The mathematical approach presented allows main features of kinematics and force transfer in the loaded natural tibiofemoral joint (TFJ) or in loaded knee endoprostheses with asymmetric condyles to be deduced from the spatial curvature morphology of the articulating surfaces. The mathematical considerations provide the theoretical background for the development of total knee replacements (TKR) which closely reproduce biomechanical features of the natural TFJ. The model demonstrates that in flexion/extension such kinematic features as centrodes or slip ratios can be implemented in distinct curvature designs of the contact trajectories in such a way that they conform to the kinematics of the natural TFJ in close approximation. Especially the natural roll back in the stance phase during gait can be reproduced. Any external compressive force system, applied to the TFJ or the TKR, produces two joint reaction forces which - when applying screw theory - represent a force wrench. It consists of a force featuring a distinct spatial location of its line and a torque parallel to it. The dependence of the geometrical configuration of the force wrench on flexion angle, lateral/medial distribution of the joint forces, and design of the slopes of the tuberculum intercondylare is calculated. The mathematical considerations give strong hints about TKR design and show how main biomechanical features of the natural TFJ can be reproduced.
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Spinal biomechanics is still known just fragmentary since the only description by angle-torque characteristics without simultaneous recording of migration of the instantaneous helical axis (IHA) is not sufficient. Time-dependent flexion/extension following a cyclic laterally directed torque was measured at all six degrees of freedom by a highly precise custom-made 6D apparatus. In order to enhance the localizing resolution of IHA migration as the function of the flexional/extensional angle, small ranges of motion (ROM) were used at several degrees of pre-extension. 4 L3/L4, 3 L4/L5 and 2 T2/T3 human segments were investigated. In extensional motion, wide dorsal IHA-migrations were measured in lumbar segments and correlated with the distinct asymmetric shapes of the characteristics in extensional motion. The respective increase of differential stiffness could mainly be traced back to the enlarging geometrical moment of inertia of the segments by the dorsally migrating IHA. Both thoracic segments showed a predominant IHA-migration in cranial/caudal direction. A simple model makes it evident that the opposite curvature morphology of lumbar and thoracic joint facets conditions the different directions of IHA migration.
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