Using matrix algebra, a mathematical model is formulated for a particular type of external fixator with wires (system developed by Ilizarov) for the treatment of bone fractures. The mathematical model is used to give a linear estimate of the stiffness under lateral and axial loads in a representative number of practical conditions. Relative displacements of the bone ends at the fracture site are calculated not only in the common case of a gap, but also for various angles of inclined sliding contact; in this case, a realistic load is applied and nonlinear stiffening of the wires under transversal loads is iteratively taken into account.

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