The center of gravity of the shell starts coincident with the center of gravity of Earth. So as long as the shell keeps its integrity, and the center of mass o

The center of gravity of the shell starts coincident with the center of gravity of Earth. So as long as the shell keeps its integrity, and the center of mass of the Earth is inside the spherical shell, it is effectively unattached to the Earth by gravity. Let's also assume that the first round of robot-building made the Earth a perfectly smooth ellipsoid. So now you have a spherical shell on a spherical planet, standing on trillions of robot wheels. All the robots sync up, and do some math, and at the same millisecond mark, start turning their wheels. So the shell starts spinning faster than Earth. Its increase in angular momentum is subtracted from Earth's angular momentum. The robots now have to link arms pretty tightly to keep their wheels in contact with the surface. They connect to each other with cables of adjustable length. Escape velocity at Earth's surface is about 11.2 km/s. That's not practical due to atmospheric drag. Even a stable orbit at 200 km altitude requires 7.8 km/s. So the shell runs as fast as it can in air. Then all the robots simultaneously jettison their legs and spool out their cables, and the whole thing jumps in altitude. Now they start sacrificing. The robots nearest the spin axis twist as hard as they can on their own cables, slowing their own spin and increasing that of the remaining robots in the shell. Then they let go and drop back to Earth. The next opposing rings of robots do the same. Eventually, you reach a point where a spherical ring section of the shell is spinning fast enough to keep the linkages under a reasonable amount of tension, entirely outside the atmosphere. Now each robot deploys a solar sail, and angles it to accelerate the ring towards the winter end of Earth's axis, until Earth gravity starts pulling it back. Then the sails tack, and start pushing in the opposite direction. It's like pumping your legs on a playground swing. Eventually, the entire ring achieves Earth-escape velocity and flies off. Then you repeat with a new shell. [Edit:] Actually, let's make the shell an ellipsoid with greater eccentricity than the Earth during the spin-up phase. The robots nearest the poles can therefore keep running with wheels on the surface until their arms get torn off. Then the polar discs get sacrificed.