I think I understand SIE’s posted sketches, and have simplified it into the following:

The outer ring engages (such as with gear teeth) with the outer eccentric ring (as “slew” simply means “turn in place”, something all the rings in the machine do, I refer to the original drawing’s 2 “slew” rings as “eccentric” rings, since they don’t share the axis of the other 2 rings). The outer ring’s radius is about twice that of the inner ring (let’s say 2 m and 1 m). The inner ring engages with the inner eccentric ring. The inner and outer rings are connected, such as by a back plate, so that they turn together. The eccentric rings are not connected, and turn independently. A system of axles and/or bearings (not included in my sketch) allow the rings to rotate, but prevent their axes of rotation from moving.
The idea for how this machine can produce output work without input work is, as best I can surmise and summarize:
The inner eccentric ring (let’s assume the eccentric rings each mass about 10 kg) exerts a downward, counter-clockwise turning force on the inner ring of about 100 N. The outer ring exerts a downward, clockwise turning force on the outer ring of about 100 N. The joined outer and inner rings thus experience a net clockwise torque of

. Connected to an external work-consumer, such as an electrical generator, it’ll produce up to

per revolution. If allowed to turn at 1 revolution/s (60 RPM), it’ll produce up to 628 W power.
The flaw with this reasoning is that, for the axes of the eccentric rings to be prevented from moving, the net force vector on the rings must be zero. Because the downward force of gravity must originate from the rings center of mass, we aren’t free to choose to have all – or any – of the opposing force originating from the contact points of the rings and eccentric rings. Thus, the assumed downward force on the inner and outer rings due to the force of gravity on the eccentric rings is zero. No part of the machine accelerates or outputs work at all.
SIE appears to try to avoid this by having the system that prevents the axes of the eccentric rings from moving consist of a single “shepherd wheel” positioned such that it can’t exert force with a nonzero vertical component, reasoning that if the shepherd wheel can’t exert any vertical force, and the eccentric wheels’ axes don’t move, all of the vertical force must be exerted by the inner and outer rings originating at their contact points with their eccentric rings. This reasoning is flawed, however, because no possible force originating from these points can be equal and opposite to the force of gravity on the eccentric rings originating at their centers.
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