A Critical Study of Cottenden et al.'s An Analytical Model of the Motion of a Conformable Sheet Over a General Convex Surface in the Presence of Frictional Coupling

TL;DR

This paper critically examines Cottenden et al.'s model, showing it derives the capstan equation and is unsuitable for calculating skin-fabric friction due to tissue deformability, challenging its practical application.

Contribution

It clarifies the limitations of belt-friction models in biological contexts and emphasizes the need for models accounting for tissue deformability in skin-fabric friction analysis.

Findings

The capstan equation is derived from a specific dynamic membrane model.

Belt-friction models are inappropriate for in-vivo skin-fabric friction estimation.

Deformable soft tissue affects force measurements, leading to overestimated friction coefficients.

Abstract

In our analysis, we show that what Cottenden et al. accomplish is the derivation of the ordinary capstan equation, and a solution to a dynamic membrane with both a zero-Poisson's ratio and a zero-mass density on a rigid right-circular cone. The authors states that the capstan equation holds true for an elastic obstacle, and thus, it can be used to calculate the coefficient of friction between human skin and fabrics. However, using data that we gathered from human trials, we show that this claim cannot be substantiated as it is unwise to use the capstan equation (i.e. belt-friction models in general) to calculate the friction between in-vivo skin and fabrics. This is due to the fact that such models assume a rigid foundation, while human soft-tissue is deformable, and thus, a portion of the applied force to the fabric is expended on deforming the soft-tissue, which in turn leads to the illusion of a higher coefficient of friction when using belt-friction models.