What is the shifting principle of gearbox?

As we know, the automobile engine can reach the best state at a certain speed, when the power is relatively large and the fuel economy is relatively good. Therefore, we hope that the engine will always work in the best condition. However, cars need to have different speeds when they are used, which creates contradictions. This contradiction should be solved by transmission. The function of automobile transmission can be summarized in one sentence, which is called speed change and torque change, that is, speed increase and torque decrease or speed decrease and torque increase. Why can deceleration increase the twist, while the growth rate should be reduced? Assuming that the power output by the engine is constant, the power can be expressed as N = wT, where w is the rotational speed and t is the torque. When n is fixed, w is inversely proportional to t, so the growth rate will decrease and the deceleration will increase. According to the principle of variable speed and torque, the gear transmission of automobile transmission is divided into different gears corresponding to different transmission ratios to adapt to different working conditions. A general manual transmission is equipped with an input shaft, an intermediate shaft and an output shaft, also known as a three-shaft type, and a reverse shaft. Three-axis transmission is the main structure. The rotational speed of the input shaft is also the rotational speed of the engine, while the rotational speed of the output shaft is the rotational speed generated by the meshing of different gears between the intermediate shaft and the output shaft. Different gear meshes have different transmission ratios, so they have different rotational speeds.