Yes, raised V is neccessary, still angular momentum and RKE only increase at re-extending, because of the increasing MoI term which is subject to R^2 multiplicator. And right, without applying any torque from the outside, that's the real importance of it. "The wheel's own inner force must come into being, without external momentum being applied"..basically, by switching our 'inertia' terms between that of rest mass for linear and MoI for angular, we're not just switching momentum terms but also energy terms.
After the first input stroke on the right hand side, we leave that corner with a raised V and if we don't extend on the straight, we enter the left hand corner with the same amount of momentum and KE we had upon leaving the right hand corner..
..but if we do extend on the straight, then we enter the left side corner with more angular momentum and RKE than we had upon leaving the right hand corner.
So we're 'creating' angular momentum and RKE merely by extending on the straight - without applying torque, or, thus, counter torque! We just 'magic' it from nowhere by flipping the 'inertia' component of both fields, from rest mass, to MoI.
This seems really exciting..
Another interesting point...
If we consider the inertial brake which has the capacity to continuously slow down anything attached to it by periodically performing the "extending to infinite radius" trick... Then where the momentum goes? It's lost to... To basically nowhere. It's simply lost via inertial interactions. A hardcore physicist would possibly theorize Higgs-field or space-time, etc. But the real interesting point: If somebody manage to reverse this process by a "retracting through an infinite radius" trick, then it would mean that momentum simply comes into being, essentially from nowhere. That would be extraordinary... I am also thinking about this for several years by now.
Is it not possible to design the straight line path to be vertical (in gravity field) or tangential to slightly below 3 o'clock? Just an idea.As for gravity, i've considered your suggestion already, but haven't (yet) found a promising trajectory that can be constrained to the Robernoster itself - if we retract at 12 o' clock, we'd need to extend again before entering the corner. Entering the corner at full extension seems to be a necessary condition.
Yeah, I know how much a pain that can be! :DThe only reason i gave up on such designs was their computational complexity in terms of simulation - the key problem the Robernoster was intended to solve, insofar as involving no collisions or friction. One full cycle of a simulated paternoster can take many hours to complete, if at all, half the time bugging out due to collision errors, either spontaneously exploding, or else the belt / chain falling through the wheels / sprockets. Just try making a sprocket and chain assembly and you'll see what i mean..
I have a simple pulley simulation with formulas in all the main orientations. I attach it for you, perhaps it can help at something... It can be also put into a rotational frame, pulleys riding a main wheel. In that case the formulas need to be corrected with the main wheels rotation, but it's possible. There are formulas for the connecting points to the pulley and for the rods/ropes too. You can also use rigid changing length rods on this type of pulley. It's not always easy to mess around with these, but check it out if you like.