Frictional Interaction of a Spiral Rope and a Cylinder – 3D-Generalization of the Euler-Eytelwein Formula Considering Pitch

Abstract

Historically, following e.g. Holzer (2005) the problem of the definition of frictional rope forces appearing in a rope sliding over a cylinder has been formulated in the dissertation of Gautier (1717). The solution of this problem was reported by Euler in his Remarks on the effect of friction on equilibrium published by the Berlin Academy of science, see Euler (1769). Since the first time publishing the Euler solution by Eytelwein (1808) in his Handbuch der Statik fester Körper in 1808 the problem is spread through practical applications and became known as Euler-Eytelwein problem in standard books of technical mechanics see e.g. in Gross et.al. (2004), and is also known as belt or coil friction formula see e.g. in Maurer and Roark (1944), or as capstan friction problem, see e.g. in Meriam (1978).