Coupling characteristics of nonparallel dielectric waveguides

We consider a distributed system consisting of autonomous mobile computing entities called robots moving in the three-dimensional space (3D-space). The robots are anonymous, oblivious, fully-synchronous and have neither any access to the global coordinate system nor any explicit communication medium. Each robot cooperates with other robots by observing the positions of other robots in its local coordinate system. One of the most fundamental agreement problems in 3D-space is the plane formation problem that requires the robots to land on a common plane, that is not predefined. This problem is not always solvable because of the impossibility of symmetry breaking. While existing results assume that the robots agree on the handedness of their local coordinate systems, we remove the assumption and consider the robots without chirality. The robots without chirality can never break the symmetry consisting of rotation symmetry and reflection symmetry. Such symmetry in 3D-space is fully described by 17 symmetry types each of which forms a group. We extend the notion of symmetricity [Suzuki and Yamashita, SIAM J. Compt. 1999] [Yamauchi et al., PODC 2016] to cover these 17 symmetry groups. Then we give a characterization of initial configurations from which the fully-synchronous robots without chirality can form a plane in terms of symmetricity.

We consider composite materials consisting of continuous or discontinuous fibers embedded in a matrix. Such a composite is heterogeneous, and the properties vary from point to point. On a scale that is large with respect to the fiber diameter, the fiber and matrix properties may be averaged, and the material may be treated as homogeneous. This assumption, commonly employed in macromechanical analyses of composites, is adopted here. Hence, the material is considered to be quasi-homogeneous, which implies that the properties are taken to be the same at every point. These properties are not the same as the properties of either the fiber or the matrix but are a combination of the properties of the constituents. In this chapter, equations are presented for calculating the displacements, stresses, and strains when the structure undergoes only small deformations and the material behaves in a linearly elastic manner. Continuous fiber-reinforced composite materials (and structures made of such materials) often have easily identifiable preferred directions associated with fiber orientations or symmetry planes. It is therefore convenient to employ two coordinate systems: a local coordinate system aligned, at a point, either with the fibers or with axes of symmetry, and a global coordinate system attached to a fixed reference point (Fig. 2.1). In this book the local and global Cartesian coordinate systems are designated respectively by x 1 , x 2 , x 3 and the x, y, z axes.

Conservation laws of the J k-vector for microcrack damage in piezoelectric materials

Three-dimensional ankle joint moments were calculated in two separate coordinate systems, from 18 healthy men during the stance phase of walking, and were then compared. The objective was to determine the extent of differences in the calculated moments between these two commonly used systems and their impact on interpretation. Video motion data were obtained using skin surface markers, and ground reaction force data were recorded from a force platform. Moments acting on the foot were calculated about three orthogonal axes, in a global coordinate system (GCS) and also in a segmental coordinate system (SCS). No differences were found for the sagittal moments. However, compared to the SCS, the GCS significantly (p < .001) overestimated the predominant invertor moment at midstance and until after heel rise. It also significantly (p < .05) underestimated the late stance evertor moment. This frontal plane discrepancy was attributed to sensitivity of the GCS to the degree of abduction of the foot. For the transverse plane, the abductor moment peaked earlier (p < .01) and was relatively smaller (p < .01) in the GCS. Variability in the transverse plane was greater for the SCS, and attributed to its sensitivity to the degree of rearfoot inversion. We conclude that the two coordinate systems result in different calculations of nonsagittal moments at the ankle joint during walking. We propose that the body-based SCS provides a more meaningful interpretation of function than the GCS and would be the preferred method in clinical research, for example where there is marked abduction of the foot.

A novel distance estimation approach for 3D localization in wireless sensor network using multi dimensional scaling

Because of a large number of tower elements in transmission tower, and direction of cross section is complex, it is difficult to quickly set up a space model at the same direction with the actual transmission line tower structure. In this paper, using the method of vector orientation. Define tower element cross section in the local coordinate system, and by targeting vector method locating element of tower in the global coordinate system. The orientation of vector method of tower material has simple steps, easy to implement, and modelling fast. 1 Foreword Because of a large number of the tower element in the power transmission tower, section of the tower element consists of the angle steel and the steel tube etc several types, and direction of the cross section of the tower element is very complex, it is difficult to quickly set up a space model which is consistent with direction of the tower element in the actual power transmission tower structure (1) , orientation of the tower element in the power transmission tower becomes the main technical bottle neck for modelling of the spatial model of the power transmission tower. The beam unit modelling of the power transmission tower is realized if orientation of the tower element in the power transmission tower structure is solved. Finite element model of the power transmission tower generally applies the rod unit model for modelling. The rod unit model is characterized with bearing drawing and compressing and not bearing bending moment. This characteristic isn't same as the real model tower, the real model tower is also affected by the bending moment. Therefore orientation direction of the section shall be considered during modelling of the beam unit. Only when orientation of the tower element is basically consistent with actual conditions, accurate simulation effect can be obtained (2) .

An intuitive approach for the structural synthesis of serial robotic manipulator subject to specific motion constraints is presented in this paper. According to the required f-DOF αRβT motion of the end-effector, for f = 2, 3, … or 6 and α, β = 0, 1, 2 or 3, all feasible serial-type robot structures can be systematically generated via the proposed method. The approach begins at the enumeration of joint connectivity, proceeds with the assignment of joint types, and continues by the consideration of motion constraints for the robot. A couple of examples, including the synthesis of the 3-, 4- and 5-DOF serial manipulators, are furnished for illustration. It shows that this method is especially exploitable when the end-effector is required to be immovable in certain orientations or directions with respect to either local coordinate system or global coordinate system. The result is particularly beneficial for practical industrial applications.

An edge‐based smoothed finite element method using 3‐node triangular membrane elements (ES‐FEM‐T3) is proposed to analyze three‐dimensional (3D) spatial membrane structures under large deflection, rotation, and strain. In our 3D formulation, co‐rotational local coordinate systems associated with the edge‐based smoothing domains are constructed. Edge‐based gradient smoothing for the spatial membrane structure is performed in global Cartesian coordinate system and transformed into the co‐rotational local coordinate system. The smoothed strain and stress can then be properly evaluated in the co‐rotational local coordinate system after the elimination of the rigid body motions simply by coordinates transformation. Explicit time integration scheme is used to compute the transient response of the 3D spatial membrane structure to time‐domain excitations, and the dynamic relaxation method is employed to obtain steady‐state solutions. The numerical results demonstrate that the proposed method produces much better solution accuracy and computational efficiency than the standard FEM using T3 membrane element. Copyright © 2010 John Wiley & Sons, Ltd.

In the field of 3D object vision measurement, accurately determining the transformation relationship between local and global coordinate systems is crucial. However, existing methods reduce the accuracy of global unification by ignoring global errors among coordinate system transformations. This paper solved this problem by establishing a global measurement system based on optimized coded mark points. Subsequently, a global loop constraint was constructed to calculate the pose of the scanner. Finally, the 3D point cloud of the measured object was unified globally by each pose. The effectiveness of the measuring system and method was evaluated through comprehensive experimentation. The reprojection root-mean-square error(RMSE) with global unified accuracy is less than 0.1mm, and the RMSE of the measurement for standard ball diameter was 0.074mm. The experimental results demonstrate that the method exhibits robust unification capabilities in the reconstruction of 3D objects.

This paper describes accurate position control in an object coordinate system. When motion control of an industrial robot placed in a global coordinate system is taken to be in an object coordinate system, it is preferable and convenient to decide its motion by having the operator teach the robot. However, the teaching procedure requires considerable time and effort. Moreover, whenever the relative position between the robot and the object is changed, the operator needs to teach the operation again. To improve the above issue, a strategy that decides the robot motion without the teaching must be developed. This paper proposes a control strategy that does not require teaching and enables the creation of the desired motion without affecting the relative position error between the robot and the target object in object coordinate space defined by a PSD (Position Sensor Detector). In the proposed approach, the estimation algorithm of the kinetic transformation between the global and the object coordinates is introduced by using PSD output, and the error of coordinate transformation estimated by the proposed approach is compensated for in the global coordinate system. The validity of the proposed method is shown using simulations and experiments. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 155(3): 53–61, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20354

Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes

Optimal spatial orientation which minimizes bias error in model-based radiostereometric analysis for a cementless tibial baseplate is not aligned with the anatomic orientation defined by the global coordinate system.

The difficulty of singular integral occurred when we compute the electromagnetic scattering by surfaces of arbitrary shape using the model presented by Sadasiva M. Rao. To solve it, we proposed an algorithm, which is analytical and is of high precision and speed. In this algorithm, we transform the problem from the global three-dimension rectangular coordinate system to a local two-dimension polar coordinate system by shifting and rotating. After the singular point is eliminated, we can analytically work out the singular integral of original question.

Stability analysis of milling process by combining the gyroscopic effect with the symmetry and runout of the cutter

Fluid flow in a rock fracture bounded by two irregular surfaces is complex even under a laminar flow regime. The major factor causing deviation of predicted fracture flow behavior from the ideal parallel plate theory is the nature of nonparallel and nonsmooth geometry of fracture surfaces. Important questions on the validity of the cubic law and the Reynolds equation for complicated fracture geometries have been studied by many researchers. The general conclusion from these efforts is that the cubic law is valid provided that an appropriate average aperture can be defined. Many average apertures have been proposed, and for some cases, some work better than others. Nonetheless, to date, these efforts have not converged to form a unified definition on the fracture aperture needed in the cubic law, which stimulates the current effort to develop a general governing equation for fracture flow from a fundamental consideration. In this study, a governing equation stemming from the principle of mass conservation and the assumption that the cubic law holds locally is derived for incompressible laminar fluid flow in irregular fractures under steady state conditions. The equation is formulated in both local and global coordinates and explicitly incorporates two vectorial variables of fracture geometry: true aperture and tortuosity. Under the assumption of small variations in both tortuosity and aperture, the governing equation can be reduced to the Reynolds equation. Two examples are provided to show the importance and generality of the new governing equation in both local and global coordinate systems. In a simple fracture with two nonsmooth and nonparallel surfaces, the error in permeability estimation can be induced using the Reynolds equation with the apparent aperture and can reach 10% for a 25° inclination between the fracture surfaces. In a fracture with sinusoidal surfaces, the traditional method can cause significant errors in both permeability and pressure calculation.