From a small bicycle, discard the front wheel, replace the
handlebars with a fixed handle to hold onto and then move
the seat back so the centre of mass is under the remaining
(rear) wheel. Keep the one wheel, the seat, the pedals,
and enough of the frame to connect them together.
Mount two
spinning gyroscopes on gimbals, with a normally
vertical spin axis.
One gyroscope (A) has gimbals that normally prevent
tilting left or right relative to the vehicle, but allow tilting
backwards and forward. This is used to prevent the the
vehicle leaning left or right - if there's torque trying to
push it over, instead you get precession tilting the gyro
forwards or backwards.
The other gyroscope (B) has gimbals that normally prevent
tilting forward or back relative to the vehicle, but allow
tilting left and right. This is used to prevent the the
vehicle leaning forward or back - if there's torque trying to
push it over, instead you get precession tilting the gyro left
or right.
Also if the active stabilisation system needs to make the
vehicle lean left or right, it can apply torque between the
gyro (A) and the vehicle, as if to tilt one forward and one
back. But due to precession, (A) tilts left or right, making
the vehicle lean left or right, and (B) prevents the vehicle
from leaning forward or back, instead (B) tilts left or right.
Similarly, the active stabilisation system can make the
vehicle lean forward or back when it needs to by applying
torque to (B)
If you've been leaning left too much, the (A) gyroscope
may be off level, so the active stabilisation system makes
you lean right for a bit until they go back to level.
Similarly, it can correct for too much leaning right,
forwards, or backwards.
Batteries power the gyroscopes and the active stabilisation
system, so if they are charged you can turn it on and wait
for it to be stable before you get on. A generator powered
from the pedals or wheel recharges the batteries. When
the batteries have plenty of charge you can also power the
drive wheel, otherwise you have to pedal to move.
I'm not sure about turning. There could be handlebar
control that turns the wheel against another gyroscope,
but if you keep making left turns and there was any
friction on the ground resisting turning, eventually the
gyroscope precession would build up and the active
stabilisation couldn't do much about it except try to get
you to turn right instead. Otherwise when you lean the
vehicle left or right, the curve of the wheel makes you
turn, but it might not be the right amount. Or you could
drag your foot on one side to turn.
If you want to be able to lean left and right, e.g. for a
turn, you can unlock the normally locked gimbal on
gyroscope (A), so that the bike can tilt left and right
without tilting the gyro. Similarly you can unlock (B) to
lean forward or back for acceleration and braking.
Note you can also shift your weight relative to the vehicle,
so you can lean back while braking without the vehicle also
needing to lean back.
After you dismount you can leave the gyro stabilisers on
while you transport it upright on its wheel, then turn it off
once you've finished. It folds down smaller when not in
use.