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Based on the linear complementarity formulation of a unilaterally inextensible wire model, the behavior of motion and stability of wire-suspended dynamical systems is addressed in this paper. The concept of tension properness is developed to determine kinematical motion property, particularly the instantaneous degrees-of-freedom. Further, motion determinacy in spite of tension indeterminacy is proven. The notion of tension closure is described to help analyze the stability behavior of wire-suspended dynamical systems. By analyzing the maximal closure-domain of relative tension closure, one can assess the stability behavior of wire-suspended systems qualitatively as well as somewhat quantitatively. Some numerical examples and simulations will clarify and corroborate the theoretical results of this paper.