Derivation of the stiffness terms for a multi-cable spreader suspension system with stiff elastic cables

At its simplest a multi-cable spreader suspension system consists of a rectangular spreader suspended below a rectangular trolley by four cables of equal length. These four cables are attached to the corners of the spreader and when the system is in its undisturbed configuration they are all vertical, and consequently parallel. If we insist that all the cables are inextensible and remain taut then in the case of combined translation and rotation of the spreader this is not a well defined problem because it represents an over-determined system. In fact, if the cables are inextensible then one of them will go slack in the case of combined translational and rotational motions. As an alternative approach we can assume that the cables stretch slightly and this is the modelling strategy adopted here. That is, in this paper we present the initial development of an analytical model of a multi-cable spreader suspension system where the four cables are approximated by linear elastic cables of high stiffness K. To be more specific, we derive the fundamentally all-important stiffness terms in the equations of motion for the above problem.