ABSTRACTmThis paper presents the results of an investigation evaluating the forces present in a statically loaded bicycle chain prior to and beyond sprocket engagement. Comparisons are made with previous investigations that have been limited to industrial chains and sprockets. The chain drive system for a bicycle differs from the industrial standard types not only in its size but in its operation. A high degree of lateral flexibility is required in the bicycle chain for it to operate with noncoplanar sprockets having an effective misalignment of 3 deg or more. The experimental analysis in this paper considers chain loads for a range of sprocket sizes and angles of misalignment. Results indicate that localized bending arising from misalignment between chain and sprocket can increase or decrease the strain on the side plates by a substantial fraction of the direct strain due to chain tension. The work presented here is part of a more general study of bicycle chain efficiency for competition applications.KEY WORDS--Bicycle chain, bicycle sprocket, strain gage, mechanicsIn conjunction with Hans Renold's bush roller chain patented in 1880, the English bicycle manufacturer Starley became the first to produce what would become known as the "safety bicycle." The advantages of using the chain as a drive system quick!y became apparent, and the fundamental engineering details of the chain have remained essentially unchanged to this day. Two further inventions allowed the chain to become even more useful for the bicyclist. The first of these, a bushingless chain, permitted lateral flexibility, allowing the chain to run on a series of parallel sprockets of different sizes. The second was the derailleur gear mechanism, which shifts the chain between these sprockets. As part of a program of experiments investigating the efficiency of the bicycle chain, it was decided to analyze the forces experienced by a link as it approaches and then engages a driving sprocket in an effort to locate where some of the efficiency losses occur.The wide range of applications for industrial chains has yielded a substantial literature over the past 20 years or so, the major proportion of which relates more to chain application and durability than fundamental analysis of forces and transmission efficiency. Industrial chains tend to operate under more favorable conditions than their bicycle counterparts (e.g., coplanar sprockets, enclosed lubrication and steadystate running), thereby resulting in higher transmission efficiencies; hence, the need for such detailed analysis has not been great. However, another factor in this bias is the undoubted complexity in analyzing the basic mechanics of operation of a modern chain drive system.The distribution of chain load from tight to slack side depends fundamentally on the size of the sprocket, the amount of chain wrapped around it, the tooth pressure angle and the materials used. Much of the founding work on chain and sprocket mechanics was developed by Binder 1 in 1956. This classical work analyzes the dist...
The paper presents a kinematic analysis of a two-degree-of-freedom (2-DOF) steering mechanism based on the Ackermann principle and of a type found in rigid-axle vehicles. Using an iterative approach to solve the equations of constraint, major features of the mechanism are investigated, e.g. sensitivity to geometry changes, steering errors induced by axle displacement, motion and force transmission functions. This approach enables the performance and characteristics of the proposed mechanism to be assessed easily and quickly, and a case study is given of a light agricultural tractor.
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