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Kinematic Analysis of an 8-Speed Bicycle Transmission Hub

A transmission hub is a speed changing mechanism which is an important device in the transmission system of bicycles. This paper presents the kinematic analysis of an 8-speed bicycle transmission hub by using the fundamental circuit method. First, a distributed-flow type planetary gear mechanism, which consists of two parallel-connected transmission units and one differential unit, and the corresponding clutch sequence table of an 8-speed transmission hub are introduced. Based on the fundamental circuits, four kinematic equations of the transmission hub are derived. Then, the speed ratio of each speed is formulated, which is a function of gear ratios of external and internal gear pairs. By submitting the numbers of gear teeth into these formulas, the value of speed ratio at each speed can be calculated. Finally, the power-flow diagrams at related speeds are presented to illustrate the power-flow paths of the transmission hub.