Contact geometry of equidistant tubes

We consider equilibrium configurations of two flexible tubes arranged in space such that their centrelines are separated by a constant distance. Depending on their configuration, the two centrelines may exhibit single or double contact. We will discuss the contact geometry of one such configuration that exhibits double contact, called the orthogonal clasp, where the two centrelines are assumed to lie in orthogonal planes. Based on this example, we will motivate a “capstan” like equation governing tension decay along the centreline of a flexible tube wrapped around a rigid hook with friction.