Mechanics question ;-) Forces on wheels…

[JaXanim]

You need to consider the moment of each force at the fulcrum in each scenario. The moment is the product of the force applied and the distance from the fulcrum.
In the catherine wheel, each jet produces the same moment, so if the radius of the wheel is 'r' and the thrust/force is 'f', then the total moment is 4fr.
In the other case, the moment of each jet varies according to its position relative to the fulcrum. The range is between 2fr and zero per jet. So in the rolling wheel case the jets have twice the turning moment when located at the top and zero moment at the bottom. Assuming no other losses, the net turning force remains the same in each scenario.

JaX

[JaXanim]

Hodgkinson wrote:
It seems unusual that simply by omitting the virtual connecting rod and placing the wheel directly on the ground that, from each of the rockets producing a constant moment that suddenly we find that the rockets passing nearest the ground have little effect on the motion of the wheel, whereas those positioned furthest away have the greatest effect.

The lower jet still has moment about the centre (as they all do), but that would only be apparent if the contact between the wheel and the ground were less than 100% efficient. In other words, if the wheel could slip due to low frictional contact, then it would tend to skid round and tend towards the free catherine Wheel motion. You can visualise the work done by each jet in driving the wheel by plotting the locus of the point as the wheel rolls. I believe you'll see a sine curve - or is it series of semi-circles(?).
(work = force x distance travelled)

JaX