For the first time, a closed-form analysis is presented for the time-varying operation of belt-drives. The analysis is developed as a perturbation away from the analysis of a steadily rotating belt-drive. The intent is to derive expressions for the span tensions, the pulley tension distributions, and the driven pulley angular velocity; and to document the existence of a lone slip zone for a belt-drive operating under time-varying conditions. A lone slip zone on the trailing edge of each pulley is well-known for steady operating conditions [Johnson, K.L., 1984],[Smith, D.P., 1999]. An alternative computational solution using an in-house finite element code is also presented, which demonstrates excellent agreement with the response quantities predicted by the analytical solution, and which also verifies the existence of a lone slip zone preceded by a stick zone.

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