When we cannot even agree how to pronounce “helical” it should not be a surprise that there is so much confusion about “proper” limits on helix angles. [Those of you saying “Heel-lik-al” need to stop it right now. “Hell-lik-al” is the only correct way to say it according to me.] Helix angles are a frequent topic for “Ask the Expert” questions, so it seems worthwhile to use this blog to combat some of the misinformation floating about. If I miss any of your favorite heresies, please let me know. In the beginning, whenever and wherever that was, someone made a spur gear. It was wonderfully simple, just some pegs pounded into a piece of log, but it multiplied the available power. All too soon, people got more power so the pegs were turned into planks, but even those were not strong enough; so the gears became metal. Then life got faster and the neighbors started to complain about noise. So the gear folks set to arguing about the shape and the depth of the teeth in an effort to appease the complainers. Someone suggested that the noise was caused by the load transferring from one tooth to the next; let’s put the teeth at an angle to the shaft axis so that sound goes away. Almost immediately the arguments started over how much of an angle was needed. Physics, always lurking at the edge of the crowd, chose that moment to remind that his [or her] laws had to be obeyed. “If you want to use my wonderful angles, you have to take the thrust force that comes with it. And since that thrust force is not located at the center of the shaft, it will appear as an overturning moment to vex your machinery.” But at least one of the engineers had been semi-conscious in physics class; something about “equal and opposite” forces came to mind. They would just make their new gears in two halves with opposite angles so those nasty thrust forces and overturning moments cancelled each other out. It was a brilliant solution. So the gear people went back to arguing over how much angle was needed, what shape the teeth should have, and what this new invention should be called. Multiple “inventors” applied for patents in the hope that their name would forever be associated with this advancement. As always, problems cropped up. Making teeth at an angle required new tools and machines. Accounting complained about the extra cost. One kind of noise went down, but other sounds were detected. Getting things to completely cancel out was more difficult than they thought. Apexes started wandering. The two halves of the gear did not always wear equally. There had to be a better solution than having to make two gears instead of one…