First New Bit...

In finest bottom up design methods, I'm starting at the end and working my way forwards. The nicely rendered bit above is the output shaft for the reversing box. It'll sit coaxially with the input shaft (hence the big hole in the middle) and can be driven two ways. The first (and most common) way will be for dogs to engage in the slots on the front and drive the output shaft directly. These dogs will be on a sliding collar splined to the input shaft. In this fashion there will be a non-geared direct connection between engine and output shaft.

The second way will be for a gear to turn the output shaft. If we take the drive from the input shaft via a pair of gears to a layshaft and then via two extra gears to the gear on the output shaft then we'll reverse the direction of travel of the output shaft relative to the input shaft and hey presto - reverse gear. Now given that bike engines tend to major more on power (by virtue of stratospheric rev limits) than torque, a degree of speed reduction (and hence torque multiplication) might well be a good thing as the driver won't need to necessarily slip the clutch mightily to get the thing moving in reverse.

Now for all this to work with a minimum of nasty mechanical graunching noises, all the gears will have to be in constant mesh. This will mean that the gear on the input shaft must float and only be connected when we want reverse gear. If we use the other end of the sliding collar to do the connect then we have a workable design. Everything else is metallurgy and calculations...