The programmable hexapod: Historical perspective, theoretical basis and relevance to orthopaedic practice

The Gough-Stewart platform (GSP) is a variable strut, programmable octahedral hexapod that uses six computer-controlled linear actuators to support a moveable base. These devices have been developed for a wide range of commercial uses including flight and vehicle simulators, high-precision tools, mining machines and medical instruments including programmable external fixators. The prototype hexapod external was introduced in France in 1986 and improvements in component design and computer algorithms have broadened the clinical repertoire of these devices. An increase in the number of available systems is expected in the next 18 months, owing to the expanding indications for this technology, in addition to termination of long standing patent arrangements and the associated commercial imperatives. These versatile platforms have clinical applications in acute fracture fixation; deformity surgery and limb salvage and provide an attractive combination of flexibility and ease of application. Contemporary orthopaedic practice is illustrated by two-dimensional radiological images, presented in standard anteroposterior and medio-lateral orthogonal planes. These are simplified ‘two axis’ representations of complex three-dimensional objects. It would not be possible to use an automated device to predictably reconstruct a deformed bone without the ability to mathematically describe the positions of the individual components. Pythagoras (c.570 BCE – c.495 BCE) and Euclid (c.300 BCE) are credited with defining the fundamentals of 2D and 3D geometry, and this was refined by Appolonius (c.262 BCE – c. 190 BCE), who anticipated Cartesian geometry by 1800 years. Pappus (c. A.D. 290 – c. 350) introduced a formalised approach to this area of mathematics and described a form of geometry that was not based on the concept of distance. This began with the study of the relationship between points and lines in 2D space and developed into the discipline of projective geometry. The introduction of realism in art in the Italian Renaissance relied on …