight bevels could now be set up to produce “skew” gear sets that packaged up like the higher cost hypoids — and without the need for new capital investment.
It is easy to understand why so many great gear engineers enjoyed working in the bevel gear business. It was a relatively simple idea that developed into a complex array of products that allowed machine designers to confidently let their imaginations roam. Aspiring gear people should not be put off by this apparent complexity; do your homework, learn the buzzwords, and trust the system.