DESIGN OF THE OPTIMIZED GEOMETRIC CONFIGURATION OF A DERAILLEUR FOR GEAR SHIFTING THROUGH A CHAIN ON A BICYCLE’S CHAINWHEEL

Abstract

The chain and derailleur both are important components in a sprocket-driven transmission system. However, some factors such as force applied, force direction, and geometric configuration of a derailleur, which drew scant attention in design of a conventional sprocket. Generally, short yaw of chain link and scarcity of derailleur force induce the chain to straddle on a target sprocket, even make engaged links drop to original one. Thus, gear shifting would be failure. In fact, the proper force applied and direction will contribute to mitigate lateral forces and tensile forces applied on chain links, accelerate the process of chain shifts, extend the service life of chain and sprockets, and reduce vibrations or noises in the process of gear shifting, even improve the efficiency of chain shifts. The purpose of the geometric design for derailleur is to derive an optimal profile that the minimum force applied on. Base on above, all contact points in the optimal trajectory are not linear arrangement between derailleur and chain. In this paper, the optimal geometric configuration of derailleur is formed by employing difference theory of quazi-dynamic equilibrium for transmission chain as the optimal path is derived.