The mechanics of belt friction revisited

A new insight into the mechanics of belt friction is given. A conceptual and methodological drawback in the presentation of the classical derivation of the force required to pull the belt over a fixed drum against the hold-force and the friction between the belt and a drum is pointed out, corrected and discussed. The total forces due to pressure and friction (P and F ) are evaluated in magnitude and direction. It is shown that not only the local friction force is proportional to the local pressure (f = μp), but also their resultants (F = μP ), where μ is the coefficient of static friction. The magnitude of the pressure force is P = FR/(1 + μ), where FR is the magnitude of the resultant of the pulland hold-forces applied at two ends of the belt. Different methodological approaches to the analysis are presented, which are particularly appealing from the educational point of view. These include the local and integral equilibrium considerations, the virtual work approach, and the dimensional analysis.