Functional Degrees Of Freedom Research Articles

Impact of Joint Fixation on Postural Dynamics during Single-Leg Stance

We investigated the relationship between the mechanical degrees of freedom (DoF) and its postural dynamics. The joint DoF was fixed to constrain the mechanical DoF. Nine participants were required to perform a single-leg stance task. The center of pressure trajectory data was analyzed. Ankle fixation induced a larger amount of variability in the anteroposterior direction, and less dimensionality and complexity in the mediolateral direction. These results suggest that the ankle joint fixation caused limited postural sway in the mediolateral direction; therefore, functional DoF and complexity decreased. In contrast, it increased the amount of postural sway variability in the anteroposterior direction. Our findings imply a direct relationship between the mechanical DoF of the human movement system and its postural dynamics.

A Computationally Efficient Musculoskeletal Model of the Lower Limb for the Control of Rehabilitation Robots: Assumptions and Validation

We present and validate a computationally efficient lower limb musculoskeletal model for the control of a rehabilitation robot. It is a parametric model that allows the customization of joint kinematics, and it is able to operate in real time. Methods: Since the rehabilitation exercises corresponds to low-speed movements, a quasi-static model can be assumed, and then muscle force coefficients are position dependent. This enables their calculation in an offline stage. In addition, the concept of a single functional degree of freedom is used to minimize drastically the workspace of the stored coefficients. Finally, we have developed a force calculation process based on Lagrange multipliers that provides a closed-form solution; in this way, the problem of dynamic indeterminacy is solved without the need to use an iterative process. Results: The model has been validated by comparing muscle forces estimated by the model with the corresponding electromyography (EMG) values using squat exercise, in which the Spearman’s correlation coefficient is higher than 0.93. Its computational time is lower than 2.5 ms in a conventional computer using MATLAB. Conclusions: This procedure presents a good agreement with the experimental values of the forces, and it can be integrated into real time control systems.

Three-Dimensional Displacement Fields from InSAR through Tikhonov Regularization and Least-Squares Variance Component Estimation

Synthetic aperture radar interferometry (InSAR) measures the projection of three-dimensional (3D) ground displacement in the range direction and in the azimuth direction through image processing. The incapability of InSAR in measuring the 3D displacements restricts its capability for assessing real Earth surface deformation. The near-polar orbiting characteristics of InSAR missions reduce the sensitivity of line-of-sight (LOS) displacements significantly to the north-south components of the real 3D displacement fields and weaken the geometric strength of a given configuration. Applying range measurements from various missions to address 3D displacement leads to an ill-posed inverse problem that needs to be regularized. Moreover, it needs appropriate weighting of the observations to give proper estimates of the parameters. In this study, we propose Tikhonov regularization (TR) and least-squares variance component estimation (LS-VCE) methods for retrieving 3D displacement vectors from range and azimuth displacements. Depending on the functional degree of freedom (DoF) of the inverse problem, the TR and LS-VCE methods are applied in determined and overdetermined equation systems, respectively, to stabilize the ill-conditioned models and estimate the variance components of observations. These methods were evaluated by two synthetic data sets and a real data set from the Sentinel-1 terrain observation by progressive scan (TOPS) and ALOS-2 phased array type L-band synthetic aperture radar (PALSAR-2) missions in 2015 of the MW = 8.3 Illapel earthquake in Chile. Results indicate more than 40% improvement in both the precision and accuracy of retrieving 3D deformation fields when the regularized LS-VCE (RLS-VCE) is adopted instead of the conventional method (CM) that considers primary weighting for observations. Applying the range and azimuth InSAR displacements together with adopting the LS-VCE method reveal a north-south convergent borderline near 31.2° S in the 2015 Illapel earthquake.

Principal Component Analysis Reveals the Proximal to Distal Pattern in Vertical Jumping Is Governed by Two Functional Degrees of Freedom.

The successful completion of motor tasks requires effective control of multiple degrees of freedom (DOF), with adaptations occurring as a function of varying performance constraints. In this study we sought to compare the emergent coordination strategies employed in vertical jumping under different task constraints [countermovement jump (CMJ) with arm swing-CMJas and no arm swing-CMJnas]. In order to achieve this, principal component analysis (PCA) was conducted on joint moment waveform data from the hip, knee and ankle. This statistical approach has the advantage of analyzing the whole movement within a time series and reduces multidimensional datasets to lower dimensions for analysis. Both individual and group analyses were conducted. For individual analysis, PCA was conducted on combined hip, knee, and ankle joint moment data for each individual across both CMJnas (thirty-eight participants), and CMJas (twenty-two participants) conditions. PCA was also performed comparing all data from each individual across CMJnas and CMJas conditions. The results revealed a maximum of three principal components (PC) explained over 90% of the variance in the data sets for both conditions and within individual and group analyses. For individual analysis, no more than 2PCs were required for both conditions. For group analysis, CMJas required 3PCs to explain over 90% of the variance within the dataset and CMJnas only required 2PCs. Reconstruction of the original NJM waveforms from the PCA output demonstrates a greater loading of hip and knee joint moments to PC1, with PC2 showing a greater loading to ankle joint moment. The reduction in dimensions of the original data shows the proximal to distal extension pattern in the sagittal plane, typical of vertical jumping tasks, is governed by only 2 functional DOF, at both a group, and individual level, rather than the typically reported 3 mechanical DOF in some forms of jumping.

Methodical uncertainty in the two-point measurement of parts prismatic elements linear dimensions

The article is devoted to the topical problem of the reliability of measurements of geometrical specifications of technical products. The purpose of this article is to improve the quality control of the linear dimensions of the parts by the two-point measurement method. The goal of the article is the study of advanced methodical uncertainties of measurement of linear dimensions of plane-parallel prismatic elements. The method of research is geometric modeling of deviations of the element surfaces form and position in the rectangular coordinate system. The research was carried out for various executive elements with regard to their information content corresponding to the classes of kinematic pairs in the theory of mechanics and the number of constrained degrees of freedom in function of the basic elements. Prismatic elements with informative content 3, 2, 1 and θ (zero) were studied. Uncertainty assessment of two-point measurements were made by comparing the measurements results of linear dimensions and functional dimensions of the element maximum and minimum material constrained by the limits of maximum and minimum. As a result of studies of the two-point measurements accuracy, it is found that the methodical uncertainty is formed when measuring the average size of elements for all types of form deviations. The two-point measurement method cannot account for deviations of the location dimension of the element and therefore its use for items with less than the maximum informativeness creates unacceptably large methodical uncertainties of measurement the maximum, minimum and medium linear sizes. The same methodical uncertainties occur under the arbitration control of the parts linear dimensions by the limit two-point gauges.

On classical integrability of the hydrodynamics of quantum integrable systems

Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain ‘Bethe–Boltzmann’ kinetic equation, which has the form of an integro-differential conservation law in D. The purpose of the present work is to investigate the sense in which the Bethe–Boltzmann equation defines an ‘integrable kinetic equation’. To this end, we study a class of N dimensional systems of evolution equations that arise naturally as finite-dimensional approximations to the Bethe–Boltzmann equation. We obtain non-local Poisson brackets and Hamiltonian densities for these equations and derive an infinite family of first integrals, parameterized by N functional degrees of freedom. We find that the conserved charges arising from quantum integrability map to Casimir invariants of the hydrodynamic bracket and their group velocities map to Hamiltonian flows. Some results from the finite-dimensional setting extend to the underlying integro-differential equation, providing evidence for its integrability in the hydrodynamic sense.

Gowdy-symmetric cosmological models with Cauchy horizons ruled by non-closed null generators

Smooth Gowdy-symmetric generalized Taub-NUT solutions are a class of inhomogeneous cosmological models with spatial three-sphere topology. They have a past Cauchy horizon with closed null-generators, and they have been shown to develop a second, regular Cauchy horizon in the future, unless in special, well-defined singular cases. Here we generalize these models to allow for past Cauchy horizons ruled by non-closed null generators. In particular, we show local and global existence of such a class of solutions with two functional degrees of freedom. This removes a periodicity condition for the asymptotic data at the past Cauchy horizon that was required before. Moreover, we derive a three-parametric family of exact solutions within that class and study its properties.

C0 Layerwise Model with Fixed Degrees of Freedom and Variable In- and Out-of-Plane Kinematics by Strain Energy Updating Technique

Physically based zigzag models have the merit of giving accurate stress predictions for laminates and sandwiches keeping fixed the functional degrees of freedom, though at the expense of the introduction of their derivatives. In the present paper, a technique that enables deleting these derivatives is developed. The objective is finding a priori corrections of displacements, which make the energy of the model with all the derivatives neglected equivalent to that of its initial counterpart model containing all the derivatives. Numerical applications show that this technique can obtain accurate results, even for strongly asymmetrical lay-ups, keeping low the computational cost.

Development of an Efficient Zigzag Model with Variable Representation of Displacements across the Thickness

A refined three-dimensional zigzag plate model with hierarchic representation of displacements across the thickness is developed that accurately captures interlaminar stresses directly from constitutive equations with low computational effort. Thanks to the incorporation of high-order terms, the representation can be different from point to point across the thickness; thus, it can be adapted to variations of solutions. However, as in classical models, the functional degrees of freedom are the midplane displacements and the shear rotations because high-order contributions are determined without adding new unknowns. They are computed by enforcing equilibrium conditions at discrete points across the thickness and stress boundary conditions. The model fulfills a priori the interfacial stress continuity conditions at the interfaces thanks to the incorporation of appropriate continuity functions. A new approach is adopted that overcomes the drawbacks of algebraic manipulations because the expressions of high-order terms and continuity functions are derived separately only once in closed form for all conditions with a symbolic calculus tool. As shown by the numerical tests, the model accurately predicts the stress field of thick laminated and sandwich plates with abruptly changing material properties with a lower overall processing time than previously developed models by the authors.

Extension of the Strain Energy Updating Technique to a Multilayered Shell Model with Adaptive Displacements and Fixed DOF

AbstractThe strain energy updating technique (SEUPT) is extended to a new zigzag shell model with a hierarchical piecewise representation of displacements, which can adapt to a variation of solutions across the thickness. This model has the capability of being refined across the thickness without increasing the number of functional degrees of freedom (DOF) (the traditional midplane displacements and shear rotations). The purpose of the SEUPT is to improve the accuracy of standard finite elements based on equivalent single-layer models with transverse shear deformations up to the level of the zigzag model. The strain and kinetic energies and the work of external forces are updated through a postprocessing iterative procedure by starting from a local interpolation of the results of the finite-element analysis. Because no derivatives of in-plane stresses are involved, updating is fast. The current version of the SEUPT obtains accurate predictions of interlaminar stresses from constitutive equations; thus, it...

Optimal average path of the instantaneous helical axis in planar motions with one functional degree of freedom

This paper presents a model for determining the path of the instantaneous helical axis (IHA) that optimally represents human planar motions with one functional degree of freedom (fDOF). A human movement is said to have one fDOF when all degrees of freedom (DOFs) are coordinated such that all the kinematic variables can be expressed, across movement repetitions, as functions of only one independent DOF, except for a small natural intercycle variability quantified as lower than a prespecified value. The concept of fDOF allows taking into account that, due to motor coordination, human movements are executed in a repeatable manner. Our method uses the measurement of several repetitions of a given movement to obtain the optimal average IHA path. The starting point is a change of variables, from time to a joint position magnitude (generally an angle). In this way, instead of operating with the time-dependent single-valued trajectory of the successive cycles, our model permits the representation of any motion variable (e.g. positions and their time derivatives) as a cloud of points dependent on the joint angle. This allows the averaging to be performed over the displacements and their derivatives before determining the mean IHA path. We thus avoid the nonlinear magnification of errors and variability inherent in the IHA computation. Moreover, the IHA path can be considered as a geometric attribute of the joint and the type of motion, rather than of each single movement execution. An experiment was performed that show the accuracy and usefulness of the method.

Self-consistent current structures in a relativistic collisionless plasma

Based on the method of invariants of particle motion in a relativistic collisionless plasma, we obtain a series of exact nonlinear solutions describing stationary neutral current-carrying structures with self-consistent magnetic field in planar, cylindrical, and 2D geometries. The solutions correspond to space-inhomogeneous anisotropic particle distributions and have a functional degree of freedom, i.e., they do not require a known fixed form of energy distribution. Physical properties of the current sheets and filaments, including current localization and value, degree of anisotropy of the particle distribution, and constraints on the particle and magnetic-field energy-density ratio, are discussed.

P011 Functional degrees of freedom of neck movements: linear models may overestimate variability

P011 Functional degrees of freedom of neck movements: linear models may overestimate variability

Structure of correlation tensors in homogeneous anisotropic turbulence

We extend the theory of isotropic tensors, developed by Robertson, Batchelor, and Chandrasekhar, to cover the general case of turbulence with a pseudovector-preferred direction, without assuming mirror-reflection invariance. Attention is focused on two-point-correlation functions, and it is shown that the form of the decomposition into proper and pseudotensor contributions is restricted by the homogeneity requirement. We present the somewhat unexpected result that the vector- and pseudovector-preferred-direction cases yield different results: A pseudovector-preferred direction allows the correlation matrix one more functional degree of freedom than does the "proper" vector case. We present an explicit form of the two-point-correlation tensor in the presence of a uniform mean magnetic field which may be appropriate for use in analysis of magnetic fluctuations in plasma containment devices or the interplanetary medium. A procedure for determining the magnetic helicity from experimental data is presented.