. . . Albert Potter, an American watchmaker, famously designed a twelve second tourbillon with a lever escapement. There is also a carriage-less tourbillon design by A. H. Benoit. It's a pretty funky design; the lower pivot of the balance staff in the Benoit design is in a bearing fitted to the upper pivot of the escape wheel (in other words, the escape wheel and balance are co-axial with each other; the balance above and 'scape wheel below.) The balance vibrates in the usual fashion and as it does so, it also rotates with the escape wheel, revolving once for every revolution of the escape wheel. According to George Daniels the design has 15 teeth and in an 18k vph movement will turn once every six seconds. Daniels notes that the design at first blush seems perfect, as there is no cage inertia to overcome.
However (and perhaps this is the problem Mr Klings ran into, or one of them at least) the problem is that the escape wheel is unlocked by the balance spring which can only happen when the balance is oscillating at full amplitude (if I understand that section of the chapter on tourbillons correctly.) If there is even a tiny reduction in energy of the balance, the escape wheel will fail to unlock and the watch will stop.
It's a very cool idea though
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Jack