The theory has been developed for the design of a new mechanical component: variable-ratio chain drives with noncircular sprockets and minimum slack. The theory is based on a kinematic correspondence between noncircular chain drives and noncircular gears. This in turn permits the development of an algorithm for minimizing chain slack. The theory is applicable to a wide range of mechanical equipment, including bicycles and nonuniform motion transmissions involving band drives, tape drives, and timing belts. Such drives may or may not require a tensioner, but if they do, tensioner displacement will be minimal. Numerical examples illustrate applications to the design of an optimum bicycle configuration and a harmonic-motion generator.

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