A Mathematical Model in the Implementation of a Stewart-Gough Platform as an External Fixator

In orthopedical practice, simple classical devices like rods, pins and hinges are widely used to deal with orthopedical disorders. However, these simple-looking tools complicate the pre-operative planning in removing such disorders as bone misalignments in connection with the extremity fracture and deformity cases. Thus, a novel approach is needed to take this burden off the orthopedist. In this work, a simplified procedure is proposed, in which a robotic frame is initially fixated easily at first to the fracture site and then fine-tuning in the alignment is done after processing medical input data within the framework of a mathematical model of the system. The robotic frame considered here is the so-called (6-6) type of Stewart-Gough Platform that consists of two platforms to which proximal and distal fragments are attached by means of six adjustable legs through the six spherical and six universal joints. Here, a mathematical model is developed to transform the medical input data obtained from antero-posterior (AP) and lateral (L) X-ray films and clinical examination into appropriate leg lengths required for the alignment process. To validate the mathematical model, the process is demonstrated on an example involving a specially designed and manufactured model of Stewart-Gough platform of (3-3) type as an external fixator and a physical model containing synthetic bone fragments.