how does a semi automatic gearbox on a bike work?

Answer 1

The transmission gears shift the same on both types.
The automatic has the same type clutch.
On the automatic, instead of using a clutch lever to disengage the clutch, the shift shaft linkage operates it.
The major difference between the two types, is the automatic has an additional clutch (centrifugal clutch).
It looks like a drum brake of a car - instead of brake shoes it has clutch shoes.
The drum spins freely on the crankshaft.
When it turns, it turns the regular clutch, which turns the transmission gears and then the rear wheel.
The shoes are turned by the crankshaft.
When the engine speeds up, centrifugal force spreads the shoes apart and grab the drum of the centrifugal clutch.
Which then turns the regular clutch - transmission gears - rear wheel.
Shift it like a regular bike to go through the gears, except no clutch lever is needed.

Answer 2

How Does A Gearbox Work