Rotational Degrees Of Freedom Research Articles

Experimental Study of the Mechanical Properties of a Spherical Parallel Link Mechanism With Arc Prismatic Pairs

A two-degrees-of-freedom spherical parallel link mechanism (2-DOF SPM) was designed to ensure that it only has rotational degrees of freedom in two directions around a fixed center. In general, 2-DOF SPM includes passive rotating pairs, and at least two actuators are needed to change the end-effector posture. The arrangement of the links and pairs determines the characteristics and performance of SPM, so 2-DOF SPMs were designed considering various requirements, such as output torque, accuracy, and space constraints for applications. To satisfy these requirements, arc prismatic pairs can be used in SPMs. In order to use in SPMs, as for arc prismatic pairs, the concrete configuration and design methods for arc prismatic pairs have been studied. Furthermore, in order to compensate for the influence of friction on the positioning error, the control model considering the friction has been proposed by constructing a feedback loop containing experimentally found parameters. However, the conventional model is not a mechanical model of friction. Therefore, it is not suitable for calculating the friction force and understanding how the limit of the workspace changes due to the influence of friction. In this study, we construct a mechanical friction model considering the intersection angle change between the input and the rail slide direction. In addition, using the friction model, we clarify the influences of friction on the workspace and driving the SPM to realize high-performance 2-DOF SPM. First, we theoretically clarified the influence of friction on the workspace by considering the case of a slider-type differential-drive 2-DOF SPM. Second, the driving torque was experimentally measured, and the influence of friction on driving was examined.

Unsupervised learning of ferroic variants from atomically resolved STEM images

An approach for the analysis of atomically resolved scanning transmission electron microscopy data with multiple ferroic variants in the presence of imaging non-idealities and chemical variabilities based on a rotationally invariant variational autoencoder (rVAE) is presented. We show that an optimal local descriptor for the analysis is a sub-image centered at specific atomic units, since materials and microscope distortions preclude the use of an ideal lattice as a reference point. The applicability of unsupervised clustering and dimensionality reduction methods is explored and is shown to produce clusters dominated by chemical and microscope effects, with a large number of classes required to establish the presence of rotational variants. Comparatively, the rVAE allows extraction of the angle corresponding to the orientation of ferroic variants explicitly, enabling straightforward identification of the ferroic variants as regions with constant or smoothly changing latent variables and sharp orientational changes. This approach allows further exploration of the chemical variability by separating the rotational degrees of freedom via rVAE and searching for remaining variability in the system. The code used in this article is available at https://github.com/saimani5/ferroelectric_domains_rVAE.

Quantized Constrained Molecular Chains: Vibrations, Internal Rotations and Polymerization

The present work has a twofold purpose. a) It proposes a quantum-mechanical approach to constrained molecular chains and their small vibrations and rotations, by employing in a compact way vector variables and operators associated to the constituent units of the chain. The methods here differ from standard approaches based upon cartesian coordinates and normal modes and generalize previous quantum Hamiltonians describing only rotational degrees of freedom. Several models in D = 2, 3 spatial dimensions, with new Hermitean Hamiltonians, are formulated and analyzed. The chains studied successively display an increasing number of constraints: freely-jointed, freely-rotating and with constrained torsions. Conservation of total orbital angular momentum is analyzed. As a partial test, by using the present approach, the vibrational frequencies of certain triatomic molecules (water vapour, hydrogen sulfide, heavy water and sulfur dioxide) are computed and shown to be consistent with experimental data. b) A new (quantum-mechanical) analysis of polymerization, namely, the growth of a freely-jointed molecular chain (of the kind considered above) by binding an additional unit 1 to the chain, is presented. They move in a very dilute solution in a fluid at rest in thermal equilibrium about room temperature. The analysis is based upon a mixed (quantum-classical) distribution function in phase-space: a quantum Wigner-like one for unit 1 and a classical Liouville one for the chain. That leads to an approximate Schmolukowski equation for unit 1 alone and, through it, to compute the mean first passage time (MFPT) for unit 1 to become bound by the chain. The resulting MFPT displays a temperature dependence consistent with the Arrhenius formula for rate constants in chemical reactions.

Hysteretic behavior of high damping rubber bearings under multiaxial excitation

The high damping rubber bearing (HDRB) is an advanced seismic isolation component currently used in building structures with excellent energy dissipation capacity. To explore a deeper understanding of the HDRBs’ performance and effectiveness, a series of six-degree-of-freedom (6DOF) quasi-static tests were designed and conducted on three HDRB specimens with different dimensions. The main purposes of the tests are to reveal the hysteresis characteristics of the bearings in the rotational degrees of freedom, and to assess the influence of axial pressure and multiaxial coupling effect on the horizontal performance of the HDRBs. During the tests, the rotational, unidirectional, and bidirectional horizontal (coupled and uncoupled) hysteretic responses were obtained. Additionally, several important mechanical parameters are recommended and calculated to evaluate the coupling effect of axial load and rotation on HDRB performance. The results indicate that the axial pressure has a significant impact on the horizontal performance, while the effect of coupling the rotational degrees of freedom is not obvious. In addition, the tests also observed a significant level of stiffness degradation in the horizontal directions after multiple loading cycles.

Multicritical point with infinite fractal symmetries

Recently, ``Pascal's triangle model'' constructed with $\mathrm{U}(1)$ rotor degrees of freedom was introduced and it was shown that ($\mathit{i}$) this model possesses an infinite series of fractal symmetries and ($\mathit{ii}$) it is the parent model of a series of ${Z}_{p}$ fractal models each with its own distinct fractal symmetry. In this work we discuss a multicritical point of Pascal's triangle model that is analogous to the Rokhsar-Kivelson point of the better known quantum dimer model. We demonstrate that the expectation value of the characteristic operator of each fractal symmetry at this multicritical point decays as a power law of space and this multicritical point is shared by the family of descendent ${Z}_{p}$ fractal models. Afterwards, we generalize our discussion to a $(3+1)d$ model termed ``Pascal's tetrahedron model'' that has both planar and fractal subsystem symmetries. We also establish a connection between Pascal's tetrahedron model and the $\mathrm{U}(1)$ Haah's code.

Development of a cross-sectional finite element for the analysis of thin-walled composite beams like wind turbine blades

A method for structural analysis of thin-walled composite beams like wind turbine blades is presented. This method is based on the Nonhomogeneous Anisotropic Beam Section Analysis (NABSA) which consists in discretizing the beam cross section using finite elements. The proposed implementation uses 3-node line cross-sectional finite elements with nodes having rotational degrees of freedom to describe the cross-sectional warping displacements. Solutions obtained using this approach were verified against the corresponding analytical or numerical solutions. Agreement was very good to excellent for the computation of cross-sectional properties and distribution of stresses, strains and warping displacements for a broad range of possible composite beam behaviors including geometric and material couplings, open sections, multicell sections, and arbitrary laminates. For thin-walled layered structures, the proposed method provides models with fewer degrees of freedom than equivalent models based on a two-dimensional discretization of cross sections using triangular or quadrilateral elements such as conventional NABSA or VABS which suggests that computation time could be reduced.

Characterization of milling robot mode shape and analysis of the weak parts causing end vibration

The existing studies on milling robot dynamic characteristics pay little attention to robot structures, while structure mode shape analysis is significant to accurate vibration control. This paper applies the 3D scanning laser Doppler vibrometer to the milling robot, and proposes the R2-based compliance identification criterion to identify the robot deformation parts as the joints, greatly reducing the number of degrees-of-freedom (DOF) required for the mode shape characterization. Then, the multi-joint and full-DOF mode shape (MFMS) is proposed to succinctly characterize the robot mode shape by mapping the vibrations of numerous measurement points to the joints. MFMS shows that, different from the conventional studies, it is necessary to consider the robot joint compliance in multiple DOFs. For example, in this paper, all the 6 joints are deformed in the first two mode shapes, while the last 3 joints are deformed in the rotational DOFs in the 3 ∼ 6 mode shapes. Based on MFMS, the weak excitation direction at tool center point (TCP) is analyzed and the TCP amplitude is successfully predicted to be almost halved after changing the milling force direction. The weak joint-DOF dominating TCP vibration is analyzed, and it is found that there are only a few weak joint-DOFs in each mode and they vary with the mode, which is instructive for accurate vibration suppression and joint enhancement.

Limit-protection Method for Workspace of a Parallel Power Head

The position and pose of the end of 1T2R mechanism with one translational motion and two rotational degrees of freedom in the operation space is the nonlinear mapping of the servo motor action in the joint space, and the postures and states of the end of the mechanism can only be obtained through complex modeling calculation. Because of this, the key problem to be solved urgently is to realize the real-time and accurate limit protection function of this kind of structure machine tool, and to reduce the process and calculation amount of the position and pose judgment of the end of the mechanism. In this paper, a simplified algorithm for position and attitude judgment is proposed by analyzing the workspace of 1T2R mechanism. The position and attitude judgment of the terminal moving platform of the mechanism under any configuration can be realized only by summing up the length of three branch chains of the mechanism and calculating the difference. Further, the limit protection method of parallel power head based on this algorithm can be implemented based on the software and hardware conditions of the existing control system. It is easy to implement and has a small amount of calculation, which can further improve the safety of the operation of such structure machine tools.

Kinematic Analysis and Dimension Optimization of a New Reconfigurable Parallel Mechanism With 1R2T and 2R1T Operation Modes

Abstract This paper introduces a novel reconfigurable parallel mechanism (RPM) consisting of two PRU limbs (P denotes a prismatic joint, R denotes a revolute joint, U denotes a universal joint) and one PUU limb. The proposed RPM can evolve into two distinct configurations from the switch configuration, in which one configuration has one rotational degree-of-freedom (DOF) and two translational DOFs, and the other configuration has two rotational DOFs and one translational DOF. First, the DOFs of the RPM in each configuration are analyzed using screw theory. Then, position modeling for the RPM is carried out. Inverse position solutions and forward position solutions are derived. Further, performance evaluation and optimization are conducted using the motion/force transmission method. Finally, a prototype is developed, and preliminary experiments are carried out. The proposed RPM has the potential to be used in applications with multi-task requirements.

Topological state transfer in Kresling origami

Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underlying bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach to energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices.

Algebraic cluster model calculations for vibrational to gamma-unstable shape phase transition in odd-A nuclei

The Algebraic Cluster Model(ACM) is an interacting boson model that gives the relative motion of the cluster configurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable extended transitional Hamiltonian based on the SU(1;1) Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions O(4) U(3), O(7) U(6) and O(10)-U(9), respectively. We suggest that this method can be used to study of k + x nucleon structures with k = 2, 3, 4 and x = 1, 2 and so on. The obtained results in this study confirm that this ACM technique is worth extending for investigating odd-A and odd-odd nuclei. So, the clustering survives the addition of one and two particles. Our studies confirm the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and to determine the precise position of the critical point.

Marker-Based Method for Analyzing the Three-Dimensional Upper Body Kinematics of Violinists: Reproducibility.

Recently, Wolf et al. proposed a novel, marker-based method to analyze the three-dimensional upper-body kinematics of high string players for clinical application. The method provides an objective evaluation of high string players' motor strategies, especially in the shoulder complex, by distinguishing between the scapulothoracic (ST) and glenohumeral (GH) joints, while minimizing skin movement artifacts, marker occlusions, and limitations due to instrument placement. Nevertheless, reproducibility of kinematic measurements is crucial for clinical applications. The aim of this study was to assess the method's reproducibility in terms of reliability and repeatability. One healthy professional violinist underwent a total of nine bowing trials in three different laboratory sessions. Each trial was conducted by one of two different examiners. A biomechanical model was applied to motion capture data of the pelvis, thorax, spine, and head, as well as both upper limbs (consisting of the scapula, upper arm, forearm and hand). Reproducibility was assessed by calculating inter- and intra-tester, inter-session, and intra-subject measurement errors for each rotational degree of freedom in the upper-body segments and joints. Small measurement errors were accepted to be good indicators for reproducibility. Intra- and inter-tester errors were found to be small (< 3° for the most part). Both inter-session and intra-subject repeatability were found to be larger (< 5° for the most part). This study generally showed the novel, marker-based method to have good reproducibility for a healthy violinist. This indicates that the proposed method is a reliable tool for quantifying upper-body movements during violin playing across subjects, examiners, laboratories, and motion capture systems.

Learning torsional eye movements through active efficient coding

The human eye has three rotational degrees of freedom: azimuthal, elevational, and torsional. Although torsional eye movements have the most limited excursion, Hering and Helmholtz have argued that they play an important role in optimizing visual information processing. In humans, the relationship between gaze direction and torsional eye angle is described by Listing’s law. However, it is still not clear how this behavior initially develops and remains calibrated during growth. Here we present the first computational model that enables an autonomous agent to learn and maintain binocular torsional eye movement control. In our model, two neural networks connected in series: one for sensory encoding followed by one for torsion control, are learned simultaneously as the agent behaves in the environment. Learning is based on the active efficient coding (AEC) framework, a generalization of Barlow’s efficient coding hypothesis to include action. Both networks adapt by minimizing the prediction error of the sensory representation, subject to a sparsity constraint on neural activity. The policies that emerge follow the predictions of Listing’s law. Because learning is driven by the sensorimotor contingencies experienced by the agent as it interacts with the environment, our system can adapt to the physical configuration of the agent as it changes. We propose that AEC provides the most parsimonious expression to date of Hering’s and Helmholtz’s hypotheses. We also demonstrate that it has practical implications in autonomous artificial vision systems, by providing an automatic and adaptive mechanism to correct orientation misalignments between cameras in a robotic active binocular vision head. Our system’s use of fairly low resolution (100 × 100 pixel) image windows and perceptual representations amenable to event-based input paves a pathway towards the implementation of adaptive self-calibrating robot control on neuromorphic hardware.

Effect of twin grain boundary on material thermal expansion

Based on first-principles phonon calculations within the framework of quasiharmonic approximation, we study the effect of twin grain boundary (TGB) on the thermal expansion of insulating materials. We select diamond-structure solids (C, Si, and Ge) and rutile $({\mathrm{SnO}}_{2})$ as representatives of the covalent and ionic bonding materials that are important systems commonly accompanied with TGB. We found distinct effects of TGB on thermal expansion in two types of materials. For diamond-structure solids, the thermal expansion of (111)-oriented twinning structure varies subtly from that of pristine material within the temperature range studied, which is primarily induced by the modification of vibrational phonon mode by the TGB effect. Distinctly, the thermal expansion of $\mathrm{SnO}_{2}$ twinnings increase substantially by comparison with the pristine case and depend strongly on the twin orientation. The (101) twinning shows much larger thermal expansion than the (301) twinning. Further analysis indicates the physical mechanism can be mainly attributed to the effect of rotational degree of freedom of the $\mathrm{SnO}_{6}$ octahedron motif and the stress induced by TGB. Our work reveals the physical mechanism underlying the distinct effect of TGB on thermal expansion caused by different chemical bonding, and meanwhile provides an insightful understanding of the relationship between specific structural features and thermal expansion in solid-phase materials.

A cell-based smoothed radial point interpolation method applied to kinematic limit analysis of thin plates

The cell-based smoothed radial point interpolation method in conjunction with a second order cone programming is proposed for kinematic limit analysis of rigid-perfectly plastic thin plates in this paper. The transverse displacement field is interpolated by the radial point interpolation method (RPIM) and no rotational degrees of freedom are involved. The gradient smoothing technique is utilized to construct smoothed curvature field in every smoothing domain and there is no need to compute the second derivatives of shape functions. The rotational boundary conditions are satisfied in the process of curvature smoothing and the translational boundary conditions can be directly enforced without any special treatment. The limit analysis problem of thin plates is formulated by minimizing the dissipation power subject to a set of equality constraints and this minimization problem can be expressed easily as a standard second order cone programming. It is testified from the computational results that the proposed procedure can provide reasonable and satisfactory upper bound limit load multipliers for thin plates.

Synthesis of Novel Ruthenium‐Polymetallaynes and Their Application in Multistate Electrochromic Memory

AbstractMultilevel (or multistate) electrochromic devices have the potential to achieve highly compact memory capacity while instantaneously transferring data between memory and processing units. In this article, three novel solution‐processable ruthenium‐polymetallaynes (i.e., P1, P2, and P3), in which the redox‐addressable Ru center is covalently embedded into a conjugated organic polymer, are discussed. In pursuit of higher functionality (e.g., stable multistate behavior, low operating voltage), the organic ligand bridging the metal centers is systematically varied. The previously reported P1 has a bithiophene (BT) bridging ligand with a high degree of rotational freedom. By replacing BT with cyclopenta‐dithiophene in P2 and dithieno‐pyrrole (DTP) in P3, both of which are more planar than BT, the degree of freedom is decreased. By using DTP, redox‐matching is achieved between the metal center and organic ligand, leading to extra stability of the mixed‐valence (MV) state in P3. In‐depth experimental (i.e., in situ electron paramagnetic resonance and UV–vis–NIR spectroelectrochemistry) and theoretical studies (i.e., DFT calculations) are carried out on the polymer thin‐films, showing enhanced metal–metal (M–M) interaction in P2 and P3 and stable Robin–Day class III MV compound in P3. These polymers are also first time fabricated into solid‐state electrochromic devices and the stability of each oxidation state is characterized by tracing the change of transmittance over time, showing satisfactory cyclic stability and retention behavior (≈90% retention after 30 min).

Reconstructing Articular Cartilage in the Australopithecus afarensis Hip Joint and the Need for Modeling Six Degrees of Freedom.

SynopsisThe postcranial skeleton of Australopithecus afarensis (AL 288–1) exhibits clear adaptations for bipedality, although there is some debate as to the efficiency and frequency of such upright movement. Some researchers argue that AL 288–1 walked with an erect limb like modern humans do, whilst others advocate for a “bent-hip bent-knee” (BHBK) gait, although in recent years the general consensus favors erect bipedalism. To date, no quantitative method has addressed the articulation of the AL 288–1 hip joint, nor its range of motion (ROM) with consideration for joint spacing, used as a proxy for the thickness of the articular cartilage present within the joint spacing which can affect how a joint moves. Here, we employed ROM mapping methods to estimate the joint spacing of AL 288–1’s hip joint in comparison to a modern human and chimpanzee. Nine simulations assessed different joint spacing and tested the range of joint congruency (i.e., ranging from a closely packed socket to loosely packed). We further evaluated the sphericity of the femoral head and whether three rotational degrees of freedom (DOFs) sufficiently captures the full ROM or if translational DOFs must be included. With both setups, we found that the AL 288–1 hip was unlikely to be highly congruent (as it is in modern humans) because this would severely restrict hip rotational movement and would severely limit the capability for both bipedality and even arboreal locomotion. Rather, the hip was more cartilaginous than it is in the modern humans, permitting the hip to rotate into positions necessitated by both terrestrial and arboreal movements. Rotational-only simulations found that AL 288–1 was unable to extend the hip like modern humans, forcing the specimen to employ a BHBK style of walking, thus contradicting 40+ years of previous research into the locomotory capabilities of AL 288–1. Therefore, we advocate that differences in the sphericity of the AL 288–1 femoral head with that of a modern human necessitates all six DOFs to be included in which AL 288–1 could osteologically extend the hip to facilitate a human-like gait.

Generation of partial roll rotation in a hexagonal NaYF4 particle by switching between different optical trapping configurations.

Typically a rigid body can have three degrees of rotational freedom. Among these, there can be two types of out-of-plane rotational modes, called the pitch and the roll. The pitch motion is typically to turn the particle along an axis orthogonal to the axis of symmetry. However, rotation about the axis of symmetry (called the roll motion) has so far not been shown in optical tweezers. It is here that we use a hexagonal shaped particle (NaYF4) which prefers to align side on with the optical tweezers [Rodriguez-Sevilla et al., Nano Letters 16, 8005 (2016)]. In this work, we find that the stable configuration of the hexagonal particle changes while using one beam and two beams, so that when one of the tweezers beams is switched on and off, the particle tends to switch between the different configurations. Thus we get a controlled roll motion. This is the first time that controlled partial roll motions have been generated in optical tweezers.

Angular trapping of a linear-cavity mirror with an optical torsional spring

Optomechanical systems have attracted intensive attention in various physical experiments. With an optomechanical system, the displacement of or the force acting on a mechanical oscillator can be precisely measured by utilizing optical interferometry. As a mechanical oscillator, a suspended mirror is often used in over a milligram scale optomechanical systems. However, the tiny suspended mirror in a linear cavity can be unstable in its yaw rotational degree of freedom due to optical radiation pressure. This instability curbs the optical power that the cavity can accumulate in it and imposes a limitation on the sensitivity. Here, we show that the optical radiation pressure can be used to trap the rotational motion of the suspended mirror without additional active feedback control when the $g$ factors of the cavity are negative and one mirror is much heavier than the other one. Furthermore, we demonstrate experimentally the validity of the trapping. We measured the rotational stiffness of a suspended tiny mirror with various intracavity power. The result indicates that the radiation pressure of the laser beam inside the cavity actually works as a positive restoring torque. Moreover, we discuss the feasibility of observing quantum radiation pressure fluctuation with our experimental setup as an application of our trapping configuration.

Non-associated Cosserat plasticity

Frictional plasticity models with a non-associated flow rule, ubiquitous for describing failure in geomaterials, can lead to a local loss of ellipticity for low hardening rates, i.e. before entering a strain-softening regime. This leads to an excessive dependence on the spatial discretisation and to an inability of Newton–Raphson methods to converge. Higher-order continuum models can remedy this. The Cosserat continuum is particularly suitable for granular media because the rotational degrees of freedom of this model can represent the rotation of (assemblies of) grains or blocks which form the microstructure of such materials. We illustrate this analytically by the example of an infinitely long shear layer and through a three-dimensional bifurcation analysis. Numerical simulations show the consequences, i.e. the anomalies of standard continuum models and the correct behaviour of non-associated plasticity models embedded in a Cosserat continuum. The motivation for using a Cosserat continuum for granular and blocky materials is further strengthened through shear band simulations of biaxial tests, where the inclination angle shows the same dependence on the internal length scale as that on the grain size in tests. This result is the first proper explanation for this dependence.