Miguel T. Silva

A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems

This paper presents and discusses the results obtained from a parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. The main purpose of this work is to analyze the influence of the variables that affect the violation of constraints, chiefly the values of the Baumgarte parameters, the integration method, the time step and the quality of the initial conditions for the positions. In the sequel of this process the formulation of the rigid multibody systems is reviewed. The generalized Cartesian coordinates are selected as the variables to describe the bodies’ degrees of freedom. The formulation of the equations of motion uses the Newton-Euler approach that is augmented with the constraint equations that lead to a set of differential algebraic equations. Furthermore, the main issues related to the stabilization of the violation of constraints based on the Baumgarte approach are revised. Special attention is also given to some techniques that help in the selection process of the values of the Baumgarte parameters, namely those based on the Taylor’s series and Laplace transform technique. Finally, a slider crank mechanism with eccentricity is considered as an example of application in order to illustrated how the violation of constraints can be affected by different factors such as the Baumgarte parameters, integrator, time step and initial guesses.© 2009 ASME

A new wheel–rail contact model for railway dynamics

The guidance of railway vehicles is determined by a complex interaction between the wheels and rails, which requires a detailed characterization of the contact mechanism in order to permit a correct analysis of the dynamic behavior. The kinematics of guidance of the wheelsets is based on the wheels and rails geometries. The movement of the wheelsets along the rails is characterized by a complex contact with relative motions on the longitudinal and lateral directions and relative rotations of the wheels with respect to the rails. A generic wheel–rail contact detection formulation is presented here in order to determine online the contact points, even for the most general three-dimensional motion of the wheelset. This formulation also allows the study of lead and lag flange contact scenarios, both fundamental for the analysis of potential derailments or for the study of the dynamic behavior in the presence of switches. The methodology is used in conjunction with a general geometric description of the track, which includes the representation of the rails’ spatial geometry and irregularities. In this work, the tangential creep forces and moments that develop in the wheel–rail contact area are evaluated using alternatively the Kalker linear theory, the Heuristic nonlinear model or the Polach formulation. The discussion on the benefits and drawbacks of these methodologies is supported by an application to the dynamic analysis of the bogie of the railway vehicle.

Technical developments of functional electrical stimulation to correct drop foot: Sensing, actuation and control strategies

This work presents a review on the technological advancements over the last decades of functional electrical stimulation based neuroprostheses to correct drop foot. Functional electrical stimulation is a technique that has been put into practice for several years now, and has been shown to functionally restore and rehabilitate individuals with movement disorders, such as stroke, multiple sclerosis and traumatic brain injury, among others. The purpose of this technical review is to bring together information from a variety of sources and shed light on the fields most important challenges, to help in identifying new research directions. The review covers the main causes of drop foot and its associated gait implications, along with several functional electrical stimulation-based neuroprostheses used to correct it, developed within academia and currently available in the market. These systems are thoroughly analyzed and discussed with particular emphasis on actuation, sensing and control of open- and closed-loop architectures. In the last part of this work, recommendations on future research directions are suggested.

Analysis of Human Gait Based on Multibody Formulations and Optimization Tools

Abstract Human gait involves complex interaction mechanisms within the human body or with the environment as a result of variable conditions associated to different human activities. Such complexity is evident when trying to describe the characteristics of motor control and coordination exercised by the nervous system on the lower extremities of the human body during gait, under both normal and neuropathological conditions. The purpose of this work is to elucidate the neurological mechanisms that govern human locomotion under such conditions, using an inverse dynamic analysis methodology applied to 3D biomechanical models of the human body, developed on the basis of multibody formulations and optimization tools. The redundant biomechanical problem is solved through a cost function that emulates the dynamic behavior of nervous system involved in human gait and a novel global static optimization method. The outcome of this research is aimed at identifying cost functions describing the neural behavior during gait, keeping in mind their application to neuromuscular rehabilitation.

Estimation of the muscle force distribution in ballistic motion based on a multibody methodology

This work presents a general three-dimensional multibody procedure for studying the human body motion with emphasis on the locomotion apparatus. The methodology includes a three-dimensional biomechanical model, data acquisition techniques and an inverse dynamics approach. The biomechanical model is based on a multibody formulation using natural coordinates and consists of 16 anatomical segments modeled by 33 rigid bodies for a total of 44 degrees-of-freedom. The action of the muscles is introduced in the equations of motion of the multibody model by means of driver actuators defined as kinematic constraints. By associating a Lagrange multiplier to each muscle actuator the muscle forces became coupled with the biomechanical model through the Jacobian matrix of the underlying multibody system. A Hill type muscle model is used to calculate individual muscle forces. The model for the muscle apparatus comprises 43 muscle groups for each leg, which use the full three-dimensional lines of action for these muscles in their geometric description. The problem of the redundancy of the forces on the musculoskeletal structure is solved by using inverse dynamics and static optimization methods. In the process of describing the methodology the benefits of modeling in natural coordinates are highlighted. The methodology developed is demonstrated through its application to a case of ballistic motion, represented by the take-off to an aerial trajectory in order to estimate the joint torques and the muscle force distribution in the supporting leg. The time characteristics of the resultant net torques at the basic joints of the supporting leg and the time-varying muscle force patterns are presented and discussed. The results obtained are explained in terms of their relevance to the activity under study.

A superellipsoid-plane model for simulating foot-ground contact during human gait.

Abstract Musculoskeletal models and forward dynamics simulations of human movement often include foot–ground interactions, with the foot–ground contact forces often determined using a constitutive model that depends on material properties and contact kinematics. When using soft constraints to model the foot–ground interactions, the kinematics of the minimum distance between the foot and planar ground needs to be computed. Due to their geometric simplicity, a considerable number of studies have used point–plane elements to represent these interacting bodies, but few studies have provided comparisons between point contact elements and other geometrically based analytical solutions. The objective of this work was to develop a more general-purpose superellipsoid–plane contact model that can be used to determine the three-dimensional foot–ground contact forces. As an example application, the model was used in a forward dynamics simulation of human walking. Simulation results and execution times were compared with a point-like viscoelastic contact model. Both models produced realistic ground reaction forces and kinematics with similar computational efficiency. However, solving the equations of motion with the surface contact model was found to be more efficient (~18% faster), and on average numerically ~37% less stiff. The superellipsoid–plane elements are also more versatile than point-like elements in that they allow for volumetric contact during three-dimensional motions (e.g. rotating, rolling, and sliding). In addition, the superellipsoid–plane element is geometrically accurate and easily integrated within multibody simulation code. These advantages make the use of superellipsoid–plane contact models in musculoskeletal simulations an appealing alternative to point-like elements.

Multibody Dynamics Approaches for Biomechanical Modeling in Human Impact Applications

The construction of multibody biomechanical models for impact is discussed here with the emphasis on the formulation aspects. First the relations between the human or the dummy anthropometric data and the rigid bodies in the model are presented. The motion restrictions between the different anatomical segments of model can be defined as kinematic joints, suitable to represent mechanical joints of dummies or a simplified kinematics of human joints, or as contact/sliding pairs, which are used to describe realistic human like anatomical joints. Another particular aspect of biomechanical models is the representation of the range of motion of the anatomical joints. This is achieved either by setting proper contact pairs between the adjacent anatomical segments or by setting resisting muscle forces or resisting moments that develop when the relative orientation between the segments reach critical values. Another fundamental aspect of the models is the ability to represent the contact geometries and the contact forces with realism. In fact, the outcome of all injury indexes predictions is strongly dependent on the quality of the representation of the contact. Contact models suitable to be used in biomechanical models, to represent the contact between anatomical segments of the biomechanical model or between these and external objects, are presented and discussed emphasizing the requirements to develop more advanced biomechanical models. The current biomechanical models either do not include muscle actions or, at the most, include a reflexive muscle contraction. It is suggested here that for the case of standing passengers it is important to include in the biomechanical models muscle models that allow for the representation of the muscle voluntary contractions and joint stiffening. It is also suggested that the evaluation of the models leading to the identification of such actions can be done by using techniques similar to those used in the evaluation of muscle force sharing in different human motions.

Implementation of an efficient muscle fatigue model in the framework of multibody systems dynamics for analysis of human movements

The aim of this study is to implement and integrate a novel and versatile muscle fatigue model in an existing multibody formulation with natural coordinates. The equations of motion of the formulation are rearranged to deal with muscle actuators as externally concentrated forces instead of being considered as kinematic muscle actuator drivers. A muscle fatigue model, originally developed to predict the endurance time of the main body joints, is included in the multibody formulation. The model stems from the compartment theory and uses a bounded controller to rule the rate of motor units changing between the three compartments (resting, activated, and fatigued) that made up the model. The resulting formulation is applied to two example cases involving the human upper extremity, with redundant muscles, to evaluate its robustness and accuracy. Results showed that the proposed methodologies are a valid approach for the calculation of the redundant muscle forces in the presence of muscular fatigue.

Shape Analysis of the Femoral Head: A Comparative Study Between Spherical, (Super)Ellipsoidal, and (Super)Ovoidal Shapes

In this work, MacConaills classification that the articular surface of the femoral head is better represented by ovoidal shapes rather than purely spherical shapes is computationally tested. To test MacConaills classification, a surface fitting framework was developed to fit spheres, ellipsoids, superellipsoids, ovoids, and superovoids to computed tomography (CT) data of the femoral proximal epiphysis. The framework includes several image processing and computational geometry techniques, such as active contour segmentation and mesh smoothing, where implicit surface fitting is performed with genetic algorithms. By comparing the surface fitting error statistics, the results indicate that (super)ovoids fit femoral articular surfaces better than spherical or (super)ellipsoidal shapes.

A microcontroller platform for the rapid prototyping of functional electrical stimulation-based gait neuroprostheses.

Functional electrical stimulation (FES) has been used over the last decades as a method to rehabilitate lost motor functions of individuals with spinal cord injury, multiple sclerosis, and post-stroke hemiparesis. Within this field, researchers in need of developing FES-based control solutions for specific disabilities often have to choose between either the acquisition and integration of high-performance industry-level systems, which are rather expensive and hardly portable, or develop custom-made portable solutions, which despite their lower cost, usually require expert-level electronic skills. Here, a flexible low-cost microcontroller-based platform for rapid prototyping of FES neuroprostheses is presented, designed for reduced execution complexity, development time, and production cost. For this reason, the Arduino open-source microcontroller platform was used, together with off-the-shelf components whenever possible. The developed system enables the rapid deployment of portable FES-based gait neuroprostheses, being flexible enough to allow simple open-loop strategies but also more complex closed-loop solutions. The system is based on a modular architecture that allows the development of optimized solutions depending on the desired FES applications, even though the design and testing of the platform were focused toward drop foot correction. The flexibility of the system was demonstrated using two algorithms targeting drop foot condition within different experimental setups. Successful bench testing of the device in healthy subjects demonstrated these neuroprosthesis platform capabilities to correct drop foot.