Comparative Analysis of Methods for Estimating Arm Segment Parameters and Joint Torques From Inverse Dynamics

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Davide Piovesan ◽  
Alberto Pierobon ◽  
Paul DiZio ◽  
James R. Lackner
Keyword(s):  
Root Mean Square ◽  
Upper Limb ◽  
Inverse Dynamics ◽  
Estimation Method ◽  
Joint Torque ◽  
Reaching Movements ◽  
Mean Square ◽  
Body Segment ◽  
Joint Torques ◽  
Body Segment Parameters

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.

Improving Net Joint Torque Calculations Through a Two-Step Optimization Method for Estimating Body Segment Parameters

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Raziel Riemer ◽  
Elizabeth T. Hsiao-Wecksler
Keyword(s):  
Inverse Dynamics ◽  
Optimization Problems ◽  
Joint Torque ◽  
Optimization Approach ◽  
Regression Equations ◽  
Random Errors ◽  
Body Segment ◽  
Joint Torques ◽  
Body Segment Parameters ◽  
True Values

Two main sources of error in inverse dynamics based calculations of net joint torques are inaccuracies in segmental motions and estimates of anthropometric body segment parameters (BSPs). Methods for estimating BSP (i.e., segmental moment of inertia, mass, and center of mass location) have been previously proposed; however, these methods are limited due to low accuracies, cumbersome use, need for expensive medical equipment, and∕or sensitivity of performance. This paper proposes a method for improving the accuracy of calculated net joint torques by optimizing for subject-specific BSP in the presence of characteristic and random errors in motion data measurements. A two-step optimization approach based on solving constrained nonlinear optimization problems was used. This approach minimized the differences between known ground reaction forces (GRFs), such as those measured by a force plate, and the GRF calculated via a top-down inverse dynamics approach. In step 1, a series of short calibration motions was used to compute first approximations of optimized segment motions and BSP for each motion. In step 2, refined optimal BSPs were derived from a combination of these motion profiles. We assessed the efficacy of this approach using a set of reference motions in which the true values for the BSP, segment motion, GRF, and net joint torques were known. To imitate real-world data, we introduced various noise conditions on the true motion and BSP data. We compared the root mean squared errors in calculated net joint torques relative to the true values due to the optimal BSP versus traditionally-derived BSP (from anthropometric tables derived from regression equations) and found that the optimized BSP reduced the error by 77%. These results suggest that errors in calculated net joint torques due to traditionally-derived BSP estimates could be reduced substantially using this optimization approach.

scholarly journals Upper-Limb Isometric Force Feasible Set: Evaluation of Joint Torque-Based Models

Biomechanics ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 102-117
Author(s):  
Nasser Rezzoug ◽  
Vincent Hernandez ◽  
Philippe Gorce
Keyword(s):  
Upper Limb ◽  
Isometric Force ◽  
Joint Torque ◽  
Force Distribution ◽  
Prediction Errors ◽  
Feasible Set ◽  
Joint Torques ◽  
Motor Abilities ◽  
Capacity Evaluation ◽  
Measured Force

A force capacity evaluation for a given posture may provide better understanding of human motor abilities for applications in sport sciences, rehabilitation and ergonomics. From data on posture and maximum isometric joint torques, the upper-limb force feasible set of the hand was predicted by four models called force ellipsoid, scaled force ellipsoid, force polytope and scaled force polytope, which were compared with a measured force polytope. The volume, shape and force prediction errors were assessed. The scaled ellipsoid underestimated the maximal mean force, and the scaled polytope overestimated it. The scaled force ellipsoid underestimated the volume of the measured force distribution, whereas that of the scaled polytope was not significantly different from the measured distribution but exhibited larger variability. All the models characterized well the elongated shape of the measured force distribution. The angles between the main axes of the modelled ellipsoids and polytopes and that of the measured polytope were compared. The values ranged from 7.3° to 14.3°. Over the entire surface of the force ellipsoid, 39.7% of the points had prediction errors less than 50 N; 33.6% had errors between 50 and 100 N; and 26.8% had errors greater than 100N. For the force polytope, the percentages were 56.2%, 28.3% and 15.4%, respectively.

Directional Control of Planar Human Arm Movement

1997 ◽  
Vol 78 (6) ◽  
pp. 2985-2998 ◽  
Author(s):  
Gerald L. Gottlieb ◽  
Qilai Song ◽  
Gil L. Almeida ◽  
Di-An Hong ◽  
Daniel Corcos
Keyword(s):  
Control System ◽  
Arm Movement ◽  
Initial Position ◽  
Joint Torque ◽  
Reaching Movements ◽  
Rule Based ◽  
Joint Torques ◽  
Directional Control ◽  
Human Arm ◽  
Dynamic Components

Gottlieb, Gerald L., Qilai Song, Gil L. Almeida, Di-an Hong, and Daniel Corcos. Directional control of planar human arm movement. J. Neurophysiol. 78: 2985–2998, 1997. We examined the patterns of joint kinematics and torques in two kinds of sagittal plane reaching movements. One consisted of movements from a fixed initial position with the arm partially outstretched, to different targets, equidistant from the initial position and located according to the hours of a clock. The other series added movements from different initial positions and directions and >40–80 cm distances. Dynamic muscle torque was calculated by inverse dynamic equations with the gravitational components removed. In making movements in almost every direction, the dynamic components of the muscle torques at both the elbow and shoulder were related almost linearly to each other. Both were similarly shaped, biphasic, almost synchronous and symmetrical pulses. These findings are consistent with our previously reported observations, which we termed a linear synergy. The relative scaling of the two joint torques changes continuously and regularly with movement direction. This was confirmed by calculating a vector defined by the dynamic components of the shoulder and elbow torques. The vector rotates smoothly about an ellipse in intrinsic, joint torque space as the direction of hand motion rotates about a circle in extrinsic Cartesian space. This confirms a second implication of linear synergy that the scaling constant between the linearly related joint torques is directionally dependent. Multiple linear regression showed that the torque at each joint scales as a simple linear function of the angular displacement at both joints, in spite of the complex nonlinear dynamics of multijoint movement. The coefficients of this function are independent of the initial arm position and movement distance and are the same for all subjects. This is an unanticipated finding. We discuss these observations in terms of the hypothesis that voluntary, multiple degrees of freedom, rapid reaching movements may use rule-based, feed-forward control of dynamic joint torque. Rule-based control of joint torque with separate dynamic and static controllers is an alternative to models such as those based on the equilibrium point hypotheses that rely on a positionally based controller to produce both dynamic and static torque components. It is also an alternative to feed-forward models that directly solve the problems of inverse dynamics. Our experimental findings are not necessarily incompatible with any of the alternative models, but they describe new, additional findings for which we need to account. The rules are chosen by the nervous system according to features of the kinematic task to couple muscle contraction at the shoulder and elbow in a linear synergy. Speed and load control preserves the relative magnitudes of the dynamic torques while directional control is accomplished by modulating them in a differential manner. This control system operates in parallel with a positional control system that solves the problems of postural stability.

scholarly journals Single Task Optimization-Based Planar Box Delivery Motion Simulation and Experimental Validation

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
Yujiang Xiang ◽  
Shadman Tahmid ◽  
Paul Owens ◽  
James Yang
Keyword(s):  
Joint Angle ◽  
Inverse Dynamics ◽  
Optimization Method ◽  
Joint Torque ◽  
Motion Simulation ◽  
Single Task ◽  
Joint Torques ◽  
Time Integral ◽  
Design Variables ◽  
Complicated Task

Abstract Box delivery is a complicated task and it is challenging to predict the box delivery motion associated with the box weight, delivering speed, and location. This paper presents a single task-based inverse dynamics optimization method for determining the planar symmetric optimal box delivery motion (multi-task jobs). The design variables are cubic B-spline control points of joint angle profiles. The objective function is dynamic effort, i.e., the time integral of the square of all normalized joint torques. The optimization problem includes various constraints. Joint angle profiles are validated through experimental results using root-mean-square-error (RMSE) and Pearson’s correlation coefficient. This research provides a practical guidance to prevent injury risks in joint torque space for workers who lift and deliver heavy objects in their daily jobs.

scholarly journals Measures of fit impacts: Application to the causal model of consumer involvement

2018 ◽  
Vol 61 (1) ◽  
pp. 77-92
Author(s):  
Eric Rakotoasimbola ◽  
Sam Blili
Keyword(s):  
Sample Size ◽  
Root Mean Square ◽  
Goodness Of Fit ◽  
Causal Model ◽  
Estimation Method ◽  
Generalized Least Squares ◽  
Consumer Involvement ◽  
Mean Square ◽  
Fit Indices ◽  
Fit Index

Using the Monte Carlo simulation method, this study analyzes the impacts on fit indices by the degree of nonnormality of variables, the sample size, and the choice of estimation method. To address these issues, we use the causal model of consumer involvement as elaborated by Mittal and Lee. Results of this study show that adjusted goodness of fit index (AGFI) and goodness of fit index (GFI) are subject to variation in sample size, and their use requires a sample size of at least 300 observations to be reliable. Comparative fit index (CFI) and root mean square error of approximation (RSMEA) are more reliable with the generalized least squares (GLS) compared with maximum likelihood estimation (MLE) method under different settings of sample size and degree of nonnormality. Finally, for the standardized root mean square residual (SRMR), it is recommended that it is used with the MLE method. This study provides prescriptions for the choice of fit indices and the requirements of sample size and estimation method to test the causal model of consumer involvement. The method used here can be extended to any model before fitting it to real data. It helps researchers to prevent conflictual results regarding the choice of fit indices.

Women Ankle Joint Torques Comparison between Bare Foot and High Heel

2013 ◽  
Vol 378 ◽  
pp. 382-386
Author(s):  
Hai Bin Liu ◽  
Zhi Qiang He ◽  
Wen Xue Yuan ◽  
Zhao Li Meng
Keyword(s):  
Ankle Joint ◽  
Muscle Force ◽  
Inverse Dynamics ◽  
Frontal Plane ◽  
Joint Torque ◽  
Force System ◽  
Joint Torques ◽  
High Heel ◽  
Internal Phase ◽  
The Stability

Objective: Research on ankle joint torques of healthy women with high heel compared with bare foot based on Inverse Dynamics. Methods: 12 women were recruited and tested by motion and force system. Kinematical, kinetic and personal segment parameter data were used to compute ankle joint torques and compare the differences between bare foot and high heel.Conclusion: compared with bare foot, It can infer that Soleus and Gastrocnemius access the contraction in advance and keep higher muscle force. Tibia Anterior and Posterior must have to make powerful contraction that could keep the ankle joint with higher torque. Compared with sagital and frontal plane, high heel doesnt change the joint torque in horizontal plane during the whole internal phase, but the fluctuations of torque value may influence the stability during normal level walking.

scholarly journals On the Organizing Role of Nonmuscular Forces During Performance of a Giant Circle in Gymnastics

2012 ◽  
Vol 28 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Violaine Sevrez ◽  
Guillaume Rao ◽  
Eric Berton ◽  
Reinoud J. Bootsma
Keyword(s):  
Muscle Force ◽  
Inverse Dynamics ◽  
Joint Torque ◽  
Hip Joints ◽  
Joint Torques ◽  
Kinematic Pattern ◽  
Triple Pendulum ◽  
Inverse Dynamics Analysis ◽  
Induced Changes

Five elite gymnasts performed giant circles on the high bar under different conditions of loading (without and with 6-kg loads attached to the shoulders, waist or ankles). Comparing the gymnasts’ kinematic pattern of movement with that of a triple-pendulum moving under the sole influence of nonmuscular forces revealed qualitative similarities, including the adoption of an arched position during the downswing and a piked position during the upswing. The structuring role of nonmuscular forces in the organization of movement was further reinforced by the results of an inverse dynamics analysis, assessing the contributions of gravitational, inertial and muscular components to the net joint torques. Adding loads at the level of the shoulders, waist or ankles systematically influenced movement kinematics and net joint torques. However, with the loads attached at the level of the shoulders or waist, the load-induced changes in gravitational and inertial torques provided the required increase in net joint torque, thereby allowing the muscular torques to remain unchanged. With the loads attached at the level of the ankles, this was no longer the case and the gymnasts increased the muscular torques at the shoulder and hip joints. Together, these results demonstrate that expert gymnasts skillfully exploit the operative nonmuscular forces, employing muscle force only in the capacity of complementary forces needed to perform the task.

An Efficient Probabilistic Methodology for Incorporating Uncertainty in Body Segment Parameters and Anatomical Landmarks in Joint Loadings Estimated From Inverse Dynamics

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Joseph E. Langenderfer ◽  
Peter J. Laz ◽  
Anthony J. Petrella ◽  
Paul J. Rullkoetter
Keyword(s):  
Lower Extremity ◽  
Inverse Dynamics ◽  
The Body ◽  
Implant Design ◽  
Anatomical Landmarks ◽  
Body Segment ◽  
Joint Loading ◽  
Data Set ◽  
Reaction Data ◽  
Body Segment Parameters

Inverse dynamics is a standard approach for estimating joint loadings in the lower extremity from kinematic and ground reaction data for use in clinical and research gait studies. Variability in estimating body segment parameters and uncertainty in defining anatomical landmarks have the potential to impact predicted joint loading. This study demonstrates the application of efficient probabilistic methods to quantify the effect of uncertainty in these parameters and landmarks on joint loading in an inverse-dynamics model, and identifies the relative importance of the parameters and landmarks to the predicted joint loading. The inverse-dynamics analysis used a benchmark data set of lower-extremity kinematics and ground reaction data during the stance phase of gait to predict the three-dimensional intersegmental forces and moments. The probabilistic analysis predicted the 1–99 percentile ranges of intersegmental forces and moments at the hip, knee, and ankle. Variabilities, in forces and moments of up to 56% and 156% of the mean values were predicted based on coefficients of variation less than 0.20 for the body segment parameters and standard deviations of 2mm for the anatomical landmarks. Sensitivity factors identified the important parameters for the specific joint and component directions. Anatomical landmarks affected moments to a larger extent than body segment parameters. Additionally, for forces, anatomical landmarks had a larger effect than body segment parameters, with the exception of segment masses, which were important to the proximal-distal joint forces. The probabilistic modeling approach predicted the range of possible joint loading, which has implications in gait studies, clinical assessments, and implant design evaluations.

scholarly journals The Effect of Estimation Methods on SEM Fit Indices

2019 ◽  
Vol 80 (3) ◽  
pp. 421-445 ◽  
Author(s):  
Dexin Shi ◽  
Alberto Maydeu-Olivares
Keyword(s):  
Least Squares ◽  
Root Mean Square ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Estimation Methods ◽  
Equation Modeling ◽  
Model Parameters ◽  
Mean Square ◽  
Fit Indices

We examined the effect of estimation methods, maximum likelihood (ML), unweighted least squares (ULS), and diagonally weighted least squares (DWLS), on three population SEM (structural equation modeling) fit indices: the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root mean square residual (SRMR). We considered different types and levels of misspecification in factor analysis models: misspecified dimensionality, omitting cross-loadings, and ignoring residual correlations. Estimation methods had substantial impacts on the RMSEA and CFI so that different cutoff values need to be employed for different estimators. In contrast, SRMR is robust to the method used to estimate the model parameters. The same criterion can be applied at the population level when using the SRMR to evaluate model fit, regardless of the choice of estimation method.

scholarly journals A study into the propagation of the uncertainties in nuclear data to the nuclear concentrations of nuclides in burn-up calculations

2020 ◽  
Vol 6 (3) ◽  
pp. 161-166
Author(s):  
Alexander N. Pisarev ◽  
Valerii V. Kolesov
Keyword(s):  
Neutron Flux ◽  
Root Mean Square ◽  
Estimation Method ◽  
Nuclear Data ◽  
Reaction Rates ◽  
Mean Square ◽  
Fuel Burn ◽  
Calculation Results ◽  
Effective Multiplication Factor ◽  
Effective Multiplication

The key papers on estimating the uncertainties in nuclear data deal with the influence of these uncertainties on the effective multiplication factor by introducing the so-called sensitivity factors and only some of these are concerned with the influence of such uncertainties on the life calculation results. On the other hand, the uncertainties in reaction rates, the neutron flux, and other quantities may lead to major distortions in findings, this making it important to be able to determine the influence of uncertainties on the nuclear concentrations of nuclides in their burn-up process. The possibility for the neutron flux and reaction rate uncertainties to propagate to the nuclear concentrations of nuclides obtained as part of burn-up calculations are considered using an example of a MOX-fuel PWR reactor cell. To this end, three burn-up calculation cycles were performed, and the propagation of uncertainties was analyzed. The advantages of the uncertainty estimation method implemented in the VisualBurnOut code consists in that all root-mean-square deviations are obtained as part of one calculation as the statistical method, e.g. GRS (Generation Random Sampled), requires multiple calculations. The VisualBurnOut calculation results for the root-mean-square deviations in nuclear concentrations were verified using a simple model problem. It is shown that there is a complex dependence of the propagation of the root-mean-square deviations in the nuclear concentrations of nuclides in the process of fuel burn-up, and, therefore, further studies need to aim at investigating the influence of uncertainties in nuclear data on the nuclear concentrations of nuclides.

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