Why can't gears have less than 17 teeth? What would happen if they were missing?

Gears are a widely used spare part in daily life, whether it is used in aviation, cargo ships, automobiles, and so on. However, there are requirements for the number of teeth in the design and processing of gears. Some people say that if it is less than 17 teeth, it cannot rotate, while others say it is wrong. Gears with less than 17 teeth are common. Actually, these statements are all correct. Do you know why? Welcome to leave a message for discussion. Why is it 17? And not other numbers? As for 17, we need to start with the machining method of gears, as shown in the figure below. 

A widely used method is to use a rolling cutter to cut. When the number of teeth is small, root cutting occurs, which affects the strength of the manufactured gear. What is root cutting? It means the root has been cut. Pay attention to the red box in the picture:

When the intersection point between the tooth tip of the gear and the meshing line exceeds the limit meshing point of the gear being cut, a part of the involute profile of the tooth root of the gear being cut is cut off, which is called root cutting.

So under what circumstances can root cutting be avoided? The answer is this 17 (when the tooth crest height coefficient is 1 and the pressure angle is 20 degrees).

Firstly, the reason why gears can rotate is because a good transmission relationship needs to be formed between the upper and lower gears. Only when the connection between the two is in place, can its operation be a smooth relationship. For example, when it comes to involute gears, good meshing between two gears is necessary to fully utilize their function, which can be further divided into two types: spur cylindrical gears and helical cylindrical gears.

The coefficient of tooth crest height for a standard spur gear is one, the coefficient of tooth heel height is 1.25, and its pressure angle degree needs to reach 20 degrees. When machining gears, if the tooth blank and the tool are like two gears.

If the number of teeth in the embryo is less than a specific value, the root of the tooth will be partially excavated, which is called root cutting. If the root cutting is too small, it will affect the strength and stability of the gear. The 17 mentioned here are for gears. If we don't talk about the efficiency of gears, they will work and operate regardless of how many teeth they have.

In addition, 17 is a prime number, which means that a certain tooth of a gear has the least number of overlaps with other gears at a certain number of turns, and will not remain at this point for a long time when subjected to force. Gears are precision instruments, and although errors may occur on each gear, the probability of wheel axle wear caused by 17 is too high. Therefore, if it is 17, it is okay to move for a while in the short term, but not in the long term.