This paper presents a unification of kinematic and torque balance methods for the analysis of two-input epicyclic-type transmission trains. A method for the derivation of the velocity ratio of an epicyclic gear train in a symbolic form is developed. A single kinematic equation is derived to study the kinematic characteristics of fundamental gear entities. The method relies on previous work on graph theory. It improves on existing techniques used for automatic transmission mechanisms in its ability to accurately solve the kinematics of geared mechanisms and estimating their velocity ratios and arranging them in a descending order in a simpler manner. The results are then used for assignment of the various links of a given two-input epicyclic gear mechanism. This study contributes to the development of a systematic methodology for the torque and power flow analyses of two-input epicyclic gear mechanisms with a reaction link, based upon the concept of fundamental circuit. Specifically, this study presents for the first time a complete design and analysis of two-input velocity changer to be used as a power coupling in a new generation of tandem bicycles. Two new designs are demonstrated.