A Short Story on Long Pinions

The design of automotive transmissions with multiple planetary gear sets leads to various interesting mathematical problems. Once a powerflow with favorable characteristics is established, there are many ways in which it can be mechanized. Factors such as manufacturability, packaging, availability of common component sets, etc., determine the selections leading to the final physical layout of a transmission. Several manufacturers use “long pinions” as building block elements in the design. This is an interesting architectural arrangement that combines certain packaging and functional attributes. In the present article, the algebraic use of the long pinion is demonstrated in the creation of vastly different transmission architectures from the same powerflow.