Serrancoli, G.; Font-Llagunes, J.M.; Barjau, A. Proceedings of the Institution of Mechanical Engineers. Part K, journal of multi-body dynamics Vol. 228, num. 3, p. 241-11 DOI: 10.1177/1464419314530110 Date of publication: 2014-09-01 Journal article
The human body is an over-actuated multi-body system, as each joint degree of freedom can be controlled by more than one muscle. Solving the force-sharing problem (i.e. finding out how the resultant joint torque is shared among the muscles actuating that joint) calls for an optimization process where a cost function, representing the strategy followed by the central nervous system to activate muscles, is minimized. The main contribution of the present study has been the particular formulation of that cost function for the case of the pathological gait of a single subject suffering from anterior cruciate ligament rupture. Our hypothesis was that the central nervous system does not weight equally the muscles when trying to compensate for a lower limb injury during gait (in contrast to what is the usual practice for healthy gait where all muscles are weighted equally). This hypothesis is supported by the fact that muscle activity in injured individuals differs from that of healthy subjects. Different functions were tested until we finally came out with a cost function that was consistent with experimental electromyography measurements and inverse dynamics results for a subject suffering this particular pathology.
This article proposes a simple linear-by-part approach for perfectly elastic 3D multiple-point impacts in multibody systems with perfect constraints and no friction, applicable both to nonredundant and redundant cases (where the normal velocities of the contact points are not independent). The approach is based on a vibrational dynamical model, and uses the so called "independent contact space." Two different time and space scales are used. At the macroscale, the impact interval is negligible, and the overall system configuration is assumed to be constant. Consequently, the inertia and Jacobian matrices appearing in the formulation are also constant. The dynamics at the contact points is simulated through stiff springs undergoing very small deformations and generating system vibrations at the microscale. The total impact interval is split into phases, each corresponding to a constant set of compressed springs responsible for an elastic potential energy. For each phase, a reduced inertia matrix associated with a set of contact points, and a reduced stiffness matrix obtained from the potential energy (associated with all contact points undergoing compression) are introduced. From these matrices, a modal analysis is performed yielding an all-analytical solution within each phase. The main difference between the redundant and nonredundant cases concerns the inertia and stiffness matrices for modal analysis. While in the former case, both are related to the total set of contact points (total contact space), in the latter one they are related to two subsets: a subset of independent points for the inertia matrix (independent contact space), and the total set for the stiffness matrix. A second difference concerns the calculation of the normal impulses generated at each contact point. For the nonredundant case, they can be directly obtained from the total incremental normal velocities of the contact points through the inertia and stiffness matrices. For the redundant one, they can be obtained by adding up their incremental values at each impact phase. This requires an updating of a new effective stiffness matrix depending on the contact points undergoing compression at each phase. Four planar application cases are presented involving a single body and a multibody system colliding with a smooth ground.
Serrancoli, G.; Walter, J.P.; Kinney, A.L.; Barjau, A.; Fregly, B.J.; Font-Llagunes, J.M. Reunión del Capítulo Español de la Sociedad Europea de Biomecánica p. 1 Presentation's date: 2013-10-24 Presentation of work at congresses
Two approaches are used when studying impact problems: impulsive ones and compliant ones. In an
impulsive approach, the time interval where the collision takes place is considered to be negligible, and so
the system configuration is assumed to be constant. The final mechanical state of the colliding system is
obtained directly from the initial one through algebraic equations and energy dissipation assumptions. In a
compliant approach, the colliding surfaces are modelled through springs and dampers (usually nonlinear),
and the equations of motion are integrated during the impact time interval to obtain the final state.
Though both approaches have been widely used in the field of biomechanics, no comparative study can
be found in the literature that could justify choosing one or another. In this paper, we present both
approaches and compare them when applied to two examples related to gait problems: a passive walker
and a simple model of crutch locomotion. We will show that the results are really close whenever
nonsliding conditions are assumed at the impact points.
Vincent, G.; Barjau, A.; Kaelig, C.; Etienne, B. Physical review E, statistical physics, plasmas, fluids, and related interdisciplinary topics Vol. 67, p. 006660-9 DOI: 10.1103/PhysRevE.67.066609 Date of publication: 2003-06 Journal article
Barjau, A.; Gibiat, V.; Chareyron, D. FORUM ACUSTICUM Sevilla 2002. 3rd. European Congress on Acoustics XXXIII SPANISH CONGRESS ON ACOUSTICS-Tecniacústica 2002 p. 1-6 Presentation of work at congresses