Position-dependent Force Research Articles

Quantising a Hamiltonian curl force

Abstract Classical curl forces are position-dependent Newtonian forces (accelerations) that are not the gradient of a scalar potential, and in general cannot be described by Hamiltonians. However, a special class of curl forces can be described by Hamiltonians, with the unusual feature that the kinetic energy is anisotropic in the momentum components. Therefore they can be quantised conventionally. We quantise the simplest such case: motion in the plane, with a curl force azimuthally directed and linear. As expected, the quantum propagator, and the way this drives Gaussian wavepackets, directly reflects the spiralling classical curl force dynamics. Two classes of stationary states—eigenfunctions of a continuous spectrum for the unbounded Hamiltonian—are described. They possess unusual singularities and an unfamiliar quantisation condition; their explanation requires asymptotics and unfamiliar singularities in the underlying families of classical trajectories. The analysis is supported and illustrated numerically.

Inertial spin model of flocking with position-dependent forces.

We propose an extension to the inertial spin model (ISM) of flocking and swarming. The model has been introduced to explain certain dynamic features of swarming (second sound, a lower than expected dynamic critical exponent) while preserving the mechanism for onset of order provided by the Vicsek model. The inertial spin model (ISM) has only been formulated with an imitation ("ferromagnetic") interaction between velocities. Here we show how to add position-dependent forces in the model, which allows to consider effects such as cohesion, excluded volume, confinement, and perturbation with external position-dependent field, and thus study this model without periodic boundary conditions. We study numerically a single particle with an harmonic confining field and compare it to a Brownian harmonic oscillator and to a harmonically confined active Browinian particle, finding qualitatively different behavior in the three cases.

Servo kontrollü maliyet etkin bir aktif kuvvet duyargası tasarımı ve denenmesi

In this work, the computerized control of a hydraulic system with analog characteristics is examined, and within this scope, a novel force sensor is designed. The system consists of two main structures: an analog subsystem comprising a four-way servo valve, hydraulic piston, servo amplifier, and the designed force sensor, and a digitizing subsystem responsible for comparison and control, composed of a desktop computer. Throughout this work, a cost-effective force sensor was designed by integrating a compression spring, guides, a support frame and a linear variable differential transformer (LVDT). In this integrated system, the force applied at a specific magnitude and frequency from an external force measurement and feedback unit is converted into electrical signals by horizontal motion of the LVDT core. These electrical signals from the force sensor are digitized and fed back to the computer and data acquisition card. The digitized data transferred to the software developed in this study continuously compare with the reference data, enabling position-dependent force control. Experiments conducted with the force sensor placed between two hydraulic pistons controlled by a servo valve revealed that it caused the pistons to move right and left, providing the desired control of the system with the reference force input. The system was observed to operate much more stably, especially for high-frequency signal inputs.

High Precision Hybrid Reluctance Actuator With Integrated Orientation Independent Zero Power Gravity Compensation

This article presents a novel method for enabling energy-efficient and orientation-independent gravity compensation in active vibration isolation systems by taking advantage of the inherent negative stiffness of a hybrid reluctance actuator (HRA). Counteracting the gravitational force acting on the mover of an HRA with the position dependent force of the actuator’s integrated permanent magnet, the gravitational force can be compensated without the need for an additional actuation. An HRA-system with two translational degrees of freedom (DOF) is developed, comprising a permanent magnet for generating a constant biasing flux for both system axes and two actuator coils per axis for actively controlling the position of the mover. The system prototype has an actuation range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.7 mm in both DOF, while enabling energy efficient gravity compensation of payloads up to 500 g by an additional current feedback control loop. Experiments demonstrate that the current consumption for compensation of a 500 g payload is reduced from 1.58 A to 10 mA, which corresponds to a reduction of the power consumption by a factor of 25 000.

Individual Differences in Sensorimotor Adaptation Are Conserved Over Time and Across Force-Field Tasks.

Sensorimotor adaptation enables the nervous system to modify actions for different conditions and environments. Many studies have investigated factors that influence adaptation at the group level. There is growing recognition that individuals vary in their ability to adapt motor skills and that a better understanding of individual differences in adaptation may inform how motor skills are taught and rehabilitated. Here we examined individual differences in the adaptation of upper-limb reaching movements. We quantified the extent to which participants adapted their movements to a velocity-dependent force field during an initial session, at 24 h, and again 1-week later. Participants (n = 28) displayed savings, which was expressed as greater initial adaptation when re-exposed to the force field. Individual differences in adaptation across various stages of the experiment displayed weak-strong reliability, such that individuals who adapted to a greater extent in the initial session tended to do so when re-exposed to the force field. Our second experiment investigated if individual differences in adaptation are also present when participants adapt to different force fields or a force field and visuomotor rotation. Separate groups of participants adapted to position- and velocity-dependent force fields (Experiment 2a; n = 20) or a velocity-dependent force field and visuomotor rotation in a single session (Experiment 2b; n = 20). Participants who adapted to a greater extent to velocity-dependent forces tended to show a greater extent of adaptation when exposed to position-dependent forces. In contrast, correlations were weak between various stages of adaptation to the force-field and visuomotor rotation. Collectively, our study reveals individual differences in adaptation that are reliable across repeated exposure to the same force field and present when adapting to different force fields.

Reconfigurable millimeter-range optical binding of dielectric microparticles in hollow-core photonic crystal fiber.

Optical binding of microparticles offers a versatile playground for investigating the optomechanics of levitated multi-particle systems. We report millimeter-range optical binding of polystyrene microparticles in hollow-core photonic crystal fiber. The first particle scatters the incident LP01 mode into several LP0n modes, creating a beat pattern that exerts a position-dependent force on the second particle. Particle binding results from the interplay of the forces created by counterpropagating beams. A femtosecond trapping laser is used so that group velocity walk-off eliminates disturbance caused by higher order modes accidentally excited at the fiber input. The inter-particle distance can be optically switched over 2 orders of magnitude (from 42 µm to 3 mm), and the bound particle pairs can be translated along the fiber by unbalancing the powers in the counterpropagating trapping beams. The frequency response of a bound particle pair is investigated at low gas pressure by driving with an intensity-modulated control beam. The system offers new degrees of freedom for manipulating the dynamics and configurations of optically levitated microparticle arrays.

Higher-order saddle potentials, nonlinear curl forces, trapping and dynamics

The position-dependent non-conservative forces are called curl forces introduced recently by Berry and Shukla (J Phys A 45:305201, 2012). The aim of this paper is to study mainly the curl force dynamics of non-conservative central force $$\ddot{x} = -xg(x,y)$$ and $$\ddot{y} = -yg(x,y)$$ connected to higher-order saddle potentials. In particular, we study the dynamics of the type $$\ddot{x}_i = -x_ig \big (\frac{1}{2}(x_{1}^{2} - x_{2}^{2}) \big )$$ , $$i=1,2$$ and its application towards the trapping of ions. We also study the higher-order saddle surfaces, using the pair of higher-order saddle surfaces and rotated saddle surfaces by constructing a generalized rotating shaft equation. The complex curl force can also be constructed by using this pair. By the direct computation, we show that all these motions of higher-order saddles are completely integrable due to the existence of two conserved quantities, viz. energy function and the Fradkin tensor. The Newtonian system $$\ddot{x} = {{\mathcal {X}}}(x,y)$$ , $$\ddot{y} = {{\mathcal {Y}}}(x,y)$$ has also been studied with an energy like first integral $$I(\mathbf{x}, \dot{\mathbf{x}}) = \frac{1}{2}\dot{\mathbf{x}}^TM(\mathbf{x})\dot{\mathbf{x}} + U(\mathbf{x})$$ , where $$M(\mathbf{x})$$ is a $$(2 \times 2)$$ matrix of which the components are polynomials of degree less than or equal to two and the condition on $${{\mathcal {X}}}$$ and $${{\mathcal {Y}}}$$ for which the curl is non-vanishing is also obtained.

The effect of sequence learning on sensorimotor adaptation

Motor skill learning involves both sensorimotor adaptation (calibrating the response to task dynamics and kinematics), and sequence learning (executing task elements in the correct order at the necessary speed). These processes typically occur together in natural behavior and share much in common, such as working memory demands, development, and possibly neural substrates. However, sensorimotor and sequence learning are usually studied in isolation in research settings, for example as force field adaptation or serial reaction time tasks (SRTT), respectively. It is therefore unclear whether having predictive sequence information during sensorimotor adaptation would facilitate performance, perhaps by improving sensorimotor planning, or if it would impair performance, perhaps by occupying neural resources needed for sensorimotor adaptation. Here we evaluated adaptation to a position-dependent force field in two different SRTT contexts: In Experiment 1, 28 subjects reached between 4 targets in a sequenced or random order. In Experiment 2, 40 subjects reached to one target, but 3 force field directions were applied in a sequenced or random order. No consistent influence of target position sequence on force field adaptation was observed in Experiment 1. However, sequencing of force field directions facilitated sensorimotor adaptation and retention in Experiment 2. This is inconsistent with the idea that sensorimotor and sequence learning share neural resources in any mutually exclusive fashion. These findings indicate that under certain conditions, sequence learning interacts with sensorimotor adaptation in a facilitatory manner. Future research will be needed to determine what circumstances and features of sequence learning are facilitatory to sensorimotor adaptation.

Deltoid muscle contribution to shoulder flexion and abduction strength: an experimental approach

The rotator cuff (RC) and the deltoid muscle are 2 synergistic units that enable the functionally demanding movements of the shoulder. A number of biomechanical studies assume similar force contribution of the force couple (RC and deltoid) over the whole range of motion, whereas others propose position-dependent force distribution. There is a lack of invivo data regarding the deltoid's contribution to shoulder flexion and abduction strength. This studyaimed to create reliable invivo dataquantifying the deltoid's contribution to shoulder flexion and abduction strength throughout the range of motion. Active range of motion and isometric muscle strength of shoulder abduction and flexion in 0°, 30°, 60°, 90°, and 120° of abduction/flexion as well as internal and external rotation in 0° and 90° of abduction were obtained in 12 healthy volunteers on the dominant arm before and after an ultrasound-guided isolated axillary nerve block. Needle electromyography was performed before and after the block to confirm deltoid paralysis. Radiographs of the shoulder and an ultrasonographic examination were used to exclude relevant shoulder pathologies. Active range of motion showed a minimal to moderate reduction to 94% and 88% of the preintervention value for abduction and flexion. Internal and external rotation amplitude was not impaired. The abduction strength was significantly reduced to 76% at 0° (P = .002) and to 25% at 120° (P < .001) of abduction. The flexion strength was significantly reduced to 64% at 30° (P < .001) and to 30% at 120° (P < .001) of flexion. The strength reduction was linear, depending on the flexion/abduction angle. The maximal external rotation strength showed a significant decrease to 53% in 90° (P < .001) of abduction, whereas in adduction no strength loss was observed (P = .09). The internal rotation strength remained unaffected in 0° and 90° of abduction (P = .28; P = .13). The deltoid shows a linear contribution to maximal shoulder strength depending on the abduction or flexion angle, ranging from 24% in 0° to 75% in 120° of abduction and from 11% in 0° to 70% in 120° of flexion, respectively. The overall contribution to abduction strength is higher than to flexion strength. The combination of deltoid muscle and teres minor contributes about 50% to external rotation strength in 90° of abduction. The internal rotation strength is not influenced by a deltoid paralysis. This study highlights the position-dependent contribution of the shoulder muscles to strength development and thereby provides an empirical approach to better understand human shoulder kinematics.

Flux-Controlled Hybrid Reluctance Actuator for High-Precision Scanning Motion

To achieve highly precise and linear scanning motion by a hybrid reluctance actuator (HRA), this article proposes a flux-controlled mode that uses regulated magnetic flux as the control input for the actuator operation and evaluates its performance in comparison with the conventional current-controlled mode. In the conventional case, HRAs exhibit magnetic nonlinearities (e.g., hysteresis) and position-dependent force that can make the system unstable. A model-based analysis reveals that they are included in the variable magnetic flux of an HRA. Thus, they are captured by flux estimation and rejected by flux feedback control for high-quality scanning motion. For the estimation, sensor fusion with a current monitor and a search coil is used. Proportional integral (PI) controllers are used for the flux feedback control, as well as for current feedback control of the benchmarking current-controlled mode. During scanning, feedforward control is used to compensate linear dynamics. When sine motions are experimentally tested at 60-300 Hz, the current-controlled mode exhibits a nonlinearity between 6% and 23%, which is decreased to less than 5% by the flux-controlled mode. For a ±75 μm triangular motion at 100 Hz, the flux-controlled mode decreases the tracking error by a factor of 19 to 3.2 μm, successfully demonstrating its high-quality linear scanning motion.

Identification and Compensation of Dynamic Interaction in a Non-Contact Dual-Stage Actuator System.

Dynamic interaction seriously limits the overall performance of a Dual-Stage Actuator (DSA) system. This paper aims to identify and compensate for the dynamic interaction in a non-contact DSA system. The effects of the interaction in the non-contact DSA system are initially classified as non-contact position-dependent disturbance forces (PDDFs) and velocity-dependent disturbance forces (VDDFs). The PDDFs in the three degrees of freedom (DoFs) motion space between the two stages of the DSA system are directly identified in the time domain, and VDDFs are indirectly identified in the form of damping values in frequency domains. The feedforward networks of the force are subsequently applied to compensate the PDDFs and VDDFs, which are indexed with relative displacement and velocity, respectively. Experiments are finally conducted to investigate the effectiveness of compensation, which infers that the final positioning error in the time domain can be reduced from 260 nm to 130 nm with PDDFs and VDDFs compensation. The gain of the interaction transfer is decreased in the frequency range of up to 45 Hz with PDDFs and VDDFs compensation. With this method, some weak dynamic interaction can be completely compensated for by the force feedforward compensation, and the positioning accuracy of non-contact DSA systems can be greatly improved.

The effect of local wake model on collision probability for risers subjected to current and random waves

The present paper provides a method to estimate the clearance between two flexible risers in tandem arrangement by taking into account the hydrodynamic wake interference when subjected to a current flow and a combined current plus waves flow. Modelling of the wake interference in the near wake field is based on the modification of the mean wake velocity deficit in the far wake field. Two modified wake models are introduced in the presented paper. The wake effects in steady current and in current plus waves are investigated by using both wake models. For the current-only flow, the deflection shapes of a pair of tandem risers in steep-wave configuration are presented, highlighting the importance of the wake effect on clearance estimation. For combined current plus waves, the wake interference is investigated by considering the position-dependent drag force, with different combinations of riser natural frequency and wave frequency. The collision failure probability is predicted when the risers are subjected to current plus random waves.

Quantifying Local Molecular Tension Using Intercalated DNA Fluorescence.

The ability to measure mechanics and forces in biological nanostructures, such as DNA, proteins and cells, is of great importance as a means to analyze biomolecular systems. However, current force detection methods often require specialized instrumentation. Here, we present a novel and versatile method to quantify tension in molecular systems locally and in real time, using intercalated DNA fluorescence. This approach can report forces over a range of at least ∼0.5–65 pN with a resolution of 1–3 pN, using commercially available intercalating dyes and a general-purpose fluorescence microscope. We demonstrate that the method can be easily implemented to report double-stranded (ds)DNA tension in any single-molecule assay that is compatible with fluorescence microscopy. This is particularly useful for multiplexed techniques, where measuring applied force in parallel is technically challenging. Moreover, tension measurements based on local dye binding offer the unique opportunity to determine how an applied force is distributed locally within biomolecular structures. Exploiting this, we apply our method to quantify the position-dependent force profile along the length of flow-stretched DNA and reveal that stretched and entwined DNA molecules—mimicking catenated DNA structures in vivo—display transient DNA–DNA interactions. The method reported here has obvious and broad applications for the study of DNA and DNA–protein interactions. Additionally, we propose that it could be employed to measure forces in any system to which dsDNA can be tethered, for applications including protein unfolding, chromosome mechanics, cell motility, and DNA nanomachines.

Coherent Multimodal Sensory Information Allows Switching between Gravitoinertial Contexts.

Whether the central nervous system is capable to switch between contexts critically depends on experimental details. Motor control studies regularly adopt robotic devices to perturb the dynamics of a certain task. Other approaches investigate motor control by altering the gravitoinertial context itself as in parabolic flights and human centrifuges. In contrast to conventional robotic experiments, where only the hand is perturbed, these gravitoinertial or immersive settings coherently plunge participants into new environments. However, radically different they are, perfect adaptation of motor responses are commonly reported. In object manipulation tasks, this translates into a good matching of the grasping force or grip force to the destabilizing load force. One possible bias in these protocols is the predictability of the forthcoming dynamics. Here we test whether the successful switching and adaptation processes observed in immersive environments are a consequence of the fact that participants can predict the perturbation schedule. We used a short arm human centrifuge to decouple the effects of space and time on the dynamics of an object manipulation task by adding an unnatural explicit position-dependent force. We created different dynamical contexts by asking 20 participants to move the object at three different paces. These contextual sessions were interleaved such that we could simulate concurrent learning. We assessed adaptation by measuring how grip force was adjusted to this unnatural load force. We found that the motor system can switch between new unusual dynamical contexts, as reported by surprisingly well-adjusted grip forces, and that this capacity is not a mere consequence of the ability to predict the time course of the upcoming dynamics. We posit that a coherent flow of multimodal sensory information born in a homogeneous milieu allows switching between dynamical contexts.

Two-Dimensional Kinetic Shape Dynamics: Verification and Application

A kinetic shape (KS) is a smooth two- or three-dimensional shape that is defined by its predicted ground reaction forces as it is pressed onto a flat surface. A KS can be applied in any mechanical situation where position-dependent force redirection is required. Although previous work on KSs can predict static force reaction behavior, it does not describe the kinematic behavior of these shapes. In this article, we derive the equations of motion for a rolling two-dimensional KS (or any other smooth curve) and validate the model with physical experiments. The results of the physical experiments showed good agreement with the predicted dynamic KS model. In addition, we have modified these equations of motion to develop and verify the theory of a novel transportation device, the kinetic board, that is powered by an individual shifting their weight on top of a set of KSs.

Heat flux of a granular gas with homogeneous temperature

A steady state of granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position-dependent force or by enclosing the grains inside a curved 2D silo. At a macroscopic level, the state is identified with one solution to the inelastic Navier–Stokes equations, due to the coupling between the heat flux induced by the density gradient and the external force. In contrast, at the mesoscopic level, by exactly solving a BGK model or the inelastic Boltzmann equation in an approximate way, a one-parametric family of solutions is found. Molecular dynamics simulations of the system in the quasi-elastic limit are in agreement with the theoretical results.

Transport of a partially wetted particle at the liquid/vapor interface under the influence of an externally imposed surfactant generated Marangoni stress

Marangoni flows offer an interesting and useful means to transport particles at fluid interfaces with potential applications such as dry powder pulmonary drug delivery. In this article, we investigate the transport of partially wetted particles at a liquid/vapor interface under the influence of Marangoni flows driven by gradients in the surface excess concentration of surfactants. We deposit a microliter drop of soluble (sodium dodecyl sulfate) aqueous surfactant solution or pure insoluble liquid (oleic acid) surfactant on a water subphase and observe the transport of a pre-deposited particle. Following the previous observation by Wang et al. [1] that a surfactant front rapidly advances ahead of the deposited drop contact line and initiates particle motion but then moves beyond the particle, we now characterize the two dominant, time- and position-dependent forces acting on the moving particle: (1) a surface tension force acting on the three-phase contact line around the particle periphery due to the surface tension gradient at the liquid/vapor interface which always accelerates the particle and (2) a viscous force acting on the immersed surface area of the particle which accelerates or decelerates the particle depending on the difference in the velocities of the liquid and particle. We find that the particle velocity evolves over time in two regimes. In the acceleration regime, the net force on the particle acts in the direction of particle motion, and the particle quickly accelerates and reaches a maximum velocity. In the deceleration regime, the net force on the particle reverses and the particle decelerates gradually and stops. We identify the parameters that affect the two forces acting on the particle, including the initial particle position relative to the surfactant drop, particle diameter, particle wettability, subphase thickness, and surfactant solubility. We systematically vary these parameters and probe the spatial and temporal evolution of the two forces acting on the particle as it moves along its trajectory in both regimes. We find that a larger particle always lags behind the smaller particle when placed at an equal initial distance from the drop. Similarly, particles more deeply engulfed in the subphase lag behind those less deeply engulfed. Further, the extent of particle transport is reduced as the subphase thickness decreases due to the larger velocity gradients in the subphase recirculation flows.

Using DQM method on residual vibration analysis of an electrostatically actuated microswitch structure

Using the Differential quadrature method (DQM) on Residual vibration analysis of an Electrostatically actuated microswitch structure is focused to study in this work. The application of external voltage between an electrode and a microbeam results in microbeam vibration during the transient period before the beam reaches its permanent position. The lifetime of a microswitch or a modulator is dependent on the number of switching-cycles it performs; therefore severe residual vibrations may reduce the lifetime of the micro-actuator and introduce operating delays. Consequently, understanding and controlling the residual vibration in a micro-actuator is paramount. In this study, the effects of design parameters on the dynamic responses of a microswitch were formulated and considered. The models proposed use the DQM combined with the Wilson- q method, to treat the nonlinear transient problem of microswitches, and simultaneously consider the effects of position-dependent electrostatic force, mechanical restoring force, and squeeze-film damping. Additionally, the effects of the electrode in various positions on the residual vibration of the microbeam were explored. Variations of residual vibrations with variously shaped beams and electrodes were simulated and studied to control the settling time of the micro-actuator. Analysis results indicate that the residual vibration of microswitches can be markedly changed by effects of the shape and tip thickness of beam, and length and position of electrode of an electrostatically actuated microswitch structure system.

Minimal Assist-as-Needed Controller for Upper Limb Robotic Rehabilitation

Robotic rehabilitation of the upper limb following neurological injury is most successful when subjects are engaged in the rehabilitation protocol. Developing assistive control strategies that maximize subject participation is accordingly an active area of research, with aims to promote neural plasticity and, in turn, increase the potential for recovery of motor coordination. Unfortunately, state-of-the-art control strategies either ignore more complex subject capabilities or assume underlying patterns govern subject behavior and may therefore intervene suboptimally. In this paper, we present a minimal assist-as-needed (mAAN) controller for upper limb rehabilitation robots. The controller employs sensorless force estimation to dynamically determine subject inputs without any underlying assumptions as to the nature of subject capabilities and computes a corresponding assistance torque with adjustable ultimate bounds on position error. Our adaptive input estimation scheme is shown to yield fast, stable, and accurate measurements regardless of subject interaction and exceeds the performance of current approaches that estimate only position-dependent force inputs from the user. Two additional algorithms are introduced in this paper to further promote active participation of subjects with varying degrees of impairment. First, a bound modification algorithm is described, which alters allowable error. Second, a decayed disturbance rejection algorithm is presented, which encourages subjects who are capable of leading the reference trajectory. The mAAN controller and accompanying algorithms are demonstrated experimentally with healthy subjects in the RiceWrist-S exoskeleton.

Imaging the position-dependent 3D force on microbeads subjected to acoustic radiation forces and streaming.

Acoustic particle manipulation in microfluidic channels is becoming a powerful tool in microfluidics to control micrometer sized objects in medical, chemical and biological applications. By creating a standing acoustic wave in the channel, the resulting pressure field can be employed to trap or sort particles. To design efficient and reproducible devices, it is important to characterize the pressure field throughout the volume of the microfluidic device. Here, we used an optically trapped particle as probe to measure the forces in all three dimensions. By moving the probe through the volume of the channel, we imaged spatial variations in the pressure field. In the direction of the standing wave this revealed a periodic energy landscape for 2 μm beads, resulting in an effective stiffness of 2.6 nN m(-1) for the acoustic trap. We found that multiple fabricated devices showed consistent pressure fields. Surprisingly, forces perpendicular to the direction of the standing wave reached values of up to 20% of the main-axis-values. To separate the direct acoustic force from secondary effects, we performed experiments with different bead sizes, which attributed some of the perpendicular forces to acoustic streaming. This method to image acoustically generated forces in 3D can be used to either minimize perpendicular forces or to employ them for specific applications in novel acoustofluidic designs.