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It is a well-known result in engineering statics that the tensions TA and TB at the ends of a rope or belt wra?
It is a well-known result in engineering statics that the tensions TA and TB at the ends of a rope or belt wrapped round a capstan are related by
TB = TA e^ (µ ß)
where µ is the coefficient of friction between rope and capstan, and ß is the angle of wrap.
This is generally derived for a cylindrical capstan. Prove that it also applies to other smooth cross-sectional shapes.
Any smooth cross-section can be considered as combination of many cylindrical cross-sections.
Let the angle of wraps between consecutive cylindrical cross-sections be ß1, ß2, ß3 etc.
Then TB = TA e^(µ ß1) * e^(µ ß2) * ...
= TA e^[µ (ß1 + ß2 + ...)]
= TA e^(µ ß)
where ß is the total angle of wrap.
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Teac X-1000RBL Capstan Belt Shift under Normal Operation