Representation Of Kinematics Research Articles

An enriched shell element formulation for modeling of inter- and intralaminar crack propagation in laminates

In traditional finite element modeling of progressive failure in laminated fiber reinforced polymers, inter- and intralaminar cracks are normally treated in different ways. Interlaminar cracks are normally described explicitly by building up the laminate using stacked elements (solids or shells) connected by cohesive interface elements. Intralaminar cracks, one the other hand, are more often accounted for by using a continuum damage approach, (e.g. a smeared crack approach). In this paper, we propose a modeling concept which instead can accurately represent both intralaminar and interlaminar cracks with an extended kinematical representation, whereby cracks can be explicitly accounted for without excessive use of degrees of freedom. With this concept, we aim to take one step closer to more efficient FE analyses of progressive laminate failure, since only one shell element through the thickness is required, and where arbitrary inter- and intralaminar crack propagation are accounted for only in areas where it is needed. We show that the current shell formulation proposed can be utilized to describe the kinematics of a laminate containing multiple inter- and intralaminar cracks. Thus, we see significant potential for this modeling concept in analyses in which computational efficiency is of major importance.

Beyond reward prediction errors: the role of dopamine in movement kinematics.

We recorded activity of dopamine (DA) neurons in the substantia nigra pars compacta in unrestrained mice while monitoring their movements with video tracking. Our approach allows an unbiased examination of the continuous relationship between single unit activity and behavior. Although DA neurons show characteristic burst firing following cue or reward presentation, as previously reported, their activity can be explained by the representation of actual movement kinematics. Unlike neighboring pars reticulata GABAergic output neurons, which can represent vector components of position, DA neurons represent vector components of velocity or acceleration. We found neurons related to movements in four directions—up, down, left, right. For horizontal movements, there is significant lateralization of neurons: the left nigra contains more rightward neurons, whereas the right nigra contains more leftward neurons. The relationship between DA activity and movement kinematics was found on both appetitive trials using sucrose and aversive trials using air puff, showing that these neurons belong to a velocity control circuit that can be used for any number of purposes, whether to seek reward or to avoid harm. In support of this conclusion, mimicry of the phasic activation of DA neurons with selective optogenetic stimulation could also generate movements. Contrary to the popular hypothesis that DA neurons encode reward prediction errors, our results suggest that nigrostriatal DA plays an essential role in controlling the kinematics of voluntary movements. We hypothesize that DA signaling implements gain adjustment for adaptive transition control, and describe a new model of the basal ganglia (BG) in which DA functions to adjust the gain of the transition controller. This model has significant implications for our understanding of movement disorders implicating DA and the BG.

Multipole expansion of continuum dislocations dynamics in terms of alignment tensors

The development of a dislocation-based continuum theory of plasticity remains one of the central challenges of applied physics and materials science. Developing a continuum theory of dislocations requires the solution of two long-standing problems: (i) to find a faithful representation of dislocation kinematics with a reasonable number of variables and (ii) to derive averaged descriptions of the dislocation dynamics (i.e. material laws) in terms of these variables. In the current paper, we solve the first problem, i.e. we develop tensorial conservation laws for distributions of oriented lines. This is achieved through a multipole expansion of the dislocation density in terms of so-called alignment tensors containing information on the directional distribution of dislocation density and dislocation curvature. A hierarchy of evolution equations of these tensors is derived from a higher dimensional dislocation density theory. Low-order closure approximations of this hierarchy lead to continuum dislocation dynamics models of plasticity with only few internal variables. Perspectives for more refined theories and current challenges in dislocation density modelling are discussed.

An enriched shell element formulation for efficient modeling of multiple delamination propagation in laminates

In the modeling of progressive damage in fiber reinforced polymers, the kinematical representation of delamination is normally treated in one of two ways. Either efficient or accurate modeling of delamination is considered. In the first case, delamination is disregarded or implicitly included in the material modeling. In the second case, delamination is explicitly modeled at a significant numerical cost where all plies are represented by separate elements in the thickness direction, connected by interlaminar cohesive zone elements. In this paper, we therefore aim to take one step closer to more efficient FE analyses by presenting a modeling concept which supports laminate failure analyses requiring only one shell element through the thickness. With this concept, arbitrary delamination propagation is accounted for only in areas where it is needed. In addition, by using this concept, the model preparation time is reduced. We show that the current shell formulation proposed can be utilized to accurately simulate propagating delamination cracks as well as to accurately describe the kinematics of a laminate containing multiple delaminations through the thickness. Thus, we see significant potential for this modeling concept in analyses in which computationally efficiency is of major importance, such as for large scale crash analyses.

Sensor positioning and experimental constraints influence estimates of local dynamic stability during repetitive spine movements

Application of non-linear dynamics analyses to study human movement has increased recently, which necessitates an understanding of how dependent measures may be influenced by experimental design and setup. Quantifying local dynamic stability for a multi-articulated structure such as the spine presents the possibility for estimates to be influenced by positioning of kinematic sensors used to measure spine angular kinematics. Oftentimes researchers will also choose to constrain the spine׳s movement by physically restraining the pelvis and/or using targets to control movement endpoints. Ten healthy participants were recruited, and asked to perform separate trials of 35 consecutive cycles of spine flexion under both constrained and unconstrained conditions. Electromagnetic sensors that measure three-dimensional angular orientations were positioned over the pelvis and the spinous processes of L3, L1, and T11. Using the pelvic sensor as a reference, each sensor location on the spine was used to obtain a different representation of the three-dimensional spine angular kinematics. Local dynamic stability of each kinematic time-series was determined by calculating the maximum finite-time Lyapunov exponent (λmax). Estimates for λmax were significantly lower (i.e. dynamically more stable) for spine kinematic data obtained from the L3 sensor than those obtained from kinematic data using either the L1 or T11 sensors. Likewise, λmax was lower when the movement was constrained. These results emphasize the importance of proper placement of instrumentation for quantifying local dynamic stability of spine kinematics and are especially relevant for repeated measures designs where data are obtained from the same individual on multiple days.

The granularity of grasping: Comment on “Grasping synergies: A motor-control approach to the mirror neuron mechanism” by A. D'Ausilio et al.

The idea that mirror neuron systems in the human and the macaque monkey could provide a link between perceiving an action and performing it has spurred intense research [1,2]. Hundreds of papers now examine if this link exists and what it might contribute to human behaviour. The review article from D’Ausilio et al. [3] highlights how relatively few papers have considered the granularity of coding with mirror neuron systems, and even fewer have directly tested different possibilities. Granularity refers to the critical question of what actually is encoded within the mirror system – are neurons selective for low level kinematic features such as joint angle, or for postural synergies, or for action goals? Focusing on studies of single neurons in macaques and on studies measuring the excitability of primary motor cortex with TMS, the review suggests that it is very hard to distinguish low-level kinematic from goal representations. Furthermore, these two levels are often highly correlated in real-life contexts – the kinematics needed to grasp an apple are defined by the shape of the goal (an apple tends to be a large sphere) and these kinematics differ for other possible goals (a pencil which is a narrow cylinder). In some cases, kinematics may be enough to define a goal [4]. The review suggests that it is therefore arbitrary to distinguish these levels, and that a synergy level might be a better way to understand the mirror system. Synergies are a form of coding based on commonly used hand-shapes or hand postures, which take into account the fact that some joint angles are more likely to co-occur than others. Evidence that different grasp shapes are represented separately in premotor cortex has been found [5]. These could provide an intermediate level of representation between muscle activity and goals. The review proposes that a synergy level of granularity provides the best way to consider both the motor system and the role of the mirror system in understanding actions. This is a useful proposal, but has some limitations. The proposed synergies seem much closer to a kinematic representation than to goals, and do not necessarily resolve the problem of if/how the mirror neuron system could contribute to understanding goals. Just because it is not easy to separate cognitive concepts such as kinematics and goals, does not mean it should not be done. A small number of carefully designed fMRI experiments have been able to show distinct patterns of brain activity for goals and kinematics. For example, grasping a tennis ball and grasping an apple both involve the same hand kinematics and the same hand synergies, but quite different goals. Anterior intraparietal sulcus can distinguish these actions [6] and shows cross-modal sensitivity to other action goals too [7].

Changes in Purkinje cell simple spike encoding of reach kinematics during adaption to a mechanical perturbation.

The cerebellum is essential in motor learning. At the cellular level, changes occur in both the simple spike and complex spike firing of Purkinje cells. Because simple spike discharge reflects the main output of the cerebellar cortex, changes in simple spike firing likely reflect the contribution of the cerebellum to the adapted behavior. Therefore, we investigated in Rhesus monkeys how the representation of arm kinematics in Purkinje cell simple spike discharge changed during adaptation to mechanical perturbations of reach movements. Monkeys rapidly adapted to a novel assistive or resistive perturbation along the direction of the reach. Adaptation consisted of matching the amplitude and timing of the perturbation to minimize its effect on the reach. In a majority of Purkinje cells, simple spike firing recorded before and during adaptation demonstrated significant changes in position, velocity, and acceleration sensitivity. The timing of the simple spike representations change within individual cells, including shifts in predictive versus feedback signals. At the population level, feedback-based encoding of position increases early in learning and velocity decreases. Both timing changes reverse later in learning. The complex spike discharge was only weakly modulated by the perturbations, demonstrating that the changes in simple spike firing can be independent of climbing fiber input. In summary, we observed extensive alterations in individual Purkinje cell encoding of reach kinematics, although the movements were nearly identical in the baseline and adapted states. Therefore, adaption to mechanical perturbation of a reaching movement is accompanied by widespread modifications in the simple spike encoding.

Extreme structural response values from various methods of simulating wave kinematics

In offshore engineering, the main forces that are loaded onto ocean structures come from wind-generated random waves. The prediction of wave forces that are applied onto slender cylindrical members is usually based on the Morison's equation, in which the wave force at any section of a member is expressed directly in terms of wave kinematics. It is essential to be able to estimate sensible kinematics at all levels of a structure to determine accurate prediction of wave forces and corresponding responses of these structures in a random wave field. Linear random wave theory (LRWT) is the simplest and most often used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record. However, water particle kinematics calculated from LRWT grossly overpredicts the kinematics above the mean water level (MWL). Methods have been introduced to overcome this problem of high kinematics above the MWL, which consists of using linear wave theory (such as Wheeler, vertical stretching, effective node elevation and effective water depth methods) to provide a more realistic representation of near-surface wave kinematics. This is promising as there is some evidence that the water particle kinematics from the Wheeler method are underestimated and that those from the vertical stretching method are somewhat exaggerated. In this paper, the comparisons of the probability distributions of extreme values from different methods of simulation wave kinematics are investigated by using conventional time simulation procedure.

Nonlinear three-dimensional beam theory for flexible multibody dynamics

In flexible multibody systems, it is convenient to approximate many structural components as beams or shells. Classical beam theories, such as Euler–Bernoulli beam theory, often form the basis of the analytical development for beam dynamics. The advantage of this approach is that it leads to a very simple kinematic representation of the problem: the beam’s section is assumed to remain plane and its displacement field is fully defined by three displacement and three rotation components. While such an approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. This paper presents a different approach to the problem. Based on a finite element discretization of the cross-section, an exact solution of the theory of three-dimensional elasticity is developed. The proposed approach is based on the Hamiltonian formalism and leads to an expansion of the solution in terms of extremity and central solutions. Kinematically, the problem is decomposed into an arbitrarily large rigid-section motion and a warping field. The sectional strains associated with the rigid-section motion and the warping field are assumed to remain small. As a consequence of this kinematic decomposition, the governing equations of the problem fall into two distinct categories: the equations describing geometrically exact beams and those describing local deformations. The governing equations for geometrically exact beams are nonlinear, one-dimensional equations, whereas a linear, two-dimensional analysis provides the detailed distribution of three-dimensional stress and strain fields. Within the stated assumptions, the solutions presented here are the exact solution of three-dimensional elasticity for beams undergoing arbitrarily large motions.

Digital Image Correlation Development for the Study of Materials Including Multiple Crossing Cracks

This study reports on the digital image correlation (DIC) procedure and its limitation in the case of fracture analysis. A comparison of three different algorithms was carried out for the case of crossing cracks. An improvement of the DIC procedure was proposed to solve the uncertainty problems at the vicinity of the junction of two cracks. This procedure was proposed to perform an evaluation of the displacement when multiple cracks are present in the subset. It was developed using classical minimization process, including Heaviside functions in the kinematical field representation. Some tests were performed to demonstrate the performances of this new algorithm. An application of the multiple fractures on Argillite rock is shown to validate the efficiency and the robustness of the proposed method.

Three-Dimensional Beam Theory for Flexible Multibody Dynamics

In multibody systems, it is common practice to approximate flexible components as beams or shells. More often than not, classical beam theories, such as the Euler–Bernoulli beam theory, form the basis of the analytical development for beam dynamics. The advantage of this approach is that it leads to simple kinematic representations of the problem: the beam's section is assumed to remain plane and its displacement field is fully defined by three displacement and three rotation components. While such an approach is capable of accurately capturing the kinetic energy of the system, it cannot adequately represent the strain energy. For instance, it is well known from Saint-Venant's theory for torsion that the cross-section will warp under torque, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, sectional stiffnesses are computed based on sophisticated mechanics of material theories that evaluate the complete state of deformation. These sectional stiffnesses are then used within the framework of a Euler–Bernoulli beam theory based on far simpler kinematic assumptions. While this approach works well for simple cross-sections made of homogeneous material, inaccurate predictions may result for realistic configurations, such as thin-walled sections, or sections comprising anisotropic materials. This paper presents a different approach to the problem. Based on a finite element discretization of the cross-section, an exact solution of the theory of three-dimensional elasticity is developed. The only approximation is that inherent to the finite element discretization. The proposed approach is based on the Hamiltonian formalism and leads to an expansion of the solution in terms of extremity and central solutions, as expected from Saint-Venant's principle.

A non-linear vehicle dynamics model for accurate representation of suspension kinematics

A non-linear full vehicle model for simulation of vehicle ride and handling performance is proposed. The model effectively estimates the suspension spring compressions, thus improving the accuracy of normal force calculations. This is achieved by developing models for suspension kinematics, which are then integrated with the commonly used 14 degrees of freedom vehicle dynamics models. This integrated model effectively estimates parameters like camber angles, toe angles and jacking forces, which are capable of significantly affecting the handling performance of the vehicle. The improvements in the accuracy of spring compressions help in simulating the effects of non-linear suspension elements, and the accuracy of handling simulation is enhanced by the improvements in normal force estimates. The model developed in Simulink is validated by comparing the results to that from ADAMS car.

Scaling and kinematics optimisation of the scapula and thorax in upper limb musculoskeletal models

Accurate representation of individual scapula kinematics and subject geometries is vital in musculoskeletal models applied to upper limb pathology and performance. In applying individual kinematics to a model׳s cadaveric geometry, model constraints are commonly prescriptive. These rely on thorax scaling to effectively define the scapula׳s path but do not consider the area underneath the scapula in scaling, and assume a fixed conoid ligament length. These constraints may not allow continuous solutions or close agreement with directly measured kinematics.A novel method is presented to scale the thorax based on palpated scapula landmarks. The scapula and clavicle kinematics are optimised with the constraint that the scapula medial border does not penetrate the thorax. Conoid ligament length is not used as a constraint. This method is simulated in the UK National Shoulder Model and compared to four other methods, including the standard technique, during three pull-up techniques (n=11). These are high-performance activities covering a large range of motion.Model solutions without substantial jumps in the joint kinematics data were improved from 23% of trials with the standard method, to 100% of trials with the new method. Agreement with measured kinematics was significantly improved (more than 10° closer at p<0.001) when compared to standard methods. The removal of the conoid ligament constraint and the novel thorax scaling correction factor were shown to be key. Separation of the medial border of the scapula from the thorax was large, although this may be physiologically correct due to the high loads and high arm elevation angles.

Refinement of the upper limb joint kinematics and dynamics using a subject-specific closed-loop forearm model

A biofidelic multibody model of the upper limb for the quantitative assessment of joint kinematics and dynamics has the potential to become an innovative tool in many application fields. However, forearm kinematic modeling still presents challenges due to the complexity of providing a closed-loop and subject-specific definition of its multiple degrees of freedom. In this context, this study aims to refine the upper limb multibody model by means of a forearm closed-loop kinematic chain and personalized joint parameters to quantify the forearm joint kinematics and dynamics. To assess the benefits of this refinement, the proposed model is compared to four conventional models according to (i) the global and local movement reconstruction errors during inverse kinematics and (ii) the joint torque-angle pattern. Fifteen (15) healthy adults performed two cyclic dynamic tasks, namely elbow flexion–extension (FE) and forearm pronation–supination (PS). Results show that the proposed model leads to a reduction of the global reconstruction error up to 15 % and 31 % during FE and PS tasks, respectively, while computational times remain similar. The local reconstruction errors show less compensation at the shoulder and wrist for the proposed model. The PS angle and torque are increased by 24 % during the PS task for the proposed model when compared to conventional models. In conclusion, this study addresses novel methodology aspects and a comprehensive description of a forearm multibody model that can serve in multiple applications requiring a realistic representation of the upper limb kinematics and dynamics without increasing the computational time.

Learners' eye movements during construction of mechanical kinematic representations from static diagrams

We investigated the influence of numbered arrows on construction of mechanical kinematic representations by using static diagrams. Undergraduate participants viewed a two-stage diagram depicting a flushing cistern (with or without numbered arrows) and answered questions about its function, step-by-step. The arrow group demonstrated greater overall accuracy and made fewer errors on the measure of continuous relations than did the non-arrow group. The arrow group also spent more time looking at components relevant to the operational sequence and had longer first-pass fixation times and shorter saccade lengths. The non-arrow group made more saccades between the two diagrams. Analysis of transition probabilities indicated that both groups viewed components according to their continuous relations. The arrow group followed the numbered arrows whereas the unique pathway of the non-arrow group was to compare the two diagrams. These findings indicate that numbered arrows provide perceptual information but also facilitate cognitive processing.

Comparison of Extreme Offshore Structural Response from Two Alterna-tive Stretching Techniques

Linear random wave theory (LRWT) has successfully explained most properties of real sea waves with the ex-ception of some nonlinear effects for surface elevation and water particle kinematics. Due to its simplicity, it is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record; however, predicted water particle kinematics from LRWT suffer from unrealistically large high-frequency compo-nents in the vicinity of mean water level (MWL). To overcome this deficiency, a common industry practice for evaluation of wave kinematics in the free surface zone consists of using linear random wave theory in conjunction with empirical techniques (such as Wheeler and vertical stretching methods) to provide a more realistic representation of near-surface wave kinematics. It is well known that the predicted kinematics from these methods are different; however, no systematic study has been conducted to investigate the effect of this on the magnitude of extreme responses of an offshore structure. In this paper, probability distributions of extreme responses of an offshore structure from Wheeler and vertical stretching methods are compared. It is shown that the difference is significant; consequently, further research is required to deter-mine which method is more reliable.

Shallow water demultiple using hybrid multichannel prediction

This paper presents an extension of our previous effort on multiple attenuation in shallow water environment. While our previous workflow, termed as Shallow Water Demultiple (SWD), is robust in suppressing water-layer related multiples (WLRMs) with shallow seafloor, it faces difficulties when the seafloor is too shallow and complex because of the near offset gap related to acquisition. The wavelet stretch resulted from near offset extrapolation causes spectral distortion in multiple model from SWD which leads to sub-optimized subtraction result in shallow part of the data. The new method is a hybrid approach in which shallow WLRMs are handled by using the Greenâ??s function of the seafloor primary reflections, while the rest of the multiples are handled by SWD. The Greenâ??s function in this case is derived from auto-picking the traveltime of the multichannel prediction operator estimated from SWD. The approach combines the strengths of SWD and model-based methods. We show that the multichannel prediction operator estimated in SWD can be used as an accurate kinematic representation of seafloor reflection with high signal-to-noise (S/N) ratio. With this operator, the traveltime of the seafloor event can then be automatically estimated. Making use of this traveltime information, the Green's functions of the water-layer primary reflections can be modeled for tackling the shallow peg-lag multiples that have difficulty handled by SWD. We show the application of our hybrid method for suppressing shallow water multiples on field data acquired from offshore Australia

Joint Contribution to Fingertip Movement During a Number Entry Task: An Application of Jacobian Matrix

Upper extremity kinematics during keyboard use is associated with musculoskeletal health among computer users; however, specific kinematics patterns are unclear. This study aimed to determine the dynamic roles of the shoulder, elbow, wrist and metacarpophalangeal (MCP) joints during a number entry task. Six subjects typed in phone numbers using their right index finger on a stand-alone numeric keypad. The contribution of each joint of the upper extremity to the fingertip movement during the task was calculated from the joint angle trajectory and the Jacobian matrix of a nine-degree-of-freedom kinematic representation of the finger, hand, forearm and upper arm. The results indicated that in the vertical direction where the greatest fingertip movement occurred, the MCP, wrist, elbow (including forearm) and shoulder joint contributed 10.2%, 55.6%, 27.7% and 6.5%, respectively, to the downward motion of the index finger averaged across subjects. The results demonstrated that the wrist and elbow contribute the most to the fingertip vertical movement, indicating that they play a major role in the keying motion and have a dynamic load beyond maintaining posture.

Quantum geometry with a nondegenerate vacuum: A toy model

Motivated by a recent proposal (by Koslowski-Sahlmann) of a kinematical representation in loop quantum gravity (LQG) with a nondegenerate vacuum metric, we construct a polymer quantization of the parametrized massless scalar field theory on a Minkowskian cylinder. The diffeomorphism covariant kinematics is based on states that carry a continuous label corresponding to smooth embedding geometries, in addition to the discrete embedding and matter labels. The physical state space, obtained through the group averaging procedure, is nonseparable. A physical state in this theory can be interpreted as a quantum spacetime, which is composed of discrete strips and supersedes the classical continuum. We find that the conformal group is broken in the quantum theory and consists of all Poincar\'e translations. These features are remarkably different compared to the case without a smooth embedding. Finally, we analyze the length operator whose spectrum is shown to be a sum of contributions from the continuous and discrete embedding geometries, being in perfect analogy with the spectra of geometrical operators in LQG with a nondegenerate vacuum geometry.

Kinematical Implications of a New f(R) Theory of Gravity: The Redshift

In this paper, we discuss the kinematical concepts of a recently defined f(R) action (Payandeh and Fathi in Int. J. Theor. Phys., 2013, doi:10.1007/s10773-013-1770-5). Firstly, we retreat the action to obtain the kinematic representation of the standard cosmology components, and then, we go through our model, to find the cosmological redshift, according to the scalar field constituents of the theory.