Kristopher, are you sure about all that? I think you're close, but not quite.
The Allan Herschell Looper has a wheel that runs behind the tub, connected to the tub axle by way of a rider-controlled clutch. The rider operates the clutch by either operating a small foot pedal, or possibly by locking the clutch with a small lever under the grab bar intended to lock the tub for loading and unloading. I rode one of those at Enchanted Village (now Six Flags) in Washington. That's where I learned that if possible, you should balance the tub!
Where my recollection of that ride differs from Kristopher's is that in the Looper, the riders are secured by a wide belt clamped down on the outboard side of the car. I wouldn't call it a lap bar, as it is stiff, but flexible.
I've never ridden a Rok 'N Roll, but if I remember correctly, the tub axle extends inboard past the dress panel and has a pneumatic tire inboard of that panel which at points around the ride rolls on a track to force the tubs to rotate. There is no rider-controlled clutch. Not sure how riders are secured, but I thought it was a belt similar to that used on the Looper.
--Dave Althoff, Jr.