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and
Machine Theory
Mechanism and Machine Theory 43 (2008) 661–675
ate/mechmt
Capstan equation including bending rigidity and
non-linear frictional behavior
Jae Ho Jung a, Ning Pan a,*, Tae Jin Kang b
a Division of Textile and Clothing, Department of Biological System Engineering, University of California, Davis, CA 95616, USA
b School of Materials Science and Engineering, Seoul National University, Seoul 151-742, South Korea
Received 20 March 2007; received in revised form 26 May 2007; accepted 9 June 2007
Available online 8 August 2007
Abstract
More rigorous analyses have been conducted in improving the classical capstan equation by including both the rod
bending rigidity and a power-law friction (in place of the Amonton’s law) into the formula. During the analyses, the
power-law exponent was used as the indicator for the non-linear friction behavior, whereas both the capstan radius ratio
and the ing load incline angle were used as the parameters reflecting the bending rigidity. Our analyses -
plex relationships those parameters have in influencing the tension ratio or tension transmitting efficiency, a thorough
parametric study illustrates clearly such interconnections. Since in most cases, the bending rigidity of the tension member
is non-negligible and non-linear friction is mon, the new results should be more useful in practical applications.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Capstan equation; Bending rigidity; Non-linear friction; Radius ratio; Load incline angle; Apparent and actual tension ratios
1. Introduction
A tensioned rod, film, fiber or fabric in contact with a circular shaped body is frequently seen in many
mechanical setups and applications. A well-known relationship governing the mechanism is the capstan equa-
tion [1], AKA Euler’s equation of tension transmission:
lh
T 1 ¼ T 0e ð1aÞ
where T1 and T0 is the outgoing and ing tensions, l is the frictional coefficient betwe