Here's how to make a very simple one axis camera stabilizing gimbal.
The resulting footage is very much like the MotoGP gyro cam, with the horizon staying level and the bike (or plane) moving under the camera.
I'm using a 808 #16 keyring camera for my onboard footage, but this could work with a Mobius or Run Cam.
The base is heat-bent PVC plastic, the servo is a digital metal gear Corona DS939MG and the control board is a Naze 32.
The camera lens pivots in a hole in the PVC mount at the front and the camera is directly connected to the servo by a PVC bracket and small screw. The servo is mounted at the required height on soft foam using double sided tape.
This is designed as a stand alone camera mount and all it requires for power is 5V plugged into one of the unused servo positions. I run a servo lead from a spare channel on the receiver with the signal wire removed. Don't plug 12V in by mistake, bad smells will come from the Naze 32.
The camera servo is plugged into "Servo 0" pins. This is usually for the pitch servo, but I have the board turned 90 degrees to allow access to the mini USB port.
The Naze 32 is configured in Cleanflight as a gimbal. Watch the video below to see what selections are required. (Thanks to Painless 360 on YouTube for showing me how it's done)
Here are some onboard stills from my scratch built Tigermoth
Build overview and configuration instructions
I usually prefer unstabilized views that show the motion of the plane but this one axis stabilization is quite interesting.
Give it a go, it's an easy build. Keep it as light as possible so you can slap the mount on any plane. Mine weighs 58g all up.