capstan_amplifie

capstan_amplifie - Capstan-a mechanical amplifier...

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Capstan—a mechanical amplifier F control τ ω r θ out F out v v control F F + Δ F Δ θ F normal A schematic diagram of a basic capstan and a force diagram for a small segment of the rope are shown in the figures. F normal = F sin θ /2 + (F+ F) sin θ /2 In the limit of small angles F normal = F d θ /2 + (F+dF) d θ /2 Mod. Sim. Dyn. Sys. page 1 Neville Hogan Photograph removed due to copyright restrictions.
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Assuming continuous slip and Coulomb friction between rope and drum, dF = μF normal = μ 2F+dF 2 d θ dF = F d θ or d ln F = μ d θ Integrating from 0 to θ F out = e μ θ F control Note that this relation is only valid if ω r v control From continuity: v control = v out Torque required of capstan drive: τ = (F out - F control ) r = (e μ θ -1) r F control Power dissipated: P dissipated = τ ω + F
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.141 taught by Professor Nevillehogan during the Fall '06 term at MIT.

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capstan_amplifie - Capstan-a mechanical amplifier...

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