How It Works

This is not completed. I like to add some pictures. I also would like to fully understand how the syncro works:

From Wikipedia:

Generel
Under one possible design, the transmission's input shaft has just one pinion gear, which drives the countershaft1. Along the countershaft are mounted gears of various sizes, which rotate when the input shaft rotates. These gears correspond to the forward speeds and reverse. Each of the forward gears on the countershaft is permanently meshed with a corresponding gear on the output shaft. However, these driven gears are not rigidly attached to the output shaft: although the shaft runs through them, they spin independently of it, which is made possible by bearings in their hubs. Reverse is typically implemented differently, see the section on Reverse.

Reverse
The previous discussion applies to the forward gears. The implementation of the reverse gear is usually different, implemented in the following way to reduce the cost of the transmission. Reverse is also a pair of gears: one gear on the countershaft and one on the output shaft. However, whereas all the forward gears are always meshed together, there is a gap between the reverse gears. Moreover, they are both attached to their shafts: neither one rotates freely about the shaft. What happens when reverse is selected is that a small gear, called an idler gear or reverse idler, is slid between them. The idler has teeth which mesh with both gears, and thus it couples these gears together and reverses the direction of rotation without changing the gear ratio.

Syncromesh

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