Prediction of Individual Muscle Forces Using Lagrange Multipliers Method — A Model of the Upper Human Limb in the Sagittal Plane: II. Numerical Experiments and Sensitivity Analysis

2000 ◽  
Vol 3 (3) ◽  
pp. 167-182 ◽  
Author(s):  
ROSITSA RAIKOVA
Keyword(s):  
Sensitivity Analysis ◽  
Lagrange Multipliers ◽  
Numerical Experiments ◽  
Sagittal Plane ◽  
Muscle Forces ◽  
Individual Muscle ◽  
Multipliers Method ◽  
Human Limb

Quadratic Sensitivity Analysis of Fixtures and Locating Schemes for Rigid Parts

2000 ◽  
Vol 123 (3) ◽  
pp. 462-472 ◽  
Author(s):  
Johan S. Carlson
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Experiments ◽  
Geometric Constraints ◽  
Fixture Design ◽  
Practical Relevance ◽  
Sensitivity Equation ◽  
Relative Gain ◽  
Contact Points ◽  
Scheme Evaluation ◽  
Error Interaction

The main purpose of locating schemes are to position parts. The locating scheme utilizes tooling elements, referred to as locators, to introduce geometric constraints. A rigid part is uniquely positioned when it is brought into contact with the locators. By using kinematic analysis we derive a quadratic sensitivity equation that relates position error in locators with the resulting displacement of the part held by the locating scheme. The sensitivity equation which depends on the locator positions and the workpiece geometry around the contact points can be used for locating scheme evaluation, robust fixture design, tolerancing and diagnosis. The quadratic sensitivity equation derived in this paper is novel by adequate dealing with locator contact at nonprismatic surfaces, nonsmall errors, locator error interaction effects and locator errors in arbitrary directions. Theory for comparing the relative gain in precision by using the quadratic sensitivity equation instead of the linear is developed. The practical relevance of the quadratic sensitivity equation is tested through numerical experiments.

scholarly journals Using crocodilian tails as models for dinosaur tails

2015 ◽  
Author(s):  
Heinrich Mallison ◽  
Michael Pittman ◽  
Daniela Schwarz
Keyword(s):  
Sensitivity Analysis ◽  
Morphological Data ◽  
Muscle Forces ◽  
Limited Knowledge ◽  
Starting Point ◽  
Good Starting Point ◽  
Methodological Problems ◽  
Parameter Ranges

The tails of extant crocodilians are anatomically the closest approximation of the tails of non-avian dinosaurs, and therefore a good starting point for any reconstruction of non-avian dinosaur tail muscles. However, we here demonstrate some methodological problems using crocodile tails, firstly regarding the general reconstruction of tail mobility from osteology, secondly for the reconstruction of tail musculature for the quantification of muscle forces, especially the m. caudofemoralis longus, and thirdly with respect to the anatomical differences between crocodilians and non-avian dinosaurs, especially in relation to the reconstruction of m. caudofemoralis brevis. Our results show that, given the current limited knowledge of crocodilian tails, volumetric reconstructions should be created on the basis of more gross morphological data than is usually used, and that biomechanical studies should include sensitivity analysis with greater parameter ranges than often applied.

scholarly journals MM-MRE: a new technique to quantify individual muscle forces during isometric tasks of the wrist using MR elastography

2019 ◽  
Author(s):  
Andrea Zonnino ◽  
Daniel R. Smith ◽  
Peyton L. Delgorio ◽  
Curtis L. Johnson ◽  
Fabrizio Sergi
Keyword(s):  
Shear Wave ◽  
Muscle Force ◽  
Muscle Mechanics ◽  
Neuromuscular Control ◽  
Joint Torque ◽  
New Technique ◽  
Muscle Forces ◽  
Individual Muscle ◽  
Complete Set ◽  
A New Technique

AbstractNon-invasive in-vivo measurement of individual muscle force is limited by the infeasibility of placing force sensing elements in series with the musculo-tendon structures. At the same time, estimating muscle forces using EMG measurements is prone to inaccuracies, as EMG is not always measurable for the complete set of muscles acting around the joints of interest. While new methods based on shear wave elastography have been recently proposed to directly characterize muscle mechanics, they can only be used to measure muscle forces in a limited set of superficial muscles. As such, they are not suitable to study the neuromuscular control of movements that require coordinated action of multiple muscles.In this work, we present multi-muscle magnetic resonance elastography (MM-MRE), a new technique capable of quantifying individual muscle force from the complete set of muscles in the forearm, thus enabling the study of the neuromuscular control of wrist movements. MM-MRE integrates measurements of joint torque provided by an MRI-compatible instrumented handle with muscle-specific measurements of shear wave speed obtained via MRE to quantify individual muscle force using model-based estimator.A single-subject pilot experiment demonstrates the possibility of obtaining measurements from individual muscles and establishes that MM-MRE has sufficient sensitivity to detect changes in muscle mechanics following the application of isometric joint torque with self-selected intensity.

INVESTIGATION OF THE INFLUENCE OF THE ELBOW JOINT REACTION ON THE PREDICTED MUSCLE FORCES USING DIFFERENT OPTIMIZATION FUNCTIONS

2009 ◽  
Vol 12 (01) ◽  
pp. 31-43 ◽  
Author(s):  
Rositsa T. Raikova
Keyword(s):  
Objective Function ◽  
Elbow Joint ◽  
Degrees Of Freedom ◽  
Sagittal Plane ◽  
Biomechanical Model ◽  
Moment Equation ◽  
Muscle Forces ◽  
Joint Stability ◽  
Biarticular Muscles ◽  
Joint Reaction

Less attention is paid to joint reactions when optimization tasks are solved aiming to predict individual muscle forces driving a biomechanical model. The reactions are important, however, for joint stability and for prevention from injuries, especially for fast motions and submaximal loading. The purpose of the paper is to investigate the influence of the joint reaction as a criterion in an objective function and to study the possibilities for prediction of antagonistic co-contraction. Planar elbow flexions in the sagittal plane with duration from 0.4 to 2 s are simulated, and muscle forces and elbow joint reaction are calculated solving numerically optimization tasks formulated for models with one (elbow moment equation only) and two (elbow and shoulder moment equations) degrees of freedom (DOF). The objective function is a weighted sum of muscle forces and joint reaction raised to different powers. The following conclusions can be made: (1) if the joint reaction is included in the objective function, antagonistic co-contraction can be predicted even for 1 DOF model; in some situations the use of such objective function can destroy the synergistic muscles' action; (2) the prediction of antagonistic muscles' co-contraction for 2 DOF model depends on the way the biarticular muscles are modeled, and this is valid for both dynamic and quasistatic conditions; if there are no biarticular muscles, antagonistic co-contraction cannot be predicted in one joint using popular objective functions, like minimum of sum of muscle forces or muscle stresses raised to a power.

Using Musculoskeletal Properties to Develop a “Normalized Potential Moment Contribution Index” for Individual Arm Muscles

2004 ◽  
Author(s):  
Betsy V. Hunt ◽  
Roger V. Gonzalez
Keyword(s):  
Tendon Transfer ◽  
Diagnostic Tools ◽  
Muscle Forces ◽  
Individual Muscle ◽  
Musculoskeletal Models ◽  
Arm Muscles ◽  
Contribution Index ◽  
Research Tools

Musculoskeletal models serve as research tools to study the effect of individual muscle forces across multiple joints. Models are already used as diagnostic tools for treatment and rehabilitation such as in tendon transfer surgeries [1,2].

scholarly journals A Generic Optimization Algorithm for the Allocation of DP Actuators

2011 ◽  
Author(s):  
E. F. G. van Daalen ◽  
J. L. Cozijn ◽  
C. Loussouarn ◽  
P. W. Hemker
Keyword(s):  
Optimization Algorithm ◽  
Lagrange Multipliers ◽  
Linear Equations ◽  
Exact Expression ◽  
Computational Effort ◽  
Total Power ◽  
Linear Solution ◽  
Multipliers Method ◽  
Non Linear ◽  
The Cost

In this paper we present a generic optimization algorithm for the allocation of dynamic positioning actuators, such as azimuthing thrusters and fixed thrusters. The algorithm is based on the well-known Lagrange multipliers method. In the present approach the Lagrangian functional represents not only the cost function (the total power delivered by all actuators), but also all constraints related to thruster saturation and forbidden zones for azimuthing thrusters. In the presented approach the application of the Lagrange multipliers method leads to a nonlinear set of equations, because an exact expression for the total power is applied and the actuator limitations are accounted for in an implicit manner, by means of nonlinear constraints. It is solved iteratively with the Newton-Raphson method and a step by step implementation of the constraints related to the actuator limitations. In addition, the results from the non-linear solution method were compared with the results from a simplified set of linear equations, based on an approximate (quadratic) expression for the thruster power. The non-linear solution was more accurate, while requiring only a slightly higher computational effort. An example is shown for a thruster configuration with 8 azimuthing thrusters, typical for a DP semi-submersible. The results show that the optimization algorithm is very stable and efficient. Finally, some options for improvements and future enhancements — such as including thruster-thruster and thruster-hull interactions and the effects of current — are discussed.

Assessment of Internal Loads in the Joints of the Lower Extremities During the Snatch in Young Weightlifters

2019 ◽  
Vol 19 (05) ◽  
pp. 1941011
Author(s):  
Adam Czaplicki ◽  
Krzysztof Dziewiecki ◽  
Zenon Mazur ◽  
Wojciech Blajer
Keyword(s):  
Inverse Dynamics ◽  
Sagittal Plane ◽  
Lower Extremities ◽  
Lower Limbs ◽  
Muscle Forces ◽  
Kinematic Data ◽  
Lower Trunk ◽  
Left And Right ◽  
Ground Reactions ◽  
Inverse Dynamics Problem

The aim of this paper is to present the results of an assessment of internal loads in the joints of the lower limbs during the snatch performed by young weightlifters. A planar model of a weightlifter composed of 7 rigid segments (the lower trunk, thighs, lower legs and feet) connected by six hinge joints was used in the computations. The dynamic equations of the motion of the model were obtained using a projective technique. Kinematic data were recorded by a Vicon system with a sampling frequency of 200 Hz. The ground reactions were measured independently for the left and right limbs on two force platforms. The inverse dynamics problem was solved to assess the internal loads (the muscle forces and joint reactions) in the lower limbs. Relatively high differences in the reactions in the joints and muscle forces in the left and right lower extremities were identified. The obtained results also reveal that the snatch, a lift which tends to be geometrically symmetrical in the sagittal plane, is not necessarily characterized by symmetry of internal loads. Thus, this study has shown that a kinematics analysis of the lifter’s movement, which is commonly used to assess the technique of the snatch, is insufficient and should be supplemented with a dynamics analysis.

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