Physics
Planetary gearbox
Sun, planets, ring and carrier: three members turn and one equation binds them, so holding a different member gives a different ratio out of the same wheels - reduction, overdrive, reversal.
What happens
Sun, planets, ring and carrier: three members can turn and one equation binds them, so the train has no ratio at all until something is held. Hold the ring and the same wheels reduce fourfold; hold the sun and they give an overdrive; hold the carrier and the output reverses - which is why an automatic gearbox is one set of iron selected by brake bands rather than by moving anything. Let everything go and the two degrees of freedom remain: that is a differential, and the panel says so instead of printing a number. The ring's tooth count follows from the geometry rather than being chosen, and when the planets cannot be spaced evenly the panel says that too.
Equations used in the module
Equations ω_sun N_sun + ω_ring N_ring = (N_sun + N_ring) ω_carrier N_ring = N_sun + 2 N_planet ring held: i = 1 + N_ring / N_sun
