Jerk Values Research Articles

Effect of viscosity on the shaking-induced fluidization in a liquid-immersed granular medium.

A liquid-immersed granular medium is shaken vertically under a wide range of accelerations (Γ in dimensionless form) and frequencies (f) and its fluidization process is studied. The granular medium is formed by settling and consists of two size-graded layers (particle diameter d) such that the upper layer is fine grained and is less permeable. When Γ>Γ(c), a liquid-rich layer formed by the accumulated liquid at the two-layer boundary causes a gravitational instability. The upwellings of the instability are separated horizontally by a distance (wavelength) λ, and their amplitude grows exponentially with time [∝exp(pt)] at a growth rate p. We conduct experiments for two liquid viscosity cases such that the particle settling velocity (V(s)) of the same particle differs by a factor of 17. We find that for both cases, Γ(c) is at a minimum in an optimum frequency band centered at f∼100 Hz. However, the high-viscosity (HV) case has a smaller Γ(c), a shorter λ, and a faster dimensionless growth rate [p'=p/(V(s)/d)]. We also measure granular rheology under an oscillatory shear and find that (i) interparticle friction decreases when the strain amplitude becomes large and (ii) friction is smaller for the HV case. From (i), we infer that the shear strain of the shaking experiments becomes largest at around f∼100 Hz. We consider that (ii) is a consequence of liquid lubrication and is a reason for a smaller Γ(c) for the HV case. We show that the low- and high-frequency limits of the optimum frequency band can be explained by introducing critical values of dimensionless jerk (i.e., time derivative of acceleration) J and dimensionless shaking energy S. The low-frequency limit corresponds to the requirement that in order to unjam the particles, the period of shaking (1/f) must be shorter than the time needed for the particles to rearrange by settling (d/V(s)), which also explains why the HV case is fluidized at a lower f compared to the LV case. We apply the results of the linear stability analyses for Rayleigh-Taylor instability. Using the measured λ and p, we infer that (i) only a thin layer beneath the two-layer boundary is mobile and the rest of the lower layer remains jammed and (ii) the effective viscosity of the upper granular layer relative to the liquid is smaller for the HV case as a result of smaller friction.

Комбинированная система позиционного управления с задающей моделью третьего порядка

The microprocessor control systems based on the setting models with outputs changing proportionally to the diagrams of displacement, rate, acceleration (current) and derivate acceleration in time (jerk) play an important role in power saving. The authors have developed a general second-order model with three output signals proportional to the set values of speed, acceleration and jerk or to position, velocity and acceleration. This setting model is based on integral units and relay gears considering internal motor feedback. They enable development of optimum patterns of controlled coordinate change and facilitate implementation of the limits of the derivative of the armature current without a special controller of the current derivative, which complicates the system configuration and increases its sensitivity to parametric changes.

Relationship between Social Isolation and Indoor and Outdoor Physical Activity in Community-Dwelling Older Adults in Germany: Findings from the ActiFE Study

The purpose of this study was to establish the feasibility of using an aerobics class to produce potentially bone protective vertical impacts of ≥ 4g in older adults and to determine whether impacts can be predicted by physical function. Participants recruited from older adult exercise classes completed an SF-12 questionnaire, short physical performance battery, and an aerobics class with seven different components, performed at low and high intensity. Maximum g and jerk values were identified for each activity. Forty-one participants (mean 69 years) were included. Mean maximal values approached or exceeded the 4g threshold for four of the seven exercises. In multivariate analyses, age (–0.53; –0.77, –0.28) (standardized beta coefficient; 95% CI) and 4-m walk time (–0.39; –0.63, –0.16) were inversely related to maximum g. Aerobics classes can be used to produce relatively high vertical accelerations in older individuals, although the outcome is strongly dependent on age and physical function.

Formation of traffic curve of lifting mechanisms taking into account elastic properties of transmissions

Elastic mechanical vibrations adversely affect the control quality, increase the dynamic loads on the lifting mechanisms, contribute to the accumulation of fatigue stresses in the kinematic chains that cause need for their detailed consideration. In the article it is done the synthesis of mathematical relationships that are at any given parameters of lifting mechanisms allows taking into account the elastic properties of the cable transmission, calculate the actual diagram of the lift car, determine the maximum values of velocity, acceleration and jerk that allows to estimate the parameters of passenger elevators, as in the famous classical optimal control law, and in a completely arbitrary control laws. The difference between the maximum accelerations and jerky of passenger lift cabin and their calculated values is determined. The actual maximum acceleration of the passenger lift cabin on 20,0-40,0 % higher than the values determined without taking into account the elastic ties. The increase of the jerk is even more significant and can reach 60,0-140,0 %. The synthesized mathematical relations can be used in case of diagram forming of the lift car moving based on external constraints, such as heat, or if necessary, implementing the degenerate triangular diagrams. Based on the analytical expressions can be developed: nonlinear mathematical and physical models, which make it possible, in real time, in a wide range of source data, perform analysis of modes of lift drivers of various types; technical advice on damping lifting mechanisms of arbitrary passenger lifts.

PREDICTION OF TRIP SEVERITY BASED ON TRI-AXIAL ACCELEROMETRY IN HEALTHY OLDER ADULTS

Introduction: falls among elderly are apublic health problem and fall prevention is of utmost importance. The ability to recovery from a trip or not might be indicative for fall risk. Objective: toanalyse the relationship between trunk accelerations during the initial phase of tripping and the severity of a tripin healthy older adults. Methods : fourteen healthy older adults (65-73 yrs)walked multiple times over a platform with embedded obstacles and were tripped while trunk accelerations were assessed. Supported bodyweight (BW) by a safety harness was used to classify severity of the tripping outcome into high (>50%BW) or low (<50%BW). Twelve parameters obtained from the acceleration signals and their derivatives (jerk) within the first second after tripping initiation and were divided into three levels of parameter values with equal amount of trials. These low, medium and high values were tested for their association with trip severity in a logistic regression analysis. Results: three acceleration parametersappeared to be significant predictors oftrip severity. High values of minimum anterior-posterior acceleration and minimum vertical jerk showed lower likelihood of resulting in a high severity trip than in the low values (33% and 32%, respectively). Medium values of the maximum anterior-posterior acceleration showed higher likelihood of resulting in a h igh severity trip than the low values (327%). Conclusion : high acceleration and jerk peaks detected within the first second after tripping predict a more severe outcome, indicating that trunk tri-axial accelerometryhas the potential to predict the severity oftripping outcome in healthy older adults.

Characteristics of Jerk Response Spectra for Elastic and Inelastic Systems

Jerk is the time rate of acceleration and mainly represents the nonstationary component in high frequency band of the earthquake wave. The study on jerk and its response spectra can enhance the recognition of the nonstationary ground motion. The mechanical meaning and research value of jerk are described. Jerk is recommended to be solved by establishing state-space equations and Runge-Kutta method. The solution method of elastic and inelastic jerk response spectra under ground motion is established, and the accurate jerk spectrum should be calculated directly according to numerical computing instead of pseudo-acceleration spectrum. The characteristics of jerk response spectra are studied according to the influencing factors, such as site condition, amplification factor, ductility factor, and reduction factor. The concept of impact reduction factor is presented. The statistical results show that the jerk spectrum has similar rules as the acceleration spectrum, and the amplitude is relative to the predominant period, especially for structures with short or medium period. If the ductility is improved, the effective jerk will reduce obviously, and the impact reduction factor will be enhanced. Different from the strength reduction factor, the impact reduction factor is nearly not relevant to the period.

G.O.16: Reliability and validity of the ACTIVE-mini (Ability Captured Through Interactive Video Evaluation-mini) to quantify infant movement

The success of clinical trials in infants with spinal muscular atrophy (SMA) requires careful trial planning and appropriate outcomes. Traditional tests are fatiguing for SMA infants, use non-linear ordinal scales and require highly trained evaluators to grade movement. Our study provides preliminary reliability and validity data on a video-based assessment, ACTIVE-mini, which uses the Microsoft Kinect to assess infant movement. The infant lies supine and spontaneous movements are recorded using a series of 3D depth map and color images. Algorithms are used to quantify infant movement speed (i.e. velocity, acceleration, and jerk), as well as total movement volume, and the complexity of infant movement within space. Weekly longitudinal and cross-sectional data were collected over 6 months on 6 SMA infants and 30 controls. Movement speed data are plotted as kernel density plots separated in 2-week age-matched bins. Differences are seen in each movement variable in every age bin. On average the SMA infants have an average jerk value of 57.8% of age-matched peers. Tracings of the extremities and the ratio of convex hull’s surface area to volume ratio, where higher numbers indicate decreased ability, illustrate that an SMA infant has a smaller total movement excursion as well as decreased spatial complexity (upper extremity average: 139–170; lower extremity average: 756–891) when compared to age-matched controls (all extremities average range: 43–68). Preliminary results indicate ACTIVE-mini differentiates movement differences related to speed, variability, quantity, and complexity of movement in SMA infants compared to controls in the first 2 weeks of life. ACTIVE-mini has both clinical and research potential to detect movement abnormalities and measure small changes in ability over time. Further research is needed in a larger sample of diverse diagnoses to refine the statistical models of normal movement and identify typical longitudinal changes in infants.

Energy conditions for Bianchi type I universe in f(G) gravity

In this paper, we discuss energy conditions in modified Gauss-Bonnet gravity for locally rotationally symmetric Bianchi type I universe model with perfect fluid. The matter contents are constructed to discuss the energy conditions bounds. We take two specific f(G) models along with present day values of Hubble, deceleration, jerk and snap parameters. It is found that weak and null energy conditions are satisfied while strong energy conditions are violated for both models which represents the accelerated expansion of the universe.

Design and Analysis for the Handle of the Carton

In order to solve the problem of low degree of installation automation on handles of the domestic cartons, the problem that the plastic handle is not environmental friendly and the problem that the finished cartons are not convenient for piling, a threading device for the non-woven fabric handle based on a Cam mechanism is designed. Kinematics analysis is done to the simulation model of the handle threading device by utilizing a simulation software ADAMS to obtain the variation curves of the displacement, velocity, accelerated velocity and jerk. The result of analysis shows that the designed threading device of the handle is able to meet with the requirements for non-woven fabric threading technology and it further verifies the validity of the design methods; Moreover, the velocity and the accelerated velocity of the threading device have no sudden change and the jerk values are small so that high speed and high automatic threading can be achieved. Besides, the threading efficiency of the designed device is significantly improved.

Cineradiographic analysis of mouse postural response to alteration of gravity and jerk (gravity deceleration rate).

The ability to maintain the body relative to the external environment is important for adaptation to altered gravity. However, the physiological limits for adaptation or the disruption of body orientation are not known. In this study, we analyzed postural changes in mice upon exposure to various low gravities. Male C57BL6/J mice (n = 6) were exposed to various gravity-deceleration conditions by customized parabolic flight-maneuvers targeting the partial-gravity levels of 0.60, 0.30, 0.15 and μ g (<0.001 g). Video recordings of postural responses were analyzed frame-by-frame by high-definition cineradiography and with exact instantaneous values of gravity and jerk. As a result, the coordinated extension of the neck, spine and hindlimbs was observed during the initial phase of gravity deceleration. Joint angles widened to 120%–200% of the reference g level, and the magnitude of the thoracic-curvature stretching was correlated with gravity and jerk, i.e., the gravity deceleration rate. A certain range of jerk facilitated mouse skeletal stretching efficiently, and a jerk of −0.3~−0.4 j (g/s) induced the maximum extension of the thoracic-curvature. The postural response of animals to low gravity may undergo differential regulation by gravity and jerk.

Postural sway in idiopathic rapid eye movement sleep behavior disorder: A potential marker of prodromal Parkinson׳s disease

There is compelling evidence that postural instability occurs at very early clinical stages of Parkinson׳s disease (PD), making it tempting to speculate that changes in postural sway may even occur at a prodromal phase. Studies estimate that approximately half of patients with idiopathic rapid eye movement (REM) sleep behavior disorder (RBD) will eventually develop PD, so RBD may be an indicator of prodromal PD. This study was undertaken to investigate postural sway and its relation to stereopsis function in patients with RBD. We examined 24 patients with polysomnography-confirmed RBD and 23 healthy, sex-and age-matched control subjects. Postural sway was measured with an accelerometer at the center of mass at the lower spine. Subjects were asked to stand quietly for 30s under two usual conditions (eyes open and eyes closed) and three challenging conditions (eyes open with dual task, eyes closed with dual task, and tandem standing). Stereopsis was assessed using the Titmus fly test. RBD patients showed an increased variability of trunk acceleration and a decrease of smoothness of sway, compared to control subjects. These differences reached significance in the challenging conditions. RBD patients demonstrated significant impairment in stereopsis. There were statistically significant correlations between log seconds of arc of the Titmus test and some sway parameters within the RBD group. RBD patients with abnormal stereopsis showed a significant increase of JERK values compared to patients with normal stereopsis in the challenging conditions. Our results indicate that idiopathic RBD patients, especially with abnormal stereopsis, have subtle signs of postural instability under challenging conditions. Postural sway performance may serve as a biological marker for prodromal PD.

Kinematic evaluation of movement smoothness in golf: relationship between the normalized jerk cost of body joints and the clubhead

BackgroundWhen the human body is introduced to a new motion or movement, it learns the placement of different body parts, sequential muscle control, and coordination between muscles to achieve necessary positions, and it hones this new skill over time and repetition. Previous studies have demonstrated definite differences in the smoothness of body movements with different levels of training, i.e., amateurs compared with professionals. Therefore, we tested the hypothesis that skilled golfers swing a driver with a smoother motion than do unskilled golfers. In addition, the relationship between the smoothness of body joints and that of the clubhead was evaluated to provide further insight into the mechanism of smooth golf swing.MethodsTwo subject groups (skilled and unskilled) participated in the experiment. The skilled group comprised 20 male professional golfers registered with the Korea Professional Golf Association, and the unskilled group comprised 19 amateur golfers who enjoy golf as a hobby. Six infrared cameras (VICON460 system) were used to record the 3D trajectories of markers attached to the clubhead and body segments, and the resulting data was evaluated with kinematic analysis. A physical quantity called jerk was calculated to investigate differences in smoothness during downswing between the two study groups.ResultsThe hypothesis that skilled golfers swing a driver with a smoother motion than do unskilled golfers was supported. The normalized jerk of the clubhead of skilled golfers was lower than that of unskilled golfers in the anterior/posterior, medial/lateral, and proximal/distal directions. Most human joints, especially in the lower body, had statistically significant lower normalized jerk values in the skilled group. In addition, the normalized jerk of the skilled group’s lower body joints had a distinct positive correlation with the normalized jerk of the clubhead with r = 0.657 (p < 0.01).ConclusionsThe result of this study showed that skilled golfers have smoother swings than unskilled golfers during the downswing and revealed that the smoothness of a clubhead trajectory is related more to the smoothness of the lower body joints than that of the upper body joints. These findings can be used to understand the mechanisms behind smooth golf swings and, eventually, to improve golf performance.

Multi-axis Time Synchronization for Uncoordinated Motion Planning with Hard Constraints

This paper deals with multi-axis motion planning, especially with time synchronization of mutually independent axes of motions (uncoordinated motion). A novel time-optimal generator called GBAVS is used as a basic tool, utilizing the chain of integrators. The structure of generator uses 3 integrators for generating motion variables. The task is to plan the single-axis motions while respecting hard motion constraints and to achieve the final states in the same time. In contrast to other approaches the initial/final state does not necessary mean the state with zero velocity and acceleration, so called rest-to-rest motion. To reach synchronization, time scaling is based on decreasing the individual values of Jerk for each axis except the slowest one. Jerk is a parameter to be reduced as first. No initial/final state limitation and reduction of the value of Jerk primal to other motion limitations (e.g. velocity limits) are the main advantages of this approach.

Residual jerk reduction in precision positioning stages using sliding microstep-based switching

Micro precision X–Y stages have several applications in industry ranging from metal machining to positioning of optical instruments. This paper deals with the evaluation of relationship between jerk in micro precision stages and harmonics in voltage of the motor by which the stage is driven and subsequently proposes an algorithm on Arduino Mega micro controller board to reduce the jerk by shaping the velocity profile while varying the microstepping rate in motor voltage. A micro precision stage with a resolution of 1 micron, driven with a bipolar stepper motor drive is used to evaluate the algorithm. A MEMS accelerometer (ADXL 345) is placed rigidly on the stage, and the acceleration at varying speeds is measured and logged in the micro controller. The micro controller sends commands to the motor driver (L6470 driver) for driving the motor using Serial Peripheral interface. The motor driver is configured in microstepping mode. Experiments confirm the fact that there is a strong correlation between jerk in micropositioning stage and motor supply voltage harmonics. A methodology to reduce the jerk has also been facilitated. This involves use of microstepping mode in stepper motor driver with dynamic sliding in microstepping rate. A threshold value of jerk is considered and based on that, the microstepping rate is varied which subsequently reduces voltage harmonics. Reduction in voltage harmonics reduces the jerk in the stage. Maximum jerk reduction of 97.3 % was achieved in the process.

Energy conditions in f (R, T, R μν T μν ) gravity

We discuss the validity of the energy conditions in a newly modified theory named as $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity, where $R$ and $T$ represent the scalar curvature and trace of the energy-momentum tensor. The corresponding energy conditions are derived which appear to be more general and can reduce to the familiar forms of these conditions in general relativity, $f(R)$ and $f(R,T)$ theories. The general inequalities are presented in terms of recent values of Hubble, deceleration, jerk and snap parameters. In particular, we use two specific models recently developed in literature to study concrete application of these conditions as well as Dolgov-Kawasaki instability. Finally, we explore $f(R,T)$ gravity as a specific case to this modified theory for exponential and power law models.

Adaptive LQR-Control Design and Friction Compensation for Flexible High-Speed Rack Feeders

Rack feeders for the automated operation of high bay rackings are of high practical importance. They are characterized by a horizontally movable carriage supporting a tall and flexible vertical beam structure, on which a cage containing the payload can be positioned in vertical direction. To shorten the transport times by using trajectories with increased maximum acceleration and jerk values, accompanying control measures can be introduced counteracting or avoiding undesired vibrations of the flexible structure. In this contribution, both the control-oriented modeling for an experimental setup of such a flexible rack feeder and the model-based design of a gain-scheduled feedforward and feedback control structure are presented. Whereas, a kinematical model is sufficient for the vertical axis, the horizontal motion of the rack feeder is modeled as a planar elastic multibody system with the cage position as scheduling parameter. For the mathematical description of the bending deflections, a one-dimensional Ritz ansatz is introduced. The tracking control design is performed separately for both the horizontal and the vertical axes using decentralized state-space representations. Remaining model uncertainties are estimated by a disturbance observer. The resulting tracking accuracy of the proposed control concept is shown by measurement results from the experimental setup. Furthermore, these results are compared to those obtained with an alternative control concept from previous work.

Track Smoothness of Moving Axis Considering Kinematical Characteristics of Machine Tool

In multi-axis NC (Numerical Control) machining for a complex part, high feed rate may bring shock to moving axes and influence the machining quality of the part. Firstly, velocity, acceleration and jerk kinematical characteristics are worked out according to the displacement curve of a moving axis. Secondly, the acceleration curve segments which need to be smoothed are found out according to the value of jerk, and these segments are smoothed with B-spline method. Then the smoothed velocity and displacement can be calculated through numerical integration method to get the new displacement curve of the moving axis. Finally, a test example is given to demonstrate the promising use of the proposed solution. The method presented by this paper can effectively decrease the acceleration shock of machine tool and improve the machining quality of part surface.

Optimal Trajectory Planning for Parallel Robots Considering Time-Jerk

A method for optimization in trajectory planning of 3RUU robot manipulators is presented in this paper. At first, to get the optimal trajectory, position analyses has been done on the 3RUU robot, then an objective function which have two terms is minimized: first term relevant to the total execution time and another one relevant to the integral of the squared jerk (defined as the derivative of the acceleration toward time) along the trajectory and this Guarantees that the obtained trajectory is smooth. This technique let to calculate the kinematic constraints on the motion of the robot, defined as upper limits on the absolute values of velocity, acceleration and jerk. , the total execution time does not require to be set priori. The algorithm has been tested in simulation and in comparison with other important trajectory planning techniques it has been given good results.

Efficient computation of smooth minimum time trajectory for CNC machining

Previous computation approaches of smooth trajectory for computer numerical control machining either cannot fully utilize the maximum ability of machines, fail to minimum machine time, or cannot be computed efficiently because of the nonlinearity formulation of problem. In this paper, an efficient computation approach is proposed that has been designed as solving a convex optimization problem to generate smooth minimum time trajectory. Since smoothness of trajectory can be adjusted by confining the value of jerk (rate of acceleration change), the proposed approach uses a pseudo-jerk to approximate the real jerk and to realize smoothing trajectory. The difference between the real jerk and pseudo-jerk is that the proposed pseudo-jerk can be linearity formulation in the problem. By using pseudo-jerk constraints, smooth minimum time trajectory planning problem is formulated as a convex optimization problem. Since of convexity of the optimization problem, the solution process can be efficient by using ordinary gradient-based optimization techniques and the optimal numerical solution is uniqueness. The effectiveness of the approach is demonstrated in machining simulations of two plane patterns.

Research on Acceleration/Deceleration in NURBS Curve Interpolation

A non-uniform rational B-spline (NURBS) parametric curve interpolation and S-shape acceleration/deceleration (ACC/DEC) for CNC machine tool were studied. In the proposed algorithm, the commanded velocity is maintained at most of the time and adaptively reduced in large curvature areas to meet the demand of the machining accuracy requirement, while at the same time, a S-shape look ahead algorithm is proposed to limit the acceleration and jerk values within the machine’s capabilities during the whole interpolation process. It reduces mechanical shock to the machine tools. The real time performance of this interpolator is also measured to demonstrate its practical application. A NURBS curve interpolation experiments is provided to verify the feasibility and advantages of the proposed algorithm.