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One of the spatial external fixators, which can provide six degrees of freedom, three rotations and three translations, in handling extremity fractures and deformity-correction cases, is the so-called Gough-Stewart Platform Mechanism with six adjustable bars and two platforms. A mathematical model is developed for an effective deployment of the apparatus in orthopaedic processes. The model basically accepts input radiographic and clinical data and provides the bar lengths under several conditions and possibilities systematically studied, on the one hand, and predicts the behavior of the fixator assembly as to the guiding of the bone fragments in a controlled fashion determined by the treatment strategy, on the other. Numerical examples are presented to verify the model.

In handling the kinematic analysis of two rigid bodies connected to each other by six legs through the use of six double spherical joints, methods have been implemented both in the formulation and solution phases of the problem. A three-dimensional problem has been viewed, in fact, as a multitude of two-dimensional works on several planes, the intersections of which yield relationships allowing transition between adjacent planes. Thus formulation is purely based on the geometric structure consisting of eight planes of interest, ending in the three fundamental equations involving three angles between the base and side triangular planes. In solving the resulting three equations, an efficient strategy has been established to come up with 16 solution sets effectively. Extensions of the theory have been shown to include the analyses of other Stewart platform models. Efficiency and effectiveness of the approach has been verified on numerical examples.

In the field of orthopaedics, treatment of extremity deformities can be realised by means of external fixators. However, control of such biomedical system is very difficult. Some different mathematical models have been developed to improve quality of this service. Most of the parameters, which are used in these models, have been obtained from two orthogonal X-ray images: one from anteroposterior, AP, direction and the other from a lateral, L, direction. The quality of the results of this model is dependent on the accuracy of the input parameters. Measuring these parameters is a time-consuming issue, and the accuracy of the results is also low. To increase the quality of the measurement, the reference points should be chosen from the edges of the biomedical system, and it is important to find the edges without noise. To achieve this purpose, Sobel edge detector, binary large object analysis, thresholding and inverting are applied as image processing steps. The results are compared with manual measurement values which have been obtained earlier. The results show that semi-automatic measurement of the parameters is more accurate and faster than manual measurement. It shows that the efficiency of the fixator method has been improved.

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