Epicyclic Gear Train Solution Techniques with Application to Tandem Bicycling

Abstract

This thesis presents a unification of kinematic and force-based methods for the design and analysis of planetary gear trains along with a discussion of potential applications in tandem biking. Specifically, this thesis will provide a simple solution technique for the general case of a two-degree of freedom (2DOF) planetary gear train along with new graphical design aids. It will also address the use of epicyclic gear trains as a power coupling in a tandem bike. In the current literature, planetary gear trains are given a clear treatment with regard to the pure kinematics of the system, but little or no literature exists that includes the torques present in the system. By treating both the kinematics and torque balance of the most general case, this thesis attempts to fill a void in the current literature. After developing the solution to the general two-degree of freedom case using the Willis formula, a force analysis will be performed using the conservation of energy principle assuming zero losses. Once the total solution is known, nomographs will be presented as a simple design tool. These graphical aids enable the designer to simultaneously approximate both speeds and torques for the mechanism. After fully developing a satisfactory solution technique and design tools, these will be applied to the problem of coupling the power provided by the riders of a tandem bicycle.