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The description of the human knee as four-bar linkage

Dathe H., Gezzi R., Fiedler Ch., Kubein-Meesenburg D., Nägerl H.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 4

107--115

EN

Purpose: We investigate the dependence of the kinematics of the human knee on its anatomy. The idea of describing the kinematics of the knee in the sagittal plane using four-bar linkage is almost as old as kinematics as an independent discipline. We start with a comparison of known four-bar linkage constructions. We then focus on the model by H. Nägerl which is applicable under form closure. Methods: We use geometry and analysis as the mathematical methods. The relevant geometrical parameters of the knee will be determined on the basis of the dimensions of the four-bar linkage. This leads to a system of nonlinear equations. Results: The four-bar linkage will be calculated from the limits of the constructively accessible parameters by means of a quadratic approximation. Conclusions: By adapting these requirements to the dimensions of the human knee, it will be possible to obtain valuable indications for the design of an endoprosthesis which imitates the kinematics of the natural knee.

2

Characteristic points and cycles in planar kinematics with application to the human gait

Dathe H., Gezzi R., Kubein-Meesenburg D., Nägerl H.

Acta of Bioengineering and Biomechanics

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2015

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Vol. 17, no. 1

75--86

EN

Purpose: We present a novel method to process kinematical data typically coming from measurements of joints. This method will be illustrated through two examples. Methods: We adopt theoretical kinematics together with the principle of least action. We use motion and inverse motion for describing the whole experimental situation theoretically. Results: By using the principle of least action, the data contain information about inherent reference points, which we call characteristic points. These points are unique for direct and inverse motion. They may be viewed as centers of the fixed and moving reference systems. The respective actions of these characteristic points are analytically calculated. The sum of these actions defines the kinematical action. This sum is by design independent of the choice of reference system. The minimality of the kinematical action can be used again to select numerically one representative cycle in empirically given, approximately periodic motions. Finally, we illustrate the theoretical approach making use of two examples worked out, hinge movement and the sagittal component of the movement of a human leg during gait. Conclusions: This approach enables automatic cycle choices for evaluating large databases in order to compare and to distinguish empirically given movements. The procedure can be extended to three dimensional movements.

3

Mathematical study on the guidance of the tibiofemoral joint as theoretical background for total knee replacements

Fiedler Ch., Gezzi R., Frosch K.-H., Wachowski M. M., Kubein-Meesenburg D., Dörner J., Fanghänel J., Nägerl H.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 4

37-49

EN

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.

4

Construction-conditioned rollback in total knee replacement: fluoroscopic results

Wachowski M. M., Fiedler C., Walde T. A., Balcarek P., Schuttrumpf J. P., Frosch S., Frosch K. H., Fanganel J., Gezzi R., Kubein-Meesenburg D., Nägerl H.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 3

35-42

EN

Firstly, the way of implementing approximatively the initial rollback of the natural tibiofemoral joint (TFJ) in a total knee replacement (AEQUOS G1 TKR) is discussed. By configuration of the curvatures of the medial and lateral articulating surfaces a cam gear mechanism with positive drive can be installed, which works under force closure of the femoral and tibial surfaces. Briefly the geometric design features in flexion/extension are described and construction-conditioned kinematical and functional properties that arise are discussed. Due to a positive drive of the cam gear under the force closure during the stance phase of gait the articulating surfaces predominantly roll. As a result of rolling, a sliding friction is avoided, thus the resistance to motion is reduced during the stance phase. Secondly, in vivo fluoroscopic measurements of the patella tendon angle during flexion/extension are presented. The patella tendon angle/ knee flexion angle characteristic and the kinematic profile in trend were similar to those observed in the native knee during gait (0°–60°).