Research on the mapping models and designing methods of variable-ratio chain/belt drives

Based on Cesaroʹs approach in differential geometry, the continuous and discrete mapping models are established in this paper, which are effectively applied to study of the pitch curves, the velocity-ratio function, the rolling characteristic and the “polygon” effect, etc. in the variable-ratio chain/belt drives. Some important conclusions are obtained. Several numerical examples are given at the end of the paper.