12-01-2011, 04:05 PM
Christopher A. Corey
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.
Introduction
In the current literature available to engineers, planetary gear trains are given a clear treatment as far as a simple kinematic solution. Unfortunately, no publications to date present a simple, concise design and analysis technique that considers both the motion and forces present in a gear train in the general case. This thesis attempts to fill this void by presenting a technique for finding a total speed and force solution to an epicyclic gear train in the most general case possible. After developing this solution, nomographs will be used to create an intuitive design aid, allowing the designer to visualize the performance of a gear train without the need to solve equations repeatedly. Finally, the solution technique and design aids presented will be used to address the practicality of using planetary gear trains as a power coupling element in a new generation of tandem bicycles.
Motivation
The research contained herein was motivated by a design effort undertaken by the Virginia Tech Human Powered Vehicle Team in 2002. During the early design of the multi-rider entry into the annual ASME competition, it was suggested that the most effective method for coupling the relatively inconsistent inputs of two human riders would be to use a planetary gear train. The concept behind the design attempted by the human powered vehicle team was to use a gear train like the one shown in figure 1 to create a system that would allow both riders to pedal at approximately the same speed and contribute approximately the same percentage of the output power. The planetary system accommodates differences in speed and power input by the two riders. The nature of the system behavior is the focus of this.
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