Lanchester's Hypothesis

 
Mr. Lanchester proposed the completely different arrangement shown to the right. His aim was to avoid the engage-disengage procedure by using an all-geared, constantly enmeshed, full-fledged differential. But to satisfy the specification given in the Sung Shih many "misprints" (e.g. number of gears, total number of teeth) have to be assumed.

Another problem would be accuracy: It is left as an exercise to the reader to calculate the directional deviation resulting from a mismatch of only one percent in the diameters of the road wheels.
(click for details)
top view

The function is described as follows:

The gears A, A1 fixed to the road-wheels engage with horizontal intermediate wheels B, B1 (extended to B2), but these are now so arranged as to be permanently in gear with an upper and a lower bevelled wheel C1, C, the upper one of which is concentric with the shaft carrying the pointing figure but is not fixed to it. Between them run two small idling wheels D, D1 connected by a stub-shaft E from the centre of which rises up at right angles the shaft F carrying the pointing figure. Relative motions of the road-wheels will now be accurately, and inversely, reflected in the movements of the idling wheels and the pointer which they carry.

If, for instance, the left-hand road-wheel moves faster than the right, as on a westward turn, B will move while B1, B2 will be almost stationary, and C will be turning while C1 will be almost at rest. Hence D, D1 will react to precisely the same extent but in the opposite direction. They will then stay put, though C, C1 will resume their mutually opposite regular motion until further relative change of the road-wheel velocities occurs.
 

Source: Needham. Joseph: Science and Civilization in China, Volume 4, Part II, 1965