A new approach to geometrically nonlinear analysis of double cable system with a movable guide pulley

Double cable system (DCS) with a movable guide pulley (MGP) is a common component in many mechanical equipment. It is difficult to calculate the unstressed length of cable under a preload, and the form-finding analysis after obtaining the unstressed length. To solve this problem, a method of establishing double-layer nonlinear equations for calculating the unstressed length of cable under a given preload is proposed. For the inner single cable, a new cable element is presented based on Hermite interpolation. Later, initial cable form is obtained by approximating catenary as a three-point parabola, and the initial values for the nonlinear equations are derived. For the outer double cable, unstressed length is a descriptive variable of the DCS. In view of the constraints on a single cable posed by the guide pulleys, corresponding constraint equations are obtained by introducing the angle of rotation of the MGP, which is a process variable. Under a given preload at an end of single cable, equations for the DCS with a MGP are constructed. Moreover, the tangent stiffness matrixes are derived for quick solution, and unstressed length for the DCS is obtained. On this basis, by changing the partial constraint equations of the DCS, the form-finding analysis of the cable can be achieved. A few numerical examples and comparisons demonstrate the reliability of the proposed new approach for geometrically nonlinear analysis of cables.