A Real-Time Algorithm for Computing the Tension Force in a Suspended Elastic Sagging Cable

An algorithm is presented for computing the tension in an elastic cable subject to sagging under its own weight, a problem highly relevant in tethered systems such as cable-driven parallel robots. This requires solving the two coupled equations of the Irvine cable model, which give the endpoint position as a function of vertical and horizontal components of tension. Via a change of variables, we reformulate this system as a pair of uncoupled equations, which are shown to have a unique solution. We develop an efficient numerical procedure to solve one of these, after which closed-form formulas provide the solution of the second equation and ultimately the tension components.