Orthogonal Degrees Of Freedom Research Articles

Scanning the vertical and radial frequencies of curved bridges by a single-axle vehicle with two orthogonal degrees of freedom

This paper scans for the first time the vertical and radial (lateral) frequencies of a horizontal curved beam from the respective motions of a single-axle test vehicle by a theoretical approach. The vehicle is innovatively treated as a system with two orthogonal degrees of freedom (DOFs), each of a spring-dashpot unit, to capture both the vertical and lateral motions. To start, closed-form solutions are derived for the out-of-plane vibration (under the vertical and torsional contact forces) and in-plane vibration (under the centrifugal force) of the curved beam. Then the vertical and lateral motions of the vehicle are derived. Based on this, a generalized formula is derived for the corresponding contact responses. From the analyses using the generalized contact formula, it was demonstrated that: (1) the contact responses outperform the vehicle responses in that more higher bridge frequencies (out-of-plane and in-plane) can be identified; (2) the radius of curvature affects significantly the radial frequencies of the curved beam; (3) the eccentricity of the scanning vehicle has little effect on frequency identification; and (4) pavement roughness’ effect can be remedied by random traffic, and it does not appear in the radial contact response.

Improved Sampling and Free Energy Estimates for Antibiotic Permeation through Bacterial Porins.

Antibiotics enter into bacterial cells via protein channels that serve as low-energy pathways through the outer membrane, which is otherwise impenetrable. Insights into the molecular mechanisms underlying the transport processes are vital for the development of effective antibacterials. A much-desired prerequisite is an accurate and reproducible determination of free energy surfaces for antibiotic translocation, enabling quantitative and meaningful comparisons of permeation mechanisms for different classes of antibiotics. Inefficient sampling along the orthogonal degrees of freedom, for example, in umbrella sampling and metadynamics approaches, is however a key limitation affecting the accuracy and the convergence of free energy estimates. To overcome this limitation, two sampling methods have been employed in the present study that, respectively, combine umbrella sampling and metadynamics-style biasing schemes with temperature acceleration for improved sampling along orthogonal degrees of freedom. As a model for the transport of bulky solutes, the ciprofloxacin-OmpF system has been selected. The well-tempered metadynamics approach with multiple walkers is compared with its "temperature-accelerated" variant in terms of improvements in sampling and convergence of free energy estimates. We find that the inclusion of collective variables governing solute degrees of freedom and solute-water interactions within the sampling scheme largely alleviates sampling issues. Concerning improved sampling and convergence of free energy estimates from independent simulations, the temperature-accelerated sliced sampling approach that combines umbrella sampling with temperature-accelerated molecular dynamics performs even better as shown for the ciprofloxacin-OmpF system.

An efficient approach for inverse kinematics and redundancy resolution of spatial redundant robots for cluttered environment

This paper presents an optimization-based approach for solving the inverse kinematics problem of spatial redundant manipulators in cluttered workspaces. To provide better flexibility and manipulability in the narrow regions, the joints were modeled with multiple degrees of freedom (DOF) and are considered as universal joints. Each universal joint has two orthogonal DOF, which are made by pitch axis and yaw axis. The inverse kinematic (IK) problem is multimodal by nature, and it has multiple solutions. A global search and multi-start framework have been implemented to determine the multiple kinematic configurations for a given task location. The characteristic feature of the IK problem has multiple configurations for a given task space location. The process of determining the best from multiple solutions is called redundancy resolution. Secondary criteria such as joint distance minimization and collision avoidance have been chosen to perform the task of redundancy resolution. A classical constrained optimization technique has been implemented to perform the tasks of inverse kinematics and redundancy resolution. The collision avoidance scheme was implemented with a collision detection algorithm by using a bounding box approach. Simulations were performed for 9-DOF spatial manipulators with 3D obstacles in the workspace. Results are reported on IK, multiple IK solutions, and redundancy resolution of the robot in an unconstrained and cluttered environment. Results show that the proposed method is accurate and computationally efficient in determining the IK solution of spatial redundant manipulators in a multi-obstacle and restricted environment.

Hierarchical Markov State Model Building to Describe Molecular Processes.

Markov state models can describe ensembles of pathways via kinetic networks but are difficult to create when large free-energy barriers limit unbiased sampling. Chain-of-states simulations allow sampling over large free-energy barriers but are often constructed using a single pathway that is unlikely to thermodynamically average over orthogonal degrees of freedom in complex systems. Here, we combine the advantages of these two approaches in the form of a Markov state model of Markov state models, which we call a Hierarchical Markov state model. In this approach, independent Markov models are constructed in regions of configuration space that are locally well sampled but are separated by large free-energy barriers from other regions. A string method is used to construct an ensemble of pathways connecting the states of these different local Markov models, and the rate through each pathway is then estimated. These rates are then combined with the rate information from the local Markov models in a master equation to predict global rates, fluxes, and populations. By applying this hierarchical approach to tractable systems, a toy potential and dipeptides, we demonstrate that it is more accurate than the conventional single-pathway description. The advantages of this approach are that it (i) is more realistic than the conventional chain-of-states approach, as an ensemble of pathways rather than a single pathway is used to describe processes in high-dimensional systems, and (ii) it resolves the issue of poor sampling in Markov State model building when large free-energy barriers are present. The divide-and-conquer strategy inherent to this approach should make this procedure straightforward to apply to more complex systems.

High resource of azimuthal entanglement in terms of Cartesian variables of noncollinear biphotons

Single-particle and coincidence distributions of photons are analyzed for the noncollinear frequency-degenerate type-I regime of Spontaneous Parametric Down-Conversion. Noncollinearity itself is shown to provide a new mechanism of strong broadening of the single-particle distributions in Cartesian components of the photon's transverse wave vectors. Related to this, the degree of entanglement appears to be very high and, in fact, this is the same enormous resource of azimuthal entanglement which was found to occur in the formalism of spherical angles used for characterization of photon wave vectors (Phys. Rev. A, {\bf 93}, 033830, 2016). In Cartesian variables this phenomenon manifests itself as a strong broadening and a very unusual and peculiar shape of the arising single-particle distribution curves. In theory, the key reason for these effects is the reduction of the total wave function of two photons over one of two orthogonal degrees of freedom. In the suggested and discussed experimental scheme this means that all photons of the emission cone have to be taken into account rather than only photons propagating in one given plane which is a common practice in many experiments.

Quantifying Pelvic Motion During Total Hip Arthroplasty Using a New Surgical Navigation Device

BackgroundAccurate cup positioning is one of the most challenging aspects of total hip arthroplasty (THA). Undetected movement of the patient during THA surgery can lead to inaccuracies in cup anteversion and inclination, increasing the potential for dislocation and revision surgery. Investigations into the magnitude of patient motion during THA are not well represented in the literature. MethodsWe analyzed intraoperative pelvic motion using a novel navigation device used to assist surgeons with cup position, leg length, and offset during THA. This device uses an integrated accelerometer to measure motion in 2 orthogonal degrees of freedom. We reviewed the data from 99 cases completed between February and September 2016. ResultsThe mean amount of pitch recorded per patient was 2.7° (standard deviation, 2.2; range, 0.1°-9.9°), whereas mean roll per patient was 7.3° (standard deviation, 5.5; range, 0.3°-31.3°). Twenty-one percent (21 of 99) of patients demonstrated pitch of >4°. Sixty-nine percent (68 of 99) of patients demonstrated >4° of roll, and 25% (25 of 99) of patients demonstrated roll of ≥10°. ConclusionOur findings indicate that while the majority of intraoperative motion is <4°, many patients experience significant roll, with a large proportion rolling >10°. This degree of movement has implications for acetabular cup position, as failure to compensate for this motion can result in placement of the cup outside the planned safe zone, thus, increasing the potential for dislocation. Further study is warranted to determine the effect of this motion on cup position, leg length, and offset.

Visualizing Electrical Potential Distribution Using a Point-by-Point Scanning Method: Preliminary Investigation on the Bioactive Points over the Skins of Rodents

Objectives: Acupuncture points as bioactive points on human skin have special electrical properties, compared to points in surrounding areas. This article focuses on measuring skin electrical potentials in a rat model using a point-by-point scanning method. Materials and Methods: Animals were placed on a motorized stage with two orthogonal degrees of freedom. X- and Y-coordinates were set by stepper motors and determined the position of each measurement. A third orthogonal axis, the Z-axis, was under separate stepper control and was used to raise and lower the electrode, thus determining contact pressure between the electrode and the skin. The abdominal region, centered around the umbilicus, was chosen for the study. Data were processed to produce visual images. Results: Distribution mapping demonstrated the existence of high potential points that were distinct from surrounding regions. Positions and intensity of these high potential points were variable. Conclusions: High electrical potential points may have applicability in future acupuncture research.

Chatter prediction for milling of flexible pocket-structure

Flexible pocket-structures are widely used in engineering practice, especially in the aerospace industry. This paper presents a dynamic model which is suitable for predicting the chatter vibration during machining the thin bottom of flexible pocket-structures. The model is simplified as a three-degree-of-freedom (DOF) system, in which the cutter is considered to have two orthogonal degrees of freedom in its radial direction while the flexible component is considered to have one degree of freedom in the axial direction of the cutter. Modal analysis is implemented to obtain the system parameters. Thereafter, a semi-discretization method is used to plot the stability lobes. From the stability lobe, it is very easy to predict the appearance of the chatter vibration and thus decide the proper cutting conditions during milling the thin bottom of flexible pocket-structures. At the end of the paper, the developed model is demonstrated by a number of cutting experiments.

Countermeasure against chatter in end milling operations using multiple dynamic absorbers

The present study investigates the effect of multiple dynamic absorbers on chatter generated in the end milling operations by performing stability analysis and a cutting test. The dynamic absorbers proposed in the present paper are attached to a collet chuck in order to suppress tool chatter caused by the bending vibration of the tool and spindle system. The dynamic milling model is considered to have two orthogonal degrees of freedom. The dynamic absorbers, which have identical mass, damping ratio, and natural frequency, are assumed to have a single degree of freedom that rotates with a tool and spindle system. In the present paper, stability analyses are performed by means of complex eigenvalue analysis for each angular immersion of the cutting edge in order to investigate the effect of the dynamic absorbers on the stability of the dynamic milling model. The optimal natural frequency and damping ratio of the dynamic absorbers to maximize the chatter-free axial depth of cut are shown to vary with spindle speed. Furthermore, the effect of the dynamic absorbers on chatter is validated by a cutting test, and the experimental results are confirmed to agree qualitatively with the analytical results.

441 エンドミル加工中に発生するびびり振動の動的安定性解析

This work deals analytically and experimentally with the stability chart of the regenerative chatter vibration in end milling process. Dynamic milling model was considered to have two orthogonal degrees of freedom. By solving the eigenvalue problem of this model, we investigate stability of this dynamic milling system. As a result the agreement between the analytical and experimental results on the stability chart in up cut milling and down cut milling was confirmed. Furthermore, we investigate the effect of the vibration characteristics of tool and the instantaneous angular immersion of tool on stability chart.

Direct determination of reaction paths and stationary points on potential of mean force surfaces

A simulation approach is introduced for directly determining reaction paths and stationary points on potential of mean force (PMF) surfaces associated with molecular events that occur in complex environments. The nudged elastic band approach was employed to search for steepest descent paths on the PMF surface using the relevant PMF derivatives from a series of local simulations. The steepest descent path on the PMF surface corresponds to the minimum PMF path (i.e. the path with the lowest local PMF barrier), which contains important information about stationary points (e.g. saddle points) on the PMF surface, which in turn can provide useful insights into the thermodynamics and kinetics for the process of interest. By working with the PMF defined in a low-dimensional subspace rather than a potential energy function of full molecular dimensionality, the main features of the process under study are concisely represented and the orthogonal degrees of freedom are adequately sampled with the appropriate canonical distribution at the desired temperature (e.g. 300 K). Therefore, minimum PMF paths carry statistically meaningful mechanistic information and are complementary to reaction paths of full molecular dimensionality proposed in previous studies. The NEB based path optimization method is direct in the sense that no information regarding the global PMF surface is necessary for the determination of the local reaction path and stationary points along this path. Since only low-dimensional quantities (paths) are searched for, the PMF-path method is expected to scale better in terms of dimension of the PMF subspace than those aims to fully explore multi-dimensional PMF surfaces. Test applications on simple molecular systems, the alanine di-peptide in vacuum and in solution and a microsolvated proton-wire, indicate that reliable PMF paths can be determined for both conformational isomerization and chemical reaction processes. However, highly accurate PMF derivatives are required for determining more quantitative observables, such as the free energy profile along the minimum PMF path. Therefore, effective numerical algorithms for calculating local PMF derivatives and systematic protocols for defining the relevant subspace are the main focus in the near future. Finally, we emphasize that the minimum PMF path defined here includes thermal (e.g. entropic) effects associated with the orthogonal degrees of freedom, but finite kinetic energies associated with the PMF degrees of freedom are not included; this can be improved by adopting a different definition of the reaction path, such as the maximum flux path, on the PMF surface, or thermally sampling all degrees of freedom orthogonal to the one-dimensional path.

Resistive field bond graph models for hydrodynamically lubricated bearings

A lumped parameter model was developed for hydrodynamically lubricated bearings: elements that feature fully lubricated contact between surfaces in relative motion. The bearing models were represented as bond graphs. Currently, bond graphers view bearings as single-port resistance elements, which only account for losses associated with relative tangential motions between surfaces. Machine designers view bearings as devices that generate forces normal to surfaces in relative motion, to maintain position and alignment of shafts or surfaces. Both effects occur in real bearings, coupled together via physics. A lumped parameter model for hydrodynamically lubricated bearings is developed in this paper. The model includes the physical coupling between rotational degrees of freedom and orthogonal degrees of freedom associated with maintaining alignments. These lumped parameter models were synthesized from solutions of the Reynolds equation for various bearing geometries, and include normal motion and squeeze film effects. Since the forces, velocities and displacements pertaining to these orthogonal motions are physically coupled via viscous and constriction effects in the bearing's lubricant flow, the bond graph models involve resistive fields. Examples apply these concepts to thrust and journal bearings.

Resistive field bond graph models for hydrodynamically lubricated bearings

AbstractA lumped parameter model was developed for hydrodynamically lubricated bearings: elements that feature fully lubricated contact between surfaces in relative motion. The bearing models were represented as bond graphs. Currently, bond graphers view bearings as single-port resistance elements, which only account for losses associated with relative tangential motions between surfaces. Machine designers view bearings as devices that generate forces normal to surfaces in relative motion, to maintain position and alignment of shafts or surfaces. Both effects occur in real bearings, coupled together via physics. A lumped parameter model for hydrodynamically lubricated bearings is developed in this paper. The model includes the physical coupling between rotational degrees of freedom and orthogonal degrees of freedom associated with maintaining alignments. These lumped parameter models were synthesized from solutions of the Reynolds equation for various bearing geometries, and include normal motion and sque...

Unimolecular decay paths of electronically excited species. V. The à 2B1 state of H2CO+

The formaldehyde ion in its first excited state (à 2B1) dissociates to CO++H2 by an electronically adiabatic mechanism. Ab initio calculations reveal, however, that the reaction path corresponds to a low energy trough around a conical intersection between the à 2B1/2A′ and a 2A1/2A′ states. This path is characterized by an energy barrier of 0.8 eV. The reaction mechanism is intrinsically multidimensional. Curvature of the reaction path brings about a strong coupling between the coordinate and the orthogonal degrees of freedom. For this reason, the final energy partitioning does not reflect the internal energy distribution at the top of the potential barrier. Energy is presumably released preferentially as translation and rotation. The criterion for reactivity is not purely energetic: the genuine bottleneck is not located at the top of the energy barrier but rather in the region where curvature of the reaction path is largest. The à 2B1 state also dissociates to HCO+ +H fragments. A low-lying quartet state (ã 4B2) was studied but was found to play no role in the reaction. Direct coupling between state à and the dissociation continuum of the ground state X̃ is suggested.