Response of a two-dimensional dynamic model of the human knee to the externally applied forces and moments

This paper is concerned with response of a two-dimensional dynamic model of the human knee to the externally applied forces and moments. The profiles of the articulating surfaces of a normal knee joint are determined from X-ray films and they are represented by polynomials. Ligaments of the joint are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion, coupled with nonlinear constraint conditions, are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads (force and moment) are applied to the tibia and subsequent motion is investigated. 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 presented.