Very often, to describe the motion of a particular mechanism, a term such as gear ratio is used. What is it and what is its essence, let's try to figure it out now.
Each mechanism is characterized by the presence of an input and output shaft and, accordingly, input and output parameters, which, in particular, include interconnected rotational speed and angular velocity. The motor is always connected at the beginning of each device and transmits the movement to the input shaft. This shaft is also called the leading one, since then motion is transmitted through it to the mechanism as a whole and the output (driven) shaft in particular. In this case, the angular velocity of the shaft at the output changes either its value, or direction, or both. Therefore, to determine the relationship or change the rotation characteristics of the driven and drive shafts, the concept of interest to us was once introduced.
Thus, it can be argued that the gear ratio for any mechanical device can be found by dividing the final angular velocity by the initial one. Given the existing direct relationship between the characteristics of the movement of the shaft, the desired ratio is likewise found through the known values of the shaft rotation frequencies. Since the division of the same values is carried out, the found parameter will not have dimensions.
The gear ratio is determined not only for elementary gears, but also for more complex devices. These, in particular, include gearboxes, multi-stage gearboxes. This is where the peculiarities of calculations arise. We will dwell on the latest devices in more detail.
The gear ratio of the gearbox will depend on the number of stages. If it includes only one gear, then it is enough to simply calculate the desired value for it as for a simple device in order to achieve its goal. If there are several stages, then the general gear ratio can be determined by multiplying the gear ratios of all stages or by dividing the angular velocity of the shaft at the inlet of the gearbox by the angular velocity at its output. You can also use the knowledge of torque. To do this, find the ratio of the output and input. If it is more than one, then the gearbox is called up, if less - down. Whatever method you choose for your calculations, in all cases the same numerical value should be obtained. You can verify the correctness of your calculations using all of the above methods.
The gear ratio of the gear is also determined in various ways. In addition to the above, you can also use the knowledge of the number of teeth on the drive and driven wheels. To do this, it is enough to find the ratio of the last value and the first. Sometimes in the literature, the gear ratio is calculated in a similar way , while it is noted that it cannot be less than one. Recently, however, these concepts have merged, and in many modern textbooks on the course "Machine Details", it is precisely the ratio that is calculated in this way, not just the number. This, apparently, is correct, since they actually reflect the same thing: how the input and output transmission parameters change, although initially it did not matter to determine the relationship whether the output parameter is divided by the output parameter or vice versa.
Many use gear ratio to solve the inverse problem. For example, if we know this characteristic of the mechanism and its input angular velocity, then to find the output it will be enough to multiply the named parameters by each other.
I hope that the information you read made it possible to fill in some gaps in your knowledge, and you can use it when performing various engineering calculations.