Modeling of the condyle elements within a biomechanical knee model

The development of a computational multibody knee model able to capture some of the fundamental properties of the human knee articulation is presented. This desideratum is reached by including the kinetics of the real knee articulation. The research question is whether an accurate modeling of the condyle contact in the knee will lead to reproduction of the complex combination of flexion/extension, abduction/adduction and tibial rotation ob-served in the real knee? The model is composed by two anatomic segments, the tibia and the femur, whose characteristics are functions of the geometric and anatomic properties of the real bones. The biomechanical model characterization is developed under the framework of multibody systems methodologies using Cartesian coordinates. The type of approach used in the proposed knee model is the joint surface contact conditions between ellipsoids, represent-ing the two femoral condyles, and points, representing the tibial plateau and the menisci. These elements are closely fitted to the actual knee geometry. This task is undertaken by con-sidering a parameter optimization process to replicate experimental data published in the lit-erature, namely that by Lafortune and his co-workers in 1992. Then, kinematic data in the form of flexion/extension patterns are imposed on the model corresponding to the stance phase of the human gait. From the results obtained, by performing several computational simulations, it can be observed that the knee model approximates the average secondary mo-tion patterns observed in the literature. Because the literature reports considerable inter-individual differences in the secondary motion patterns, the knee model presented here is also used to check whether it is possible to reproduce the observed differences with reasonable variations of bone shape parameters. This task is accomplished by a parameter study, in which the main variables that define the geometry of condyles are taken into account. It was observed that the data reveal a difference in secondary kinematics of the knee in flexion ver-sus extension. The likely explanation for this fact is the elastic component of the secondary motions created by the combination of joint forces and soft tissue deformations. The proposed knee model is, therefore, used to investigate whether this observed behavior can be explained by reasonable elastic deformations of the points representing the menisci in the model.Fundação para a Ciência e a Tecnologia (FCT) - PROPAFE – Design and Development of a Patello-Femoral Prosthesis (PTDC/EME-PME/67687/2006), DACHOR - Multibody Dynamics and Control of Hybrid Active Orthoses MIT-Pt/BSHHMS/0042/2008, BIOJOINTS - Development of advanced biological joint models for human locomotion biomechanics (PTDC/EME-PME/099764/2008)

A case study of inverse dynamics control of manipulators with passive joints

Manipulators with both active and passive joints are examples of underactuated systems, featured by less control inputs than degrees of freedom. Due to the underactuation, in the trajectory tracking (servo-constraint) problem, the feed-forward control obtained from an inverse model is influenced by internal dynamics of the system, leading to a more involved control design than in the fully actuated case. It is demonstrated that a convenient approach to the problem solution is to formulate the underactuated system dynamics in the input-output normal form, with the arising governing equations formulated either as ODEs (ordinary differential equations) or DAEs (differential-algebraic equations). The interrelationship between the inverse dynamics control and the associated internal dynamics is then studied and illustrated using a planar manipulator with two active and one passive joint. Some simulation results for the sample case study are reported

Analysis of servo-constraint problems for underactuated multibody systems

Underactuated multibody systems have fewer control inputs than degrees of freedom. In trajectory tracking control of such systems an accurate and efficient feedforward control is often necessary. For multibody systems feedforward control by model inversion can be designed using servo-constraints. So far servo-constraints have been mostly applied to differentially flat underactuated mechanical systems. Differentially flat systems can be inverted purely by algebraic manipulations and using a finite number of differentiations of the desired output trajectory. However, such algebraic solutions are often hard to find and therefore the servo-constraint approach provides an efficient and practical solution method. Recently first results on servo-constraint problems of non-flat underactuated multibody systems have been reported. Hereby additional dynamics arise, so-called internal dynamics, yielding a dynamical system as inverse model. In this paper the servo-constraint problem is analyzed for both, differentially flat and non-flat systems. Different arising important phenomena are demonstrated using two illustrative examples. Also strategies for the numerical solution of servo-constraint problems are discussed