Deriving a closed form of equations of motion of musculoskeletal system of human body: Using Lagrangian dynamics

2011 ◽  
Author(s):  
Mohammad Gudarzi ◽  
Hossein Ehsani ◽  
Mostafa Rostami
Keyword(s):  
Closed Form ◽  
Musculoskeletal System ◽  
Human Body ◽  
Equations Of Motion ◽  
Lagrangian Dynamics

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

A Closed-Form Formalism for Controlled and Hybrid Rigid/Elastic Multibody Systems: Part II — Symbolic Implementation and Applications

1991 ◽  
Author(s):  
Junghsen Lieh ◽  
Imitiaz Haque
Keyword(s):  
Closed Form ◽  
Equations Of Motion ◽  
Structural Flexibility ◽  
Symbolic Language ◽  
Structural Vibrations ◽  
Optimal Control Strategy ◽  
Active Suspensions ◽  
Elastic Multibody Systems ◽  
System Order ◽  
Crank Mechanism

Abstract A program is developed on a DECstation using the symbolic language MAPLE which generates the equations of motion in a closed form and reduces the system order symbolically. A procedure that can make symbolic simplification and linearization is provided. The integration of shape functions is performed symbolically. Both nonlinear and linearized equations of motion with control are established in FORTRAN format. Several models including an elastic vehicle with active suspensions, an elastic robotic manipulator and an elastic slider-crank mechanism with both joint and structural flexibility are generated. Numerical simulation for the active vehicle model using an optimal control strategy is presented. The effect of active suspensions on vehicle and structural vibrations is briefly discussed. A comparison between the nonlinear and linearized robot models is given. Simulation results of the slider-crank mechanism are also presented.

Modeling of Human Reactions to Whole-Body Vibration

1987 ◽  
Vol 109 (3) ◽  
pp. 210-217 ◽  
Author(s):  
Farid M. L. Amirouche
Keyword(s):  
Human Body ◽  
Equations Of Motion ◽  
Vertical Direction ◽  
The Body ◽  
Whole Body ◽  
Connective Tissues ◽  
Finite Segment ◽  
Body Vibration ◽  
Forcing Function ◽  
Impulse Function

A computer-automated approach for studying the human body vibration is presented. This includes vertical, horizontal, and torsional vibration. The procedure used is based on Finite Segment Modeling (FSM) of the human body, thus treating it as a mechanical structure. Kane’s equations as developed by Huston et al. are used to formulate the governing equations of motion. The connective tissues are modeled by springs and dampers. In addition, the paper presents the transient response of different parts of the body due to a sinusoidal forcing function as well as an impulse function applied to the lower torso in the vertical direction.

Structural Modeling of the Human Musculoskeletal System for Clinical Treatment by Applying Joint-Connected Multibody Dynamics and System Approach

2010 ◽  
Author(s):  
Munehiro Michael Kayo ◽  
Yoshiaki Ohkami
Keyword(s):  
Musculoskeletal System ◽  
Human Body ◽  
Structural Model ◽  
Structural Modeling ◽  
Observation Data ◽  
Theory Approach ◽  
Active Motion ◽  
Invasive Approach ◽  
Clinical Observations ◽  
Square Matrix

The objective of this paper is to establish a concise structural model of the human musculoskeletal system (HMS) that can be used to clinically treat malfunctions or distortions of the human body. This model must be uncomplicated for therapists to identify the problematic areas of the human body with adequate visualization while maintaining a theoretical thoroughness in mechanics. To achieve this objective, a system theory approach called the Interpretive Structural Modeling (ISM) has been applied to bridge multi-body dynamics and clinical observations. From a mechanical engineering viewpoint, this HMS system can be treated as a collection of joint connected 15 rigid bodies in a topological tree configuration with 35 Degrees-of-Freedom (DOF). Alternatively, from a clinical viewpoint, the functioning of the joints is a major concern since most malfunctions or distortions take place around the joints. Based on 20 years of accumulated clinical observation data, we have discovered that all HMS movements can be constructed by a combination of 35 fundamental motion elements, all having a certain degree of interaction with each other. By applying the ISM for a matrix representation of the HMS system, we have obtained the following results: 1) The association between the rotation of the joints and the fundamental motion elements is represented by a square matrix of dimension N, where N is twice of the DOF 2) The determinant of this matrix, corresponding to the N-square matrix in SE terminology, gives an evaluation criteria in selecting the fundamental elements; 3) Application of the ISM reveals a distinction between an active motion element with intention versus an associated motion element that is induced by another motion element(s). In addition, the ISM yields a tiered structure of the fundamental motion elements according to the degree of activeness; and 4) most important, an overall investigation of the matrix characteristics gives a means to identify imbalances or distortions within the HMS. With the help of a motion diagram for the purpose of visualization, this research can eventually be applied to clinical observations whereby an automated identification of malfunctioning parts can be achieved with computer software. The above stated results will contribute to a holistic and non-invasive approach for medical care and rehabilitation.

Dynamical Behaviour of a Materially Damped Flexible Towed Cable

1972 ◽  
Vol 23 (2) ◽  
pp. 109-120 ◽  
Author(s):  
T C Cannon ◽  
J Genin
Keyword(s):  
Closed Form ◽  
Natural Frequencies ◽  
Equilibrium Shape ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamical Behaviour ◽  
Aerodynamic Loading ◽  
Towed Cable ◽  
Closed Form Approximation ◽  
Good Agreement

SummaryThe three-dimensional equations of motion of a flexible towed cable are developed. A closed-form approximation for the equilibrium shape of a cable subjected to arbitrary aerodynamic loading is developed and used in the study of a heavy, vibrating tow cable. Natural frequencies of vibration and cable shapes are computed for typical cables and are shown to be in good agreement with exact, numerically obtained values.

Multi-Body Modeling of Human Musculoskeletal System for an Exercise Therapy Method and its Verification

2013 ◽  
Author(s):  
Munehiro Michael Kayo ◽  
Yoshiaki Ohkami
Keyword(s):  
Exercise Therapy ◽  
Musculoskeletal System ◽  
Human Body ◽  
Structural Model ◽  
Force Plate ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Estimation Of Parameters ◽  
Human Body Model ◽  
Multi Body

The objective of this paper is to establish a concise structural model of the human musculoskeletal system (HMS) that can be applied to an exercise therapy that treats malfunctions or distortions of the human body. There exist a number of traditional exercise therapy methods in Japan and China, but any systematic approaches for learning, coaching or training are not found to the best of the author’s knowledge. Among such approaches, we deal with an exercise therapy called Somatic Balance Restoring Therapy (SBRT) in which a patient executes a series of non-invasive and painless motions in face-up/down laid posture. Although thousands of results have been piled up in a fixed-format data base, justification for the SBRT has not been provided in bio/mechanical engineering sense. The purpose of modeling is a first step for this holistic approach. For such reasons, the model must be useful and uncomplicated for therapists to identify the problematic areas of the human body with adequate visualization while maintaining a theoretical thoroughness in mechanics or dynamics. To bridge multi-body dynamics and the SBRT, we have utilized a human body model with a collection of joint connected 15 rigid bodies in a topological tree configuration as used for humanoid robot with 80 Degrees-of-Freedom (DOF). In order to achieve the purpose stated above, we have developed a static force/torque balance equation for each body element. In addition, we will describe modeling processes, derivation of static equations, and estimation of parameters/states and verification based on the analysis of the FPS experimental data, and contact forces are parameterized with quantitative values to be given by the Force Plate System (FPS), installed at CARIS at the University of British Columbia (UBC).

Active-Passive Hybrid Constrained Layer for Structural Damping Augmentation

2000 ◽  
Vol 122 (3) ◽  
pp. 254-262 ◽  
Author(s):  
Yanning Liu ◽  
K. W. Wang
Keyword(s):  
Closed Form ◽  
Viscoelastic Material ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Generic Model ◽  
Structural Damping ◽  
Active Materials ◽  
Closed Form Solutions ◽  
Fail Safe ◽  
Active Constrained Layer

A new surface-damping concept with an active-passive hybrid constraining layer (HCL) is proposed to improve the damping performance of traditional active constrained layer (ACL) systems. Instead of using a pure piezoelectric constraining layer, passive and active materials are used together to constrain the viscoelastic material layer. A generic model of the HCL treatment is presented. Nondimensional equations of motion and boundary and connecting conditions are derived. The closed-form solutions to the equations are developed and analyzed. Tabletop tests are also performed to verify the feasibility of the new damping concept. It is shown that by properly selecting a passive constraining material and assigning appropriate lengths for the active and passive constraining parts, HCL can outperform a system with a pure active PZT coversheet, both in terms of its fail-safe ability and closed-loop damping performance. [S0739-3717(00)01503-8]

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