Modelling of a planar derailleur system on bicycles with experimental verification

Abstract

The major function of the derailleur system is to provide different speed ratios on a multi-speed bicycle. In this study, a mathematical model for the planar derailleur is developed. The planar positions of the guide pulley and the tension pulley at different speed ratios are determined by using geometrical and static analysis. The tension force on the chain in static state is also obtained from the mathematical model. The simulated results are compared to the experimental data at various speed ratios. The maximum error in chain length is about 2.25% between current model and calibrated data. It is found that the effective chain length is the key factor that affects the simulation results. The influence of two torsion spring to the derailleur system is also discussed in this paper. It is found that the value of the tension force is controlled by the spring constants, and two torsion spring's constant ratio affects the positions of the guide pulley and tension pulley directly.