Abstract
Rules for the type-synthesis of compound differential mechanisms are derived from the equation relating the angular velocities of the three shafts of a single differential. Compounds incorporating up to three differentials are synthesized and listed, but the method can be used for compounds of any order. The theory is illustrated by applications to bifurcated-power transmissions and to change-speed gearboxes of the Wilson type. It is shown that there are three distinct types of two-speed box and fourteen distinct types of three-speed box.

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