Multiple Degrees Of Freedom Research Articles

Vibration suppression using tuneable flexures acting as vibration absorbers

Vibration suppression is an area of engineering that is vital for the development of manufacturing of low stiffness structures. A diversity of passive, active and semi-active vibration control techniques exist in the literature, many of them focused on the tool or the workpiece, while little attention has been paid into the dissipation capabilities of the fixtures. In this paper, the vibration attenuation capabilities of tuneable flexures are presented, proving the ability of beam-shaped supports to mitigate the vibration induced by the manufacturing process (e.g. machining loads) to the workpiece. The proposed modelling approach puts a solid theoretical basis on how to construct flexures tuned in such a way to allow their natural frequency to match the frequency of excitation, thus absorbing the energy from the workpiece and keeping it at low vibration levels. By means of a multiple-degree-of-freedom (MDOF) model and considering the system as three different bodies with springs and dampers, the dynamic behaviour of the system is examined theoretically starting from the geometry and material of the flexures on which the fixturing system is based. This is further validated with finite element analysis (FEA) as well as experimental results showing a low discrepancy between the models on the prediction of the resonant frequencies of up to a 0.6%. The importance of understanding the critical clamping load for the locking of the contact surfaces is also presented, as it is indispensable for the proper functioning of the flexures-based fixturing system. Finally, the vibration suppression capability of the flexures at the targeted frequency is experimentally validated and proved to substantially reduce (ca. 90%) the vibration response of the workpiece when compared with the non-suppressed frequencies. The proposed model represents an avenue to address the inverse problem for the design of a fixture with vibration absorption capabilities, depending on the manufacturing process parameters, the workpiece and the chatter that needs to be suppressed.

High precision six-degree-of-freedom interferometer for test mass readout

High precision six-degree-of-freedom sensing plays an important role in future gravitational space missions. In gravitational or geodesy missions, measurements of all six degrees of freedom of freely floating test mass are required for reducing the cross-coupling noise, which is frequently an important limiting factor in the performance. Interferometry and capacitive sensing have been successfully combined in LISA pathfinder to achieve six degrees of freedom measurements. In this paper, we report a six-degree-of-freedom interferometer system based on multiplex differential wavefront sensing and longitudinal pathlength sensing. Compared to conventional capacitive sensing or optical levers, it has a higher measurement accuracy. The results of our table-top experiment show motion in all six degrees of freedom of a cubic test mass are simultaneously measured with a translational and tilt sensitivity of 100 pm/Hz1/2 and 10 nrad Hz−1/2 above 1 Hz, respectively. The translational dynamic range is greater than ±10 mm with nonlinear residuals less than 6 μm, and the tilt dynamic range is approximately ±500 μrad with nonlinear residuals less than 60 μrad. The coupling errors between multiple degrees of freedom are dominated by tilt-to-translation and tilt-to-tilt coupling, which are roughly 2–4 μm and 15–25 μrad, respectively, within a range of [−500 μrad, +500 μrad].

Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths

It is very common in the literature to write down a Markovian quantum master equation in Lindblad form to describe a system with multiple degrees of freedom and weakly connected to multiple thermal baths which can, in general, be at different temperatures and chemical potentials. However, the microscopically derived quantum master equation up to leading order in system-bath coupling is of the so-called Redfield form which is known to not preserve complete positivity in most cases. Additional approximations to the Redfield equation are required to obtain a Lindblad form. We lay down some fundamental requirements for any further approximations to Redfield equation, which, if violated, leads to physical inconsistencies like inaccuracies in the leading order populations and coherences in the energy eigenbasis, violation of thermalization, violation of local conservation laws at the non-equilibrium steady state (NESS). We argue that one or more of these conditions will generically be violated in all the weak system-bath-coupling Lindblad descriptions existing in literature to our knowledge. As an example, we study the recently derived Universal Lindblad Equation (ULE) and use these conditions to show violation of local conservation laws due to inaccurate coherences but accurate populations in energy eigenbasis. Finally, we exemplify our analytical results numerically in an interacting open quantum spin system.

FAT-based robust adaptive controller design for electrically direct-driven robots using Phillips q-Bernstein operators

AbstractThis article proposes a robust and adaptive controller for industrial robot arms with multiple degrees of freedom without the need for velocity measurement. Many of the controllers designed for manipulators are model-based and require detailed knowledge of the system model. In contrast to these methods, this paper proposes a model-free controller using the Philips q-Bernstein operator as universal approximator. The designed controller can approximate uncertainties including external disturbances and unmodeled dynamics based on its universal approximation capability. Besides, most of the controllers revealed for robot arms are torque-based, which is not a realistic presumption from a practical point of view. In the proposed control method, the voltage applied to the actuator is considered as the control signal. However, unlike many voltage-based methods, the need to know the exact models of the system and the actuator has been eliminated in the presented method. Also, adaptive rules are extracted during the Lyapunov analysis to ensure system stability. Finally, to analyze the performance of the presented controller, this method is simulated for an industrial robot arm, and the results are analyzed. The proposed methodology is also compared to those of a strong state-of-the-art approximator, the Chebyshev neural network.

Photo-induced antiferromagnetic-ferromagnetic and spin-state transition in a double-perovskite cobalt oxide thin film

Investigation of ultrafast dynamic behaviors can provide novel insights about the coupling mechanisms among multiple degrees of freedom in condensed matters, such as lattice, magnetism and electronic structure. Here we investigate both the ferromagnetic (FM) and antiferromagnetic (AFM) dynamics of a strongly correlated oxide system, GdBaCo2O5.5 thin film by time-resolved x-ray magnetic circular dichroism in reflectivity (XMCDR) and resonant magnetic x-ray diffraction (RMXD). A photo-induced AFM-FM transition characterized by an increase of the transient XMCDR (sensitive to FM order) beyond the unpumped value and a decay of RMXD (sensitive to AFM order) was observed. The photon-energy dependence of the transient XMCDR and reflectivity could be interpreted as a concomitant photo-induced spin-state transition (SST). The AFM-FM transition and SST couple with each other in the time domain, resulting in unusual dynamic behaviors of the magnetism.

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

In this paper, a new methodology for the determination of the boundaries between oscillatory and non-oscillatory motion for nonviscously damped nonproportional systems is proposed. It is assumed that the damping forces are expressed as convolution integrals of the velocities via hereditary exponential kernels. Oscillatory motion is directly related to the complex nature of eigensolutions in a frequency domain and, in turn, on the value of the damping parameters. New theoretical results are derived on critical eigenmodes for viscoelastic systems with multiple degrees of freedom, with no restrictions on the number of hereditary kernels. Furthermore, these outcomes enable the construction of a numerical approach to draw the critical curves as solutions of certain parameter-dependent eigenvalue problems. The method is illustrated and validated through two numerical examples, covering discrete and continuous systems.

Seismic pounding damage to adjacent reinforced concrete frame–shear wall buildings and freestanding contents

AbstractClosely spaced tall buildings are common in modern urban areas due to limited supply of land to accommodate rapid growth of population. These buildings are vulnerable in seismically active regions particularly when earthquake‐induced pounding occurs between adjacent buildings, resulting in high floor acceleration spikes that may lead to excessive demands on building contents (BCs). This paper examines the effect of seismic pounding on damage to adjacent reinforced concrete (RC) frame–shear wall buildings and their freestanding contents using nonlinear response‐history analyses (RHA). A cascading analysis approach is adopted to obtain absolute floor accelerations of pounding tall buildings, which are then applied to determine response of freestanding contents dominated by either sliding or rocking motions. In order to provide a useful tool for practicing engineers and facilitate analyses, the buildings are simplified as story‐based multiple‐degree‐of‐freedom (MDOF) flexural‐shear models, and unanchored contents are idealized as single‐degree‐of‐freedom (SDOF) oscillators, all of which are approximated using OpenSees and verified against solutions to their exact equations of motion solved using Matlab. It is shown that seismic pounding leads to higher building damage and alters story damage distribution patterns. It is concluded that pounding significantly increases sliding potential and maximum sliding displacement demands on stocky contents, especially those on higher floors. The transitions of stick–slip response of the contents coincide well with pounding occurrences. It is also concluded that pounding has detrimental effects on slender rocking contents, but rocking rotation histories of these contents do not show abrupt changes upon impact.

Multiple strong topological gaps and hexagonal warping in Bi4Te3

The electronic topology of ${\mathrm{Bi}}_{4}{\mathrm{Te}}_{3}$, composed of alternating ${\mathrm{Bi}}_{2}$ and ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ layers, is investigated by density functional theory and angle-resolved photoemission spectroscopy. We find, remarkably, that there are three adjacent strong topological gaps with associated protected surface states within a 2-eV range of the Fermi level. The existence of three consecutive Dirac cones in $k$ space gives promise for alternative phenomena and applications, e.g., production of single photons with different energies (in the infrared and visible ranges) for multichannel transport of quantum information as well as multiple degrees of freedom in electron pumping for lasers. Additionally, a surface-state Fermi surface with strong hexagonal warping is observed.

Synergy Estimation Method for Simultaneous Activation of Multiple DOFs Using Surface EMG Signals

Surface electromyography signals are routinely used for designing prosthetic control systems. The concept of synergy estimation for muscle control interpretation is being explored extensively. Synergies estimated for a single active degree of freedom (DoF) are found to be uncorrelated and provide better results when used for single movement classification; however, an increase of simultaneously active DoFs leads to complex limb movements and multiple DoF detection becomes a challenge. Synergy estimation is a non-convex optimization technique, to provide better estimation this paper proposes the use of regularized non-negative matrix factorization for the evaluation of synergistic weights in complex movements. The use of regularization constraint makes the overall problem bounded and provide smoothness. The proposed technique showed better accuracy when tested for activation of multiple DoF simultaneously at a significantly lower computational time, i.e., by 34%.

Multi-freedom metasurface empowered vectorial holography

Abstract Optical holography capable of the complete recording and reconstruction of light’s wavefront, plays significant roles on interferometry, microscopy, imaging, data storage, and three-dimensional displaying. Conventional holography treats light as scalar field with only phase and intensity dimensions, leaving the polarization information entirely neglected. Benefiting from the multiple degrees of freedom (DOFs) for optical field manipulation provided by the metasurface, vectorial holography with further versatile control in both polarization states and spatial distributions, greatly extended the scope of holography. As full vectorial nature of light field has been considered, the information carried out by light has dramatically increased, promising for novel photonic applications with high performance and multifarious functionalities. This review will focus on recent advances on vectorial holography empowered by multiple DOFs metasurfaces. Interleaved multi-atom approach is first introduced to construct vectorial holograms with spatially discrete polarization distributions, followed by the versatile vectorial holograms with continuous polarizations that are designed usually by modified iterative algorithms. We next discuss advances with further spectral response, leading to vivid full-color vectorial holography; and the combination between the far-field vectorial wavefront shaping enabled by vectorial holography and the near-field nano-printing functionalities by further exploiting local polarization and structure color responses of the meta-atom. The development of vectorial holography provides new avenues for compact multi-functional photonic devices, potentially useful in optical encryption, anticounterfeiting, and data storage applications.

Path Planning Based on NURBS for Hyper-Redundant Manipulator Used in Narrow Space

Hyper-redundant manipulators with multiple degrees of freedom have special application prospects in narrow spaces, such as detection in small spaces in aerospace, rescue on-site disaster relief, etc. In order to solve the problems of complex obstacle avoidance planning and inverse solution selection of a hyper-redundant robot in a narrow space, a cubic B-spline curve based on collision-free trajectory using environmental edge information is planned. Firstly, a hyper-redundant robot composed of four pairs of double UCR (Universal-Cylindrical-Revolute) parallel mechanisms (2R1T, 2 Rotational DOFs and 1 Translation DOF) in series to realize flexible obstacle avoidance motion in narrow space is designed. The trajectory point envelope of a single UCR and the workspace of a single pair of UCR in Cartesian space based on the motion constraint boundaries of each joint are obtained. Then, the constraint control points according to the edge information of the obstacle are obtained, and the obstacle avoidance trajectory in the constrained space is planned by combining the A* algorithm and cubic B-spline algorithm. Finally, a variety of test scenarios are built to verify the obstacle avoidance planning algorithm. The results show that the proposed algorithm reduces the computational complexity of the obstacle avoidance process and enables the robot to complete flexible obstacle avoidance movement in the complex narrow space.

CNN-Based Hand Grasping Prediction and Control via Postural Synergy Basis Extraction.

The prediction of hand grasping and control of a robotic manipulator for hand activity training is of great significance to assist stroke patients to recover their biomechanical functions. However, the human hand and the figure joints have multiple degrees of freedom; therefore, it is complex to process and analyze all the collected data in hand modeling. To simplify the description of grasping activities, it is necessary to extract and decompose the principal components of hand actions. In this paper, the relationships among hand grasping actions are explored by extracting the postural synergy basis of hand motions, aiming to simplify hand grasping actions and reduce the data dimensions for robot control. A convolutional neural network (CNN)-based hand activity prediction method is proposed, which utilizes motion data to estimate hand grasping actions. The prediction results were then used to control a stimulated robotic model according to the extracted postural synergy basis. The prediction accuracy of the proposed method for the selected hand motions could reach up to 94% and the robotic model could be operated naturally based on patient’s movement intention, so as to complete grasping tasks and achieve active rehabilitation.

Research on coaxiality measurement system of large-span small-hole system based on laser collimation

Aiming at the problems of large-span small-hole system, such as long spatial span, small measured aperture, short hole depth, large distance between adjacent holes, limited measurement space, and lack of measurement benchmark, a non-contact coaxiality measurement system based on laser collimation with the laser displacement sensor as the core is proposed. According to the mathematical model, a position sensitive detector(PSD) and a motion platform with multiple degrees of freedom are utilized to establish a reference axis for parts at any position. Also, the relevant cross-section circle fitting and coaxiality evaluation algorithms are designed to solve the measurement problem. It is proved that this system has high coaxiality detection accuracy for the parts with large axial dimensions (total length is more than 1500 mm), small aperture (diameter is less than φ 10 mm) and large hole spacing (space between two holes is more than 750 mm), and the measurement error does not exceed 0.03 mm.

Generation of hyperentangled states and two-dimensional quantum walks using J or q plates and polarization beam splitters

A single photon can be made to entangle simultaneously in its different internal degrees of freedom (DoF)---polarization, orbital angular momentum (OAM), and frequency---as well as in its external DoF---path. Such entanglement in multiple DoF is known as hyperentanglement and provides additional advantage for quantum information processing. We propose a passive optical setup using $q$ plates and polarization beam splitters to hyperentangle an incoming single photon in polarization, OAM, and path DoF. By mapping polarization DoF to a two-dimensional coin state, and path and OAM DoF to two spatial dimensions, $x$ and $y$, we present a scheme for realization of a two-dimensional discrete-time quantum walk using only polarization beam splitters and $q$ plates ensuing the generation of hyperentangled states. The amount of hyperentanglement generated is quantified by measuring the entanglement negativity between any two DoF. We further show that hyperentanglement generation can be controlled by using an additional coin operation or by replacing the $q$ plate with a $J$ plate.

Theoretical Study of a Two-Degree-of-Freedom Piezoelectric Energy Harvester under Concurrent Aeroelastic and Base Excitation

This paper presents a study of a two-degree-of-freedom (2DOF) piezoelectric energy harvester (PEH) under concurrent aeroelastic and base excitation. The governing equations of the theoretical model under the combined excitation are developed and solved analytically using the harmonic balance method. Based on the electro-mechanical analogies, an equivalent circuit model is established. The energy harvesting performance of the 2DOF PEH under different wind speeds but the same base excitation is investigated. Voltage amplitudes of various response components with different frequencies are predicted by the analytical method and verified by the circuit simulation. The root-mean-square (RMS) voltage is used to measure the actual performance of the 2DOF PEH. Around the resonance state, the 2DOF PEH has been found to produce a larger voltage output than the conventional SDOF PEH. Moreover, several interesting phenomena, such as the quasi-periodic oscillation and the peak-to-valley transition, have been observed in the circuit simulation and explained by the analytical solution. The developed methodology in this paper can be easily adapted to analyze other similar types of multiple-degree-of-freedom (MDOF) PEHs under concurrent aeroelastic and base excitation.

The Wishart Distribution with Multiple Degrees of Freedom

The Wishart Distribution with Multiple Degrees of Freedom

High-Resolution Optical Tweezers Combined with Multicolor Single-Molecule Microscopy.

We present an instrument that combines high-resolution optical tweezers and multicolor confocal fluorescence spectroscopy. Biological macromolecules exhibit complex conformation and stoichiometry changes in coordination with their motion and activity. To further our understanding of the complex machinery of life, we need methods that can simultaneously probe more than one degree of freedom of single molecules and complexes. Fluorescence optical tweezers, or "fleezers," combine the capabilities of optical tweezers and single-molecule fluorescence microscopy into a single instrument. Here we present the latest generation of a high-resolution fleezers instrument integrated with multicolor fluorescence spectroscopy. The tweezers portion of the instrument can manipulate biological macromolecules with pN scale forces while measuring subnanometer distances. Simultaneous with tweezers measurements, the multicolor fluorescence capability allows the direct observation of multiple molecules or multiple degrees of freedom which allows, for example, the observation of multiple proteins simultaneously within a complex. The instrument incorporates three fluorescence excitation lasers, all sourced from a single-mode optical fiber allowing a reliable alignment scheme, that allows, for example, three independent fluorescent probes or fluorescence resonance energy transfer (FRET) measurements and also increases flexibility in the choice of fluorescent probes. To avoid photobleaching and improve tweezers stability, the instrument implements a timesharing (using a single trap laser to produce a pair of traps via rapid switching between two locations) and interlacing (turning the trapping beam off when the fluorescence excitation beams are on and vice versa) scheme using acousto-optic modulators (AOM) to rapidly and precisely modulate lasers. Our latest "random phase" trap AOM control method obliterates previous residual trap positioning and bead position measurement errors. Here we present the general design principles and detailed construction and testing protocols for the instrument.

The effects of intrinsic foot muscles strengthening exercises on knee kinematic in pronated foot subjects during forward jump landing

The foot and ankle are a complex set of multiple joints with multiple degrees of freedom that play an important role in static and dynamic activities. The intrinsic and extrinsic muscles of this complex play a role in controlling the deformity of the arch; thus, the aim of this study was to investigate the effect of the intrinsic foot muscle-strengthening exercises on knee kinematic parameters in pronated foot subjects during forward jump landing. This interventional study was performed on students aged 20-30-years old with foot pronation in the School of Rehabilitation. In this study, the kinematic changes of the knee in the frontal, sagittal and transverse plane before and after 6 weeks of strengthening exercises of the intrinsic foot muscles during the forward jump-landing task were examined using a motion analyser. All data analysis was performed offline using a special software program in the MATLAB software environment. Knee angle variables have a normal distribution before and after exercise. The ICC coefficient of all variables was calculated as between 0.44 and 0.71; therefore, the reproducibility of the variables under study in this study was considered moderate to good. The knee angle on the frontal plate was 2.54 ± 2.4 before the exercises and 2.49 ± 2.14 after the exercises, and there was no significant difference between them (P = 0.21). Plantar intrinsic foot muscle-strengthening exercises alone have no effect on the kinematic changes of the knee in people with foot pronation, or the duration of strengthening exercises should be increased during the day to see the effect of strengthening the intrinsic muscles among pronated foot subjects.

Age-Dependent Upper Limb Myoelectric Control Capability in Typically Developing Children.

Research in EMG-based control of prostheses has mainly utilized adult subjects who have fully developed neuromuscular control. Little is known about children's ability to generate consistent EMG signals necessary to control artificial limbs with multiple degrees of freedom. As a first step to address this gap, experiments were designed to validate and benchmark two experimental protocols that quantify the ability to coordinate forearm muscle contractions in typically developing children. Non-disabled, healthy adults and children participated in our experiments that aimed to measure an individual's ability to use myoelectric control interfaces. In the first experiment, participants performed 8 repetitions of 16 different hand/wrist movements. Using offline classification analysis based on Support Vector Machine, we quantified their ability to consistently produce distinguishable muscle contraction patterns. We demonstrated that children had a smaller number of highly independent movements (can be classified with >90% accuracy) than adults did. The second experiment measured participants' ability to control the position of a cursor on a 1-DoF virtual slide using proportional EMG control with three different visuomotor gain levels. We found that children had higher failure rates and slower average target acquisitions than adults did, primarily due to longer correction times that did not improve over repetitive practice. We also found that the performance in both experiments was age-dependent in children. The results of this study provide novel insights into the technical and empirical basis to better understand neuromuscular development in children with upper-limb loss.

Data-Efficient Gaussian Process Online Learning for Adaptive Control of Multi-DoF Robotic Arms

Adaptive control depending on parametric adaptive elements has been shown to be effective in handling system uncertainty. However, it is restricted by the fixed prior knowledge on parametric models or in the face of stochastic uncertainty. Gaussian process (GP) is a typical Bayesian nonparametric model that contains fewer adjustable parameters and can describe stochastic uncertainty owing to introducing a probabilistic framework. This paper employs an online GP-based adaptive control framework for trajectory tracking of robotic arms with multiple degrees of freedom (DoFs). Besides, four GP learning schemes are compared during robot control, including a baseline scheme called full-state learning, and three data-efficient schemes: inward cascaded learning, outward cascaded learning, and the proposed coplane learning that is inspired by the robot structure. Simulations are carried out based on a 7-DoF collaborative robot called Panda. It is demonstrated that the proposed control framework performs well for the Panda robot, and the proposed coplane learning outperforms the other three learning schemes in terms of computational efficiency and modeling accuracy.