Articular surface approximation in equivalent spatial parallel mechanism models of the human knee joint: An experiment-based assessment

By generalizing a previous model proposed in the literature, a new spatial kinematic model of the knee joint passive motion is presented. The model is based on an equivalent spatial parallel mechanism which relies upon the assumption that fibers within the anterior cruciate ligament (ACL), the medial collateral ligament (MCL) and the posterior cruciate ligament (PCL) can be considered as isometric during the knee flexion in passive motion (virtually unloaded motion). The articular surfaces of femoral and tibial condyles are modelled as 3-D surfaces of general shapes. In particular, the paper presents the closure equations of the new mechanism both for surfaces represented by means of scalar equations that have the Cartesian coordinates of the points of the surface as variables and for surfaces represented in parametric form. An example of simulation is presented in the case both femoral condyles are modelled as ellipsoidal surfaces and tibial condyles as spherical surfaces. The results of the simulation are compared to those of the previous models and to measurements. The comparison confirms the expectation that a better approximation of the tibiofemoral condyle surfaces leads to a more accurate model of the knee passive motion.

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Displacement Analysis of the Human Knee Joint Based on the Spatial Kinematic Model by Using Vector Method

Acta Mechanica et Automatica ◽

10.1515/ama-2017-0050 ◽

2017 ◽

Vol 11 (4) ◽

pp. 322-327

Author(s):

Marta Góra-Maniowska ◽

Józef Knapczyk

Keyword(s):

Knee Joint ◽

Kinematic Model ◽

Spatial Displacement ◽

Vector Method ◽

Human Knee ◽

Planar Surfaces ◽

Articular Surfaces ◽

Human Knee Joint ◽

Spatial Parallel Mechanism ◽

Position Problem

AbstractKinematic model of the human knee joint, considered as one-degree-of-freedom spatial parallel mechanism, is used to analyse the spatial displacement of the femur with respect to the tibia. The articular surfaces of femoral and tibia condyles are modelled, based on selected references, as spherical and planar surfaces. The condyles are contacted in two points and are guided by three ligaments modelled as binary links with constant lengths. In particular, the mechanism position problem is solved by using the vector method. The obtained kinematic characteristics are adequate to the experimental results presented in the literature. Additionally, the screw displacements of relative motion in the knee joint model are determined.

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A COMPARISON AND REVIEW FOR MATHEMATICAL REPRESENTING OR FITTING TECHNIQUES TO ARTICULATING SURFACES AT THE HUMAN KNEE JOINT

Biomedical Engineering Applications Basis and Communications ◽

10.4015/s1016237203000377 ◽

2003 ◽

Vol 15 (06) ◽

pp. 249-253 ◽

Cited By ~ 1

Author(s):

XI-SHI WANG ◽

RUI-PU BAI

Keyword(s):

Knee Joint ◽

Articular Surface ◽

Experimental Measurements ◽

Surface Geometry ◽

Rehabilitation Engineering ◽

Human Knee ◽

Human Knee Joint ◽

Complicated Surface

The mathematical representing or fitting articular surface of the human knee joint based on the experimental measurements is very important for biomechanical studies and clinic rehabilitation engineering. But, so far this work still maintains a challenge due to the human knee joint exhibits a complicated surface geometry. In this paper, based on the literatures [1-17], a review and comparison on the techniques of the articular surface representing or fitting at the human knee joint are presented.

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