Remote Controlled Basket Ball
I think revision 6 will be my final stage of this project.  This last revision includes an all metal gearhigh torque steering servo, custom designed servo saver, 2.5Ghz radio system and geard motor drive for higher speeds.  All RC components including the gyro and ESC are available at your local hobby shop.  All robotics such as aluminum hubs, shafts, bearings, gear motor, servos, mounts, screws etc are available at servocity.com.
Here is a sketch blueprint of the ball. 
This is the aluminum hub attached to the centerline of the bottom of the ball.
Here's a pic looking the other way.
This is the chassis.  You can make it out of one piec of Aluminum if you prefer.  This 3/4" flat stock is all I had.
There's a good pic of the gear reduction drive motor.  The pins sticking out of the hub are sanded down screws.  Those fit in the hub attached to the ball above.
You can see the steering pivot bearing under the ESC.  The radio receiver is to the right.
The round gold piece is the eflight gyro. You can see the Hitec Steering servo.  That one got stripped so I replaced it with a HS-645MG all metal high torque servo.
Click Here to see a
VIDEO
of the gyro in action
It's hard to see but the drive rotational bearing is right here. -->
It's the same type as the steering one.
Here is the robotics mounted in the ball.  It doesn't take any specialty tools it just twists together.

There's the whole chassis ready to go.
Now for the steering arm.  It's basically a piece of 3/4" flat steel bent in a U shape.  The battery pack is attached to the bottom of the U and I put lead weights on the sides for more drive torque.  On the left you see the shaft that goes through the side via a bearing.  That's part of the servo saver I designed. 
There's the bearing for the servo saver..
That's the lever for the servo saver.
There's the steering arm attached to the chassis with the servo saver.
Click here to see a
VIDEO
of the servo saver in action.
There it is inside the ball. On this end I made a steel bar that attaches to the ball with bolts.  It has a perpendicular shaft bolted to in down the centerline that slides into the drive rotational bearing.
I cut a REAL basketball in half, filled it with foam and hollowed it out so the hamster ball will fit inside. 
Here's a picture of the final product.
VIDEOS OF THIS BALL IN ACTION
Video of  remote controlled BASKETBALL -- good speed
Video of  remote controlled Hamster Ball  -- good speed
Video of  remote controlled BASKETBALL -- Motor is TOO FAST
Video of remote controlled BASKETBALL agility
Video of remote controlled Hamster Ball -- Motor is TOO FAST
Click Here if You Would Like to See The Previous 5 revisions of this ball
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If you have any questions please feel free to email me at prabbit22m@aol.com