Use of Burmester’s Circular Theory in the Determination of the Optimal Four-Bar Link Reproducing Actual Tibia-Femur Relative Motion

The paper presents an application of Burmester’s circular theory to the determination of the optimal mechanism used to reproduce the motion of the tibia with respect to the femur. The research takes its start from the idea of studying an external fixator to guide the motion of a tibia in a way physically compatible to the actual patient’s anatomy, in order to firmly guide the two bones after, for instance, joint reconstructive surgery, while avoiding any contact between the articular surfaces. The physiological data were determined in researches presented in other papers. However, in the initial research phases the idea was to determine the best position of an existing four-bar link, produced for an orthopaedic tutor, without any attempt at synthesising an ad hoc one. The idea of using Burmester’s theory in this operation was in reality an old one, but previous attempts were not successful. Naturally, the required four-bar link had also to be small in order to fit on the external fixator. The results of the research are extremely satisfactory, since it was possible to determine a mechanism which allows relative motion with errors in the order of fractions of millimetres, when the imposed motion had to keep the two bones separated by a minimum of one millimetre. As a consequence the two bones will never go in compression, while a gentle pulling of the ligaments will always be present. Using the approach, typical four-bar links for different human typologies were also determined.