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Separating the study of kinematic geometry of the human knee from the study of its behaviour under load provides insight into the complex relationship between form and function at the joint. The development of a three-dimensional mathematical model which examines the mobility and stability of the joint in sequence is described in this thesis. A previously proposed model of knee mobility, in which the ligaments and ar- ticular surfaces act as rigid constraints between the bones in a single degree-of- freedom spatial mechanism, was re-examined and its limitations addressed. A new geometric-numerical approach to solving the model kinematics, capable of handling both idealised and more anatomical representations of the articular surfaces, was developed. A database of specimen-specific motion and geometry was established, based on cadaver studies. Articular contact kinematics and ligament length patterns were also quantified. In experiment, all components of passive knee movement were found to be coupled to the flexion angle, providing justification for the underlying concept of the model of knee mobility. Specimen-specific models of mobility were successful in predicting the main fea- tures of passive knee motion through a full range of flexion. Incorporation of second order tibial articular surfaces permitted the prediction of physiological motion com- patible with more realistic contact point movement. Through incorporation of continuous three-dimensional arrays of extensible lig- ament fibres, a preliminary model of knee stability was formulated. Although in need of further refinement, sample predictions of joint behaviour during a/p drawer and axial rotation have demonstrated the potential of the model in highlighting the subtleties of ligament mechanics. It was concluded that the sequential approach is appropriate for the study of joint behaviour in three dimensions and that, based on the success of the analogous two-dimensional theory, it provides an invaluable tool in the study of joint mechanics in activity and in the design and assessment of surgical procedures for treating knee injury and disease.

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Graduation date: 1998

Energy absorption mechanisms have been investigated intensively for the past decades by various authors and institutions, and numerous articles and other literature sources are available in print, as well as on the Internet. Energy absorbers and crashworthiness structures are two main research components in the energy absorption field under investigation today. In this research geometric changes are introduced on Al 6063-T6 circular tubes in the form of horizontal and spiral grooves to asses their influence on energy absorption characteristics. The horizontal and spiral grooves were cut into the tube to a cut depth of half the wall thickness of the tubes. The pitch was varied for both the horizontal and spiral grooves, while the cut width was kept constant. A specially designed static impact sleeve was used to compress the test specimens axially in an Instron 250 kN universal hydraulic testing system. Load vs. displacement graphs were generated from the captured experimental data for the uncut, horizontal and spiral grooved tubes. Energy vs. displacement graphs were created from the experimental data. The final deformed tubes were visually examined to determine the effect the geometric change had on the circular tube form, as well as the deformation pattern of the crushed tube. A Finite Element Method model is presented for each of the experimentally investigated tube impact models. A two dimensional (2D) model for the uncut as well as horizontally grooved tube is generated and analysed using a quasi static loading approach. Non-linear material properties are assigned to the model, and the Riks algorithm is used to model the non-linear post buckling behaviour of the various tubes. The results from the FEM analysis are used to generate load vs. displacement and energy vs. displacement graphs that are compared with the experimental data. Three dimensional (3D) FEM models of the normal, spiral and horizontal cut tubes were also generated in a CAD environment. A dynamic explicit non-linear analysis was done for each of the models to determine the reaction force and energy output values of each of the models. All analyses extend into the plastic material domain. Reaction force vs. displacement and energy vs. displacement graphs are generated from these analyses. A comparison is made between the numerically and experimentally determined gradients of the energy vs. displacement graphs of each of the tubes investigated. This forms the basis for an energy absorber design with application in the transport industry. Unique geometric imperfections were investigated experimentally and numerically for aluminium tubes. A lower buckling load than that for the normal tubes was achieved with the introduction of these geometric imperfections. New deformation patterns on tubes with imperfections not previously observed were described and analysed extensively. The load vs displacement graphs showed a constant increase in the load for the spiral grooved tubes. From the comparison between the numerically and experimentally investigated geometric imperfections a design guide line was esthablished and used in the conceptual design of an energy absorber for the automotive industry. / Prof. L. Pretorius Prof. R.F. Laubscher