Capstan equation for strings with rigidity

Abstract

The effect of string rigidity on the capstan equation is considered. Two cases which cover the most likely situations are distinguished - contact of the string with the peg at a point, and contact over an arc. The analysis of these situations is facilitated by an approximation derived for the curvature for the leads of string on either side of the peg. If the friction is governed by Amontons' law the correction of the capstan equation for string rigidity will usually be small, but in the case of arc contact and load-dependent coefficient of friction, the correction could be important.