@article{ref1,
title="Dynamic modelling of human articulating joints",
journal="Mathematical modelling",
year="1983",
author="Engin, Ali Erkan and Moeinzadeh, Manssour H.",
volume="4",
number="2",
pages="117-141",
abstract="Dynamic simulation of mechanical behavior and response of the total human body to external forces provide essential input for the injury prediction criteria and subsequent design and development of crash protection systems. The most sophisticated versions of the total-human-body models are articulated and multisegmented to simulate all the major articulating joints and segments of the human body. Effectiveness of the multisegmented models to predict accurately live human response depends heavily on the proper biomechanical description and simulation of the articulating joints. This paper is concerned with a mathematical modelling of an articulating joint defined by contact surfaces of two body segments which execute a relative dynamic motion within the constraints of ligament forces. Mathematical equations for the joint model are in the form of second-order nonlinear differential equations coupled with nonlinear algebraic constraint conditions. Differential equations of motion are reduced to a set of nonlinear simultaneous algebraic equations by applying the Newmark method of differential approximation. By subsequent application of Newton–Raphson iteration process the same equations are converted to a set of simultaneous linear algebraic equations. Iteration process is continued until a solution vector of unknowns satisfying a prescribed convergence criterion is obtained. The two-dimensional version of the mathematical joint model is applied to human knee joint for several dynamic loading conditions on tibia. Results for the ligament and contact forces, contact point locations between femur and tibia and the corresponding dynamic orientation of tibia with respect to femur are obtained.<p />",
language="",
issn="0270-0255",
doi="10.1016/0270-0255(83)90024-6",
url="http://dx.doi.org/10.1016/0270-0255(83)90024-6"
}