A Lagrange-based generalised formulation for the equations of motion of simple walking models

Mcgrath, Michael; Howard, David; Baker, Richard

doi:10.1016/j.jbiomech.2017.02.013

Cited by 19 publications

(13 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Dessa maneira, automaticamente, já se eliminam as forças de restrição, ou seja, as FRS, uma vez que elas não realizam trabalho. Outra vantagem dessa formulação é que as formas fechadas das equações dinâmicas podem ser obtidas em qualquer sistema de coordenadas de maneira sistemática (McGrath et al, 2017).…”

Section: Formulação De Lagrangeunclassified

2d Spatial Model of the Human Gait Single Support Phase Based on Predict Ive Dynamics

Oliveira¹,

Gonçalves²

2019

Proceedings of the 25th International Congress of Mechanical Engineering

View full text Add to dashboard Cite

The simulation of human body movement is a valuable tool for different fields such as robotics and biomechanics. Even with the growing number of researches, there are still few groups in Brazil that work on developing models of human movement.Such simulation has been a challenging problem from a modeling and computational point of view. This dissertation brings a bibliographical review of concepts of structural dynamics and the main determinants of the dynamics of human walking. Four twodimensional models of increasing complexity found in the literature are initially analyzed to understand the influence of the various elements and degrees of freedom on the quality of the obtained results. Before introducing these models, an investigation of some kinematic variables, known as determinants of walking, is performed for the simple support phase. The simpler model considers an inverted pendulum, and then joints are added to simulate the hip, knee, ankle/foot, and finally the entire leg mechanism is replaced by a spring. The effects of successive additions of degrees of freedom are analyzed and the results are compared with Winter's experimental results for torques and reaction forces. Based on these analyzes, this work proposes a twodimensional model of human walking during the simple support phase (SSP) with seven degrees of freedom. The forces resulting from muscular actions are represented by torques at each joint. All masses of upper body segments are grouped. The model is based on inverse dynamics, with angular displacements being interpolated by 5th degree B-splines and the body kinematics is calculated using the Denavit-Hartenberg (DH) robotic formulation. The equations of motion are obtained based on a recursive Lagrangian formulation, due to its computational efficiency. An optimization problem is established to obtain the B-splines control points, where the objective function is defined by the dynamic effort. The constraints imposed on movement are of two types: the time-dependent constraints (torque/angle limits and dynamic stability defined by the PUC-Rio -Certificação Digital Nº 1712766/CA Zero Moment Point criterion) and the independent time constraints (initial and final state). The results of the model are favorably compared with Winter's experimental data, in particular the ground reaction forces.

show abstract

Section: Formulação De Lagrangeunclassified

2d Spatial Model of the Human Gait Single Support Phase Based on Predict Ive Dynamics

Oliveira¹,

Gonçalves²

2019

Proceedings of the 25th International Congress of Mechanical Engineering

View full text Add to dashboard Cite

show abstract

“…It was followed the inverted pendulum approach due to energy reasons: according with [3], there is energy conservation if the behavior of the stance leg is identical to the behavior of an inverted pendulum; the same happens if the behavior of the swing leg is identical to the behavior of a pendulum. Between Euler-Lagrange and Newton-Euler mechanics, it was chosen the first one because the prior knowledge of the ground reaction force (GRF) is not necessary, that is, Euler-Lagrange approach only requires energy calculations [4].…”

Section: Introductionmentioning

confidence: 99%

Study of Gait Cycle Using a Five-Link Inverted Pendulum Model: First Developments

Moreira

Pinheiro

Lopes

et al. 2019

2019 IEEE 6th Portuguese Meeting on Bioengineering (ENBENG)

View full text Add to dashboard Cite

Gait cycle has been the target of many studies in the last decades in order to identify the normal walking patterns of humans. The usefulness of these studies is of utmost importance to construct mathematical models that are capable to achieve stability during walking. Based on this fact, it seems justified the present effort to construct a model to simulate a complete stride in healthy humans. Thus, in this work, a five-link inverted pendulum model in the sagittal plane with 5 degrees of freedom (DOFs) based on Euler-Lagrange equations is being constructed with the main objective to concern stability during gait cycle. To do that, this study was divided into two parts: the first one is represented by this article and it is regarding to the model construction and data collection; the second part is relative to a future work and it concerns to the model validation and an analysis of the stiffness variation with the power and speed during gait cycle. Regarding to the results of the present study, good correlations were obtained between the data collected and the data presented in literature, which demonstrates a good data acquisition.

show abstract

“…A dissertação está dividida em nove capítulos (Figura 1. (Asada, 2018). Depois de encontrar as equações de movimento, é necessário um procedimento para resolvê-las, para isso os métodos são divididos em dinâmica direta, quando se parte das forças para encontrar velocidade e aceleração, e dinâmica inversa, quando se parte de dados da velocidade e aceleração para encontrar as forças que atuam no corpo (Onyshko & Winter, 1980 (McGrath et al, 2017). Essa divisão é importante, pois ela determina o processo de formulação do problema e de sua resolução.…”

Section: Organização Da Dissertaçãounclassified

“…Após calcular a energia cinética e a energia potencial, é necessário calcular a força , que provém da consideração do trabalho virtual ( ) (McGrath et al, 2017):…”

Section: Formulação De Lagrangeunclassified

“…A medição por imagem vem sendo cada vez mais utilizada (McGrath et al, 2017), (Hayot et al, 2013), (Riemer & Hsiao-Wecksler, 2008). A medição acontece por meio de marcadores anexados em pontos em que se deseja fazer a medição e um sistema de câmera é instalado para capturar o movimento dos marcadores (Winter, 2009).…”

Section: Técnica De Medição Da Cinemática Do Corpo Humanounclassified

See 1 more Smart Citation

Modelo Espacial 2d Da Fase De Apoio Simples Do Caminhar Humano Baseado Em Dinâmica Preditiva

OLIVEIRA¹

View full text Add to dashboard Cite

The simulation of human body movement is a valuable tool for different fields such as robotics and biomechanics. Even with the growing number of researches, there are still few groups in Brazil that work on developing models of human movement. Such simulation has been a challenging problem from a modeling and computational point of view. This dissertation brings a bibliographical review of concepts of structural dynamics and the main determinants of the dynamics of human walking. Four twodimensional models of increasing complexity found in the literature are initially analyzed to understand the influence of the various elements and degrees of freedom on the quality of the obtained results. Before introducing these models, an investigation of some kinematic variables, known as determinants of walking, is performed for the simple support phase. The simpler model considers an inverted pendulum, and then joints are added to simulate the hip, knee, ankle/foot, and finally the entire leg mechanism is replaced by a spring. The effects of successive additions of degrees of freedom are analyzed and the results are compared with Winter's experimental results for torques and reaction forces. Based on these analyzes, this work proposes a twodimensional model of human walking during the simple support phase (SSP) with seven degrees of freedom. The forces resulting from muscular actions are represented by torques at each joint. All masses of upper body segments are grouped. The model is based on inverse dynamics, with angular displacements being interpolated by 5th degree B-splines and the body kinematics is calculated using the Denavit-Hartenberg (DH) robotic formulation. The equations of motion are obtained based on a recursive Lagrangian formulation, due to its computational efficiency. An optimization problem is established to obtain the B-splines control points, where the objective function is defined by the dynamic effort. The constraints imposed on movement are of two types: the time-dependent constraints (torque/angle limits and dynamic stability defined by the PUC-Rio-Certificação Digital Nº 1712766/CA Zero Moment Point criterion) and the independent time constraints (initial and final state). The results of the model are favorably compared with Winter's experimental data, in particular the ground reaction forces.

show abstract

A Lagrange-based generalised formulation for the equations of motion of simple walking models

Cited by 19 publications

References 12 publications

2d Spatial Model of the Human Gait Single Support Phase Based on Predict Ive Dynamics

2d Spatial Model of the Human Gait Single Support Phase Based on Predict Ive Dynamics

Study of Gait Cycle Using a Five-Link Inverted Pendulum Model: First Developments

Modelo Espacial 2d Da Fase De Apoio Simples Do Caminhar Humano Baseado Em Dinâmica Preditiva

Contact Info

Product

Resources

About