Limit Of Motion Research Articles

The vanishing exponent limit for motion by a power of mean curvature

We discuss limit behavior of solutions to level set equation of power mean curvature flow as the exponent tends to zero, which has important applications to shape analysis in image processing. A formal limit yields a fully nonlinear singular equation that describes the motion of a surface by the sign of its mean curvature.We justify the convergence by providing a definition of viscosity solutions to the limit equation and establishing a comparison principle.

Second order threshold dynamics schemes for two phase motion by mean curvature

The threshold dynamics algorithm of Merriman, Bence, and Osher is only first order accurate in the two-phase setting. Its accuracy degrades further to half order in the multi-phase setting, a shortcoming it has in common with other related, more recent algorithms such as the equal surface tension version of the Voronoi implicit interface method. As a first, rigorous step in addressing this shortcoming, we present two different second order accurate versions of two-phase threshold dynamics. Unlike in previous efforts in this direction, we present careful consistency calculations for both of our algorithms. The first algorithm is consistent with its limit (motion by mean curvature) up to second order in any space dimension. The second achieves second order accuracy only in dimension two, but comes with a rigorous stability guarantee (unconditional energy stability) in any dimension – a first for high order schemes of its type.

Shape-Morphing Using Bistable Triangles With Dwell-Enhanced Stability

Abstract This paper presents a new design concept for a morphing triangle-shaped compliant mechanism. The novel design is a bistable mechanism that has one changeable side. These morphing triangles may be arrayed to create shape-morphing structures. The mechanism design was based on a six-bar dwell mechanism that can fit in a triangle shape and has stable positions at the motion-limit (dead-center) positions. An example of the triangle-shaped compliant mechanism was designed and prototyped: an isosceles triangle with a vertex that changes from 120 deg to 90 deg and vice versa. Three of these in the 120-deg configuration lie flat and when actuated to the 90-deg configuration become a cube corner. This design may be of use for folding and packaging assistance. The mechanism was designed using geometric constraint programming. Force and potential energy analyses characterize the triangle mechanism’s stability. Because of its dead-center motion limits, the vertex angle of the triangle cannot be extended past the range of 90–120 deg, in spite of the mechanism’s compliant joints. Furthermore, because it is a dwell mechanism, the vertex angle is almost immobile near its stable configurations, although other links in the mechanism move. This makes the stable positions of the vertex angle robust against stress relaxation and manufacturing errors. We believe this is the first demonstration of this kind of robustness in bistable mechanisms.

Switched Motion Cueing Algorithm for Flight Simulator Upset Prevention and Recovery Training

Upset prevention and recovery training (UPRT) has been mandatorily required in the Level-D flight simulator by some civil aviation authority currently. Due to the limit motion capability of six-DOF motion platform, motion perception of pilot can’t be effectively satisfied with traditional classical motion cueing algorithm (MCA) during this kind of upset scenario training. In this paper, a switched MCA which optimized by GA was proposed. The switching mechanism ensured that MCA output optimal motion simulation signal to motion platform in different upset training phases. The motion command outputs, which may have sudden change during the transit of adjacent flight phases, were smoothed by a sigmoid function window. Simulation results showed that the proposed switched motion cueing algorithm had better motion replication performance and also made better usage for the motion platform’s workspace than the classical MCA.

Evaluation of the Results of Arthroscopic Release in Limits of Movement in Knees

Introduction: Limits of movement in knees is one of the most common complications following trauma and surgery. With early diagnosis and appropriate treatment choices, knee replacement and performance improvement are expected in many patients. However, limits of movement in knees is unpleasant and should be corrected as soon as possible. In this study, we decided to evaluate the results of arthroscopic release in motion limits of knees. Methods: This was a descriptive cross-sectional study.14 patients who referred to the Shahid Sadoughi Hospital of Yazd from 2014 to 2016 and diagnosed with knee limitation (flexion or extension restriction of more than 10 degrees) were selected. Patients were undergone arthroscopic release and followed-up for 6 months. Lysholm knee score, degrees of flexion and extension, and patient satisfaction were evaluated. The results were analyzed by SPSS-18 and statistical tests Paired T-test as well as Spearman correlation. Results: The mean age of the patients was 28.92±10.99 years. The most common type of trauma in the patients was femoral distal fracture (46.7%). The frequency of the patients' satisfaction with arthroscopy was as followed: 50% (7 patients), had moderate satisfaction, 28.6% (4 ones), high satisfaction, and 21.4% (3 ones) had low satisfaction.The mean difference in Lysholm Knee Score, improvement in degree of extension, improvement in degree of flexion and pain score before and after arthroscopy were 26.21±14.11,64.78±26.13,3.57±2.92 and 4.13±1.65,respectively.There was a significant difference between the mean values of these factors before and after arthroscopy. Conclusion: According to the results obtained, we can conclude that arthroscopic release is an effective and low-complication method in motion limits of knees.

Phase separation and state oscillation of active inertial particles.

Active matter systems are of great interest for their novel out-of-equilibrium collective behavior. Active Brownian particles (ABPs) are known to exhibit clustering and motility-induced phase separation, and there have been many studies revealing this rich behavior in the overdamped limit of Brownian motion, where inertial effects are insignificant. Here we simulate an Active Inertial Particle (AIP) model where we focus on the underdamped, rather than overdamped limit, to study the interplay between particle inertia and collective behavior, such as phase separation. We show that inertia reduces particle motility due to collisions and a longer time delay for particles to regain speed, thereby suppressing phase separation relative to that observed in the overdamped limit. Additionally, we observe interesting oscillatory behavior between a phase separated steady-state and a homogeneous fluid state that results from inertia-induced collective motion within active clusters due to momentum transfer. Such oscillatory behavior has been reported for ABP systems with particle shape anisotropy, where collective motion is mediated by particle shape anisotropy. Furthermore, we confirm that there is no single characteristic frequency for the oscillatory behavior. The power spectral density is a power law in the high frequency domain, with an exponent close to -2.5.

Polynomial rate of convergence to the Yaglom limit for Brownian motion with drift

This paper deals with the rate of convergence in $1$-Wasserstein distance of the marginal law of a Brownian motion with drift conditioned not to have reached $0$ towards the Yaglom limit of the process. In particular it is shown that, for a wide class of initial measures including probability measures with compact support, the Wasserstein distance decays asymptotically as $1/t$. Likewise, this speed of convergence is recovered for the convergence of marginal laws conditioned not to be absorbed up to a horizon time towards the Bessel-$3$ process, when the horizon time tends to infinity.

Infinite stable looptrees

We give a construction of an infinite stable looptree, which we denote by $\mathcal{L}_{\alpha}^{\infty}$, and prove that it arises both as a local limit of the compact stable looptrees of Curien and Kortchemski (2015), and as a scaling limit of the infinite discrete looptrees of Richier (2017) and Bj\"ornberg and Stef\'ansson (2015). As a consequence, we are able to prove various convergence results for volumes of small balls in compact stable looptrees, explored more deeply in a companion paper. We also establish the spectral dimension of $\mathcal{L}_{\alpha}^{\infty}$, and show that it agrees with that of its discrete counterpart. Moreover, we show that Brownian motion on $\mathcal{L}_{\alpha}^{\infty}$ arises as a scaling limit of random walks on discrete looptrees, and as a local limit of Brownian motion on compact stable looptrees, which has similar consequences for the limit of the heat kernel.

Systematic Design of a Parallel Robotic System for Lower Limb Rehabilitation

This paper presents the design of an innovative robotic system for lower limb post-stroke rehabilitation of bed confined patients during the acute stage of the treatment. To establish the particularities of each targeted joint motion, experimental measurements are performed on healthy subjects. The acquired data is used to determine the operational workspace, namely the limits of the anatomic joints motion for the lower limb. Based on the prescribed operational workspace, an innovative parallel robotic architecture is designed for achieving the rehabilitation of the lower limb. A detailed kinematic modelling and analysis is carried out to demonstrate the robot capability to safely achieve the required motions. The design of the robotic rehabilitation device is discussed in detail alongside with numerical simulations for validating its performance while performing medically relevant rehabilitation motions.

The Effect of Ankle Joint Mobilization with Movement Weight Bearing Training On ROM, Balance Ability and Gait Velocity in Hemiplegic Patients

Objective: The purpose of this study was to investigate the effects of ankle range of motion(ROM), balance ability, and gait velocity of the ankle flexion when the joint Mobilization with Movement was applied. Method: Ankle joint ROM, balance ability(BBS), and gait velocity were examined before and after application. Result: In the experimental group, ROM of dorsiflexion and eversion increased significantly, the balance ability improved, and the gait velocity increased more than the control group(p<.05). Conclusion: Through this study, In addition to the symptoms of central nervous system damage in hemiplegic patients, it can be used as an effective treatment for reducing the limit of motion of the ankle due to secondary musculoskeletal problems and improving balance ability and gait velocity.

Real-time PID control of a novel RCM mechanism designed and manufactured for use in laparoscopic surgery

PurposeThe purpose of this study is to design and manufacture a new remote center of motion (RCM) mechanism for use in laparoscopic surgical operations. In addition, obtaining the forward and inverse kinematic equations of the RCM mechanism and performing real-time position control with the Proportional–Integral–Derivative (PID) control method.Design/methodology/approachAt the design stage, it is benefited from similar triangle rule. To obtain the kinematic equations in a simple way and facilitate control, two-fold displacement ratio is provided between the limbs where linear motion occurs. The rotation and displacement amounts required to move at the RCM point have been calculated by using the kinematic equations of the mechanism. Limb dimensions and motion limits are determined in the manner to avoid singularities and collisions. The x, y and z coordinates of the end effector have been defined as the reference point. Control of the mechanism was provided by PID control. To generate the user interface and control algorithm, MATLAB/Simulink real-time toolbox has been used. Four reference points were determined, control was performed and position error values were examined. MF634 Humusoft data acquisition card has been preferred to collect data from encoders.FindingsA novel RCM mechanism has been designed and manufactured. Kinematic equations of this mechanism have been obtained. Position control of the cannula tip has been performed using PID control method for four different reference points. After settlement, maximum position error has been observed as 0.45 mm.Practical implicationsStructure of the designed mechanism is quite simple. Thus, costs are quite low. The operation area of the operator is widened by hanging the mechanism from the ceiling, so operational capability of health personnel is increasing. It helps to decrease the operation time and increase the success of the operation.Originality/valueWith this study, it is aimed to contribute to the literature by designing a new RCM mechanism. The rotation of the mechanism around the RCM point is provided by only one rotary motor, and the displacement of the RCM point in the vertical axis is provided by only one linear motor. The mechanism is also a surgical robot. The designed system is suitable for use in robot-assisted laparoscopic surgery in terms of maneuverability.

Evaluation of conservative treatment of frozen shoulder: A clinical study

The frozen shoulder (adhesive capsulitis) is a clinical syndrome complicated by a surfeit of synonyms. The true mechanism has been the grist of innumerable scholarly effort. Strangely the diagnosis is not difficult although the precise cause may be elusive. The present study was conducted upon 100 patients. The inclusion criteria was to consider patients with gradual onset with classical phasic character of the disease, pain in the shoulder joint, limitation of movements which may only be slight in the beginning and objective signs of diffuse tenderness, muscle spasm or wasting of muscles. Once the diagnosis was established, the patients were divided in to three groups which were then managed accordingly with only physiotherapy, steroid and local anaesthesia injection with physiotherapy and manipulation under anaesthesia with local steroid injection. The observations were based on a twelve week follow up study of these cases. Most of the patients were in their sixth decade of life. The mean age of the patients were 50.96 years. In our study, 58% were females whereas 42% were males. 50% of the patients had involvement of right shoulder and in the remaining 50% left shoulder was involved. Only one patient had involvement of both the shoulder joint. In our series, most of the patients came to seek medical advice after some interval from the onset. The majority of them reported between 2-4 months since the onset of symptoms, average duration being 4.3 months. There was appreciable wasting of deltoid and supraspinatus in 57 cases and muscle spasm was there in 43 cases. All the patient had pain at limits of motion. The combined results at the end of 12 weeks follow-up were; out of 100 patients and 101 shoulders (one case bilateral involvement) treated, 44 graded as excellent, 39 as good, 14 as fair and remaining four as poor. The authors believe that the patients with frozen shoulder should be diagnosed promptly and regular follow up is needed for better evaluation of their response to treatment.

Tunable Coupling of a Double Quantum Dot Spin System to a Mechanical Resonator

The interaction of quantum systems with mechanical resonators is of practical interest for applications in quantum information and sensing and also of fundamental interest as hybrid quantum systems. Achieving a large and tunable interaction strength is of great importance in this field as it enables controlled access to the quantum limit of motion and coherent interactions between different quantum systems. This has been challenging with solid state spins, where typically the coupling is weak and cannot be tuned. Here we use pairs of coupled quantum dots embedded within cantilevers to achieve a high coupling strength of the singlet-triplet spin system to mechanical motion through strain. Two methods of achieving strong, tunable coupling are demonstrated. The first is through different strain-induced energy shifts for the two QDs when the cantilever vibrates, resulting in changes to the exchange interaction. The second is through a laser-driven AC Stark shift that is sensitive to strain-induced shifts of the optical transitions. Both of these mechanisms can be tuned to zero with electrical bias or laser power, respectively, and give large spin-mechanical coupling strengths.

Whiskered Parabolic Tori in the Planar $$(n+1)$$-Body Problem

The planar \((n+1)\)-body problem models the motion of \(n+1\) bodies in the plane under their mutual Newtonian gravitational attraction forces. When \(n\ge 3\), the question about final motions, that is, what are the possible limit motions in the planar \((n+1)\)-body problem when \(t\rightarrow \infty \), ceases to be completely meaningful due to the existence of non-collision singularities. In this paper we prove the existence of solutions of the planar \((n+1)\)-body problem which are defined for all forward time and tend to a parabolic motion, that is, that one of the bodies reaches infinity with zero velocity while the rest perform a bounded motion. These solutions are related to whiskered parabolic tori at infinity, that is, parabolic tori with stable and unstable invariant manifolds which lie at infinity. These parabolic tori appear in cylinders which can be considered “normally parabolic”. The existence of these whiskered parabolic tori is a consequence of a general theorem on parabolic tori developed in this paper. Another application of our theorem is a conjugation result for a class of skew product maps with a parabolic torus with its normal form generalizing results of Takens (Ann Inst Fourier 23(2):163–195, 1973), and Voronin (Funktsional Anal i Prilozhen 15(1):1–17, 96, 1981).

Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

View-Invariant Human Action Recognition Based on a 3D Bio-Constrained Skeleton Model.

Skeleton-based human action recognition has been a hot topic in recent years. Most existing studies are based on the skeleton data obtained from Kinect, which is noisy and unstable, in particular, in the case of occlusions. To cope with the noisy skeleton data and variation of viewpoints, this paper presents a view-invariant method for human action recognition by recovering the corrupted skeletons based on a 3D bio-constrained skeleton model and visualizing those body-level motion features obtained during the recovery process with images. The bio-constrained skeleton model is defined with two types of constraints: 1) constant bone lengths and 2) motion limits of joints. Based on the bio-constrained model, an effective method is proposed for skeleton recovery. Two types of new motion features, the Euclidean distance matrix between joints (JEDM), which contains the global structure information of the body, and the local dynamic variation of the joint Euler angles (JEAs) are used in describing human action. These two types of features are encoded into different motion images, which are fed into a two-stream convolutional neural network for learning different action patterns. The experiments on three benchmark datasets achieve better accuracy than the state-of-the-art approaches, which demonstrates the effectiveness of the proposed method.

3D-2D Image Registration in Virtual Long-Film Imaging: Application to Spinal Deformity Correction.

Intraoperative 2D virtual long-film (VLF) imaging is investigated for 3D guidance and confirmation of the surgical product in spinal deformity correction. Multi-slot-scan geometry (rather than a single-slot "topogram") is exploited to produce parallax views of the scene for accurate 3D colocalization from a single radiograph. The multi-slot approach uses additional angled collimator apertures to form fan-beams with disparate views (parallax) of anatomy and instrumentation and to extend field-of-view beyond the linear motion limits. Combined with a knowledge of surgical implants (pedicle screws and/or spinal rods modeled as "known components"), 3D-2D image registration is used to solve for pose estimates via optimization of image gradient correlation. Experiments were conducted in cadaver studies emulating the system geometry of the O-arm (Medtronic, Minneapolis MN). Experiments demonstrated feasibility of multi-slot VLF and quantified the geometric accuracy of 3D-2D registration using VLF acquisitions. Registration of pedicle screws from a single VLF yielded mean target registration error of (2.0±0.7) mm, comparable to the accuracy of surgical trackers and registration using multiple radiographs (e.g., AP and LAT). 3D-2D registration in a single VLF image offers a promising new solution for image guidance in spinal deformity correction. The ability to accurately resolve pose from a single view absolves workflow challenges of multiple-view registration and suggests application beyond spine surgery, such as reduction of long-bone fractures.

Strip-Mode Microwave Staring Correlated Imaging with Self-Calibration of Gain⁻Phase Errors.

Microwave staring correlated imaging (MSCI) can realize super resolution imaging without the limit of relative motion with the target. However, gain–phase errors generally exist in the multi-transmitter array, which results in imaging model mismatch and degrades the imaging performance considerably. In order to solve the problem of MSCI with gain–phase error in a large scene, a method of MSCI with strip-mode self-calibration of gain–phase errors is proposed. The method divides the whole imaging scene into multiple imaging strips, then the strip target scattering coefficient and the gain–phase errors are combined into a multi-parameter optimization problem that can be solved by alternate iteration, and the error estimation results of the previous strip can be carried into the next strip as the initial value. All strips are processed in multiple rounds, and the gain–phase error estimation results of the last strip can be taken as the initial value and substituted into the first strip for the correlated processing of the next round. Finally, the whole imaging in a large scene can be achieved by multi-strip image splicing. Numerical simulations validate its potential advantages to shorten the imaging time dramatically and improve the imaging and gain–phase error estimation performance.

A linear model for relative motion in an elliptical orbit based on a spherical coordinate system

When compared with Cartesian coordinates, curvilinear coordinates have shown significant superior accuracy when applied to a linear model for relative motion in a circular reference orbit. Experts assume the same superiority for an elliptical reference orbit. However, the curvilinear model in an elliptical reference orbit has not been established, and the superiority has not been proved. After a strictly theoretical derivation this paper establishes a linear model with spherical coordinates for relative motion in an elliptical reference orbit. The differential equation has the same form as the Lawden or Tschauner-Hempel equation and can be easily solved with the solutions from the literature. In addition both the theoretical derivation and the numerical examples prove the model's superior accuracy in leader-follower formation and formations with a large along-track distance. The proposed model reduces the approximate limits of close relative motion, and it is expected to be applied in the propagation, guidance, and control for longer term relative motion with large along-track distances.

Safe navigation of quadrotors with jerk limited trajectory

Many aerial applications require unmanned aerial systems operate in safe zones because of the presence of obstacles or security regulations. It is a non-trivial task to generate a smooth trajectory satisfying both dynamic constraints and motion limits of the unmanned vehicles while being inside the safe zones. Then the task becomes even more challenging for real-time applications, for which computational efficiency is crucial. In this study, we present a safe flying corridor navigation method, which combines jerk limited trajectories with an efficient testing method to update the position setpoints in real time. Trajectories are generated online and incrementally with a cycle time smaller than 10 μs, which is exceptionally suitable for vehicles with limited onboard computational capability. Safe zones are represented with multiple interconnected bounding boxes which can be arbitrarily oriented. The jerk limited trajectory generation algorithm has been extended to cover the cases with asymmetrical motion limits. The proposed method has been successfully tested and verified in flight simulations and actual experiments.