円柱面上を移動する糸が描く曲線

When tension acts on a yarn running on a cylindrical bobbin, the yarn leaves for a new equilibrium position and draws a curve on its surface. In this paper, we assumed that the yarn was free to bend, but did not stretch and that its inertial force was negligible compared to the external forces such as reaction force and friction force. The force balance equations, which determined a yarn path contacting with a curved surface, were developed in vector form on the basis of differential geometry. We derived a set of differential equations describing the space curve drawn by the yarn traveling on the cylindrical surface. Two experiments were compared with the simulations. The measured yarn path and tension for two actual examples turned out that the parabola obtained by our simulation was a fairly good approximation for the yarn path sliding on a cylindrical surface