Ignore for a moment the horrid material attached to this rendering as Solidworks does a poor job with plastic.
Green represents the robot chassis and how each wheel assembly may be mounted.
Red represents the variable pivot mechanism. This doesn't presume to explain how the pivot happens -- but one could use sprocket and chain, gears, rack and pinion, or a cam to achieve the required roll.
Blue represents the drivetrain. The small blue shaft is the input to the bevel gear driving the semi-spherical "wheel".
The wheel, as it were, is not a full hemisphere. The pivot point passes through the center of the sphere and thus, a full half sphere would have interfered. It represents at its largest a wheel of 8" diameter and, at its smallest, a point that has no diameter.