Cross-Over of Rope Around Drum in Multi-Layer

Abstract Cross-over of rope wound on a drum in multi-layers, is analyzed by means of differential geometry and variational principle with movable boundaries. As a geometrically nonlinear problem of the linearly elastic rope, centerline of cross-over of rope is treated as a space curve, which is constrained by surface of the rope of the lower layer. Considering the parameters of the constraining surface, the bending energy of the cross-over and the virtual work of the non-conservative tensile force are obtained. Thereby the Euler equation of the variational problem is obtained, and is changed into an implicit form. Finally the expression for the centerline of the cross-over is formulated. An experiment is made to measure the central angle of the cross-over and the data are compared with the calculated value.