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The purpose of this paper is to propose a new trajectory planning algorithm for industrial robots, which can let the robots move through a desired spatial trajectory, avoid colliding with other objects and achieve accurate movements. Trajectory planning algorithms are the soul of motion control of industrial robots. A predefined space trajectory can let the robot move through the desired spatial coordinates, avoid colliding with other objects and achieve accurate movements.

The mathematical expressions of the proposed algorithm are deduced. The speed control, position control and orientation control strategies are realized and verified with simulations, and then implemented on a six degrees of freedom (6-DOF) industrial robot platform.

A fixed-distance trajectory planning algorithm based on Cartesian coordinates was presented. The linear trajectory, circular trajectory, helical trajectory and parabolic trajectory in Cartesian coordinates were implemented on the 6-DOF industrial robot.

A simple and efficient algorithm is proposed. Enrich the kind of trajectory which the industrial robot can realize. In addition, the industrial robot can move more concisely, smoothly and precisely.

The purpose of this paper is to present new expressions in Cartesian coordinates for the potential and magnetic field of prolate and oblate spheroids with arbitrary direction of the symmetry axis in a homogeneous field.

The potentials found in prolate or oblate spheroidal coordinates are transformed to Cartesian coordinates. These results are represented in such a form that they depend only on expressions, which are invariant under rotations around the symmetry axis. Thus, it is easy to change to arbitrary directions of both the symmetry axis and of that of the primary field. The gradients of the potentials are calculated and transformed exactly to the simplest form possible.

The paper presents simple expressions for the magnetic perturbations due to homogeneous prolate or oblate spheroids in a homogeneous magnetic field.

Results are exact for single non‐ferromagnetic spheroids in a homogeneous field.

Superposition of these perturbations presupposes small values of the magnetic susceptibilities of both the spheroids and their environment as in biological tissues.

The paper presents novel formulas for fields of homogeneous spheroids in a homogeneous magnetic field which are very useful for modelling biological tissues in studies of magnetic resonance imaging and magnetic resonance spectroscopy.

In order to represent, analyze, optimize, and manufacture a component made of multi‐heterogeneous materials for high‐tech applications, a computer model of the heterogeneous component needs to be built first. Heterogeneous materials include composite, functionally graded materials, and heterogeneous materials with a periodic microstructure. Current modeling techniques focus only on capturing the geometric information and cannot satisfy the requirements from modeling the components made of multi‐heterogeneous materials. This paper develops a modeling method, which can be implemented by employing the functions of current CAD graphic software and can obtain the model including both the material information (about its microstructures and constituent composition) and the geometry information without the problems arising from too many data.

In semi-analytical modeling of spoke-type permanent-magnet (PM) machines (STPMM), the saturation effect is usually neglected (i.e. iron parts are considered to be infinitely permeable) and the PM magnetization is assumed tangential (i.e. magnetization pattern is considered to be tangential-parallel). This paper aims to present an improved two-dimensional (2D) subdomain technique for STPMM with the PM magnetization orientation in quasi-Cartesian coordinates by using hyperbolic functions considering non-homogeneous Neumann boundary conditions (BCs) in non-periodic regions and by applying the interfaces conditions (ICs) in both directions (i.e. t- and θ edges ICs).

The polar coordinate system is transformed into a quasi-Cartesian coordinate system. The rotor and stator regions are divided into primary subdomains, and a partial differential equation (PDE) is assigned to each subdomain. In the PM region, the magnetization orientation is considered in the equations. By applying BCs, the general solution of the equations is determined, and by applying the ICs, the corresponding coefficients are determined.

Using the proposed coordinate system, the general solution of PDEs and their coefficients can mathematically be simplified. The magnetic field and non-intrinsic unbalanced magnetic forces (UMF) calculations have been performed for three different values of iron core relative permeability (200, 800 and ∞), as well as different magnetization orientation values (135 and 80 degrees). The semi-analytical model based on the subdomain technique is compared with those obtained by the 2D finite-element analysis (FEA). Results disclose that the PM magnetization angle can affect directly the performance characteristics of the STPMM.

A new model for prediction of electromagnetic performances in the STPMM takes into account magnetization direction, and soft magnetic material relative permeability in a pseudo-Cartesian coordinate system by using subdomain technique is presented.

This paper aims to review various techniques used in computational electromagnetism such as the treatment of open problems, helicoidal geometries and the design of arbitrarily shaped invisibility cloaks. This seemingly heterogeneous list is unified by the concept of geometrical transformation that leads to equivalent materials. The practical set‐up is conveniently effected via the finite element method.

The change of coordinates is completely encapsulated in the material properties.

The most significant examples are the simple 2D treatment of helicoidal geometries and the design of arbitrarily shaped invisibility cloaks.

The paper provides a unifying point of view, bridging several techniques in electromagnetism.

The purpose of this study is to address the concept and the step-by-step procedure of a high-precision optical alignment test for spacecrafts using digital theodolites. The proposed scheme focuses on the non-contact alignment qualification of spacecraft components during the integration and test phases until the launch event.

The proposed approach is based on the exploitation of the auto-collimation feature of theodolites and several prisms attached to the requested component and satellite configuration. As soon as the misalignment measurement including the difference between the real and desired attitude or position aberration of an instrument is made, the results must be transformed from the component level to the system level for misalignment error identification in the spacecraft dynamic model.

The paper introduces the main instruments, the defined coordinate systems and the architecture of the optical spacecraft misalignment test. Moreover, the guideline of the test implementation and the resulting data process have been presented carefully.

There is no limitation associated with this method because the procedure is applicable for high-precision typical missions.

This paper describes a fully implementable scheme to examine any possible inaccuracy in mounting of the spacecraft components both in position and orientation. The test can be performed without the need for a huge budget or complicated hardwares.

The contribution of this work revolves around illustrating the context and procedure of the spacecraft misalignment test which has remained unknown in literature despite the frequent implementation in the different satellite projects.

The purpose of this paper is to provide a theoretical model for considering ease numerically in the clothing pattern. Classifying the pattern as a geometric Cartesian coordinate system, this model proposes the need to quantify the partly coincident variables of ease, which will enable greater control over garment fit and function, using traditional or CAD/CAM methods.

The principles of pattern/garment dimensions are considered with support from analysis of literature and contributing factors to the variables of ease are categorised. These principles support a proposed theoretical model for considering pattern/garment dimensions, in the numeric format that they exist within the context of pattern construction.

Pattern construction occurs in a 2D Cartesian coordinate system, guided by body dimensions and ease. This can be modelled in the form of an algorithm relating to the placement of cardinal points defining the pattern outline. Recognition of the numerical nature of the pattern, suggests the need to quantify the coincident variables of ease, to achieve greater control over garment fit and function.

Few sources exist enabling the recognition of ease requirements in the pattern/garment and when guidance on ease is presented, there is little rationale as to how it has been established, or what contributes to its definition.

The paper shows how current methods of pattern construction can be modelled more effectively, recognising the geometric nature on which they are based. Modelling these relationships highlights where quantification can be provided, by existing knowledge or future research.

The purpose of this paper is to introduce a new similarity method to gauge the differences between two subject hierarchical structures.

In the proposed similarity measure, nodes on two hierarchical structures are projected onto a two-dimensional space, respectively, and both structural similarity and subject similarity of nodes are considered in the similarity between the two hierarchical structures. The extent to which the structural similarity impacts on the similarity can be controlled by adjusting a parameter. An experiment was conducted to evaluate soundness of the measure. Eight experts whose research interests were information retrieval and information organization participated in the study. Results from the new measure were compared with results from the experts.

The evaluation shows strong correlations between the results from the new method and the results from the experts. It suggests that the similarity method achieved satisfactory results.

Hierarchical structures that are found in subject directories, taxonomies, classification systems, and other classificatory structures play an extremely important role in information organization and information representation. Measuring the similarity between two subject hierarchical structures allows an accurate overarching understanding of the degree to which the two hierarchical structures are similar.

Both structural similarity and subject similarity of nodes were considered in the proposed similarity method, and the extent to which the structural similarity impacts on the similarity can be adjusted. In addition, a new evaluation method for a hierarchical structure similarity was presented.

This paper aims to investigate if a Cartesian robot system for kiwifruit harvesting works more effectively and efficiently than an articulated robot system. The robot is a key component in agricultural automation. For instance, multiple robot arm system has been developed for kiwifruit harvesting recently because of the significant labor shortage issue. The industrial robots for factory automation usually have articulated configuration which is suitable for the tasks in the manufacturing and production environment. However, this articulated configuration may not fit for agricultural application due to the large outdoor environment.

The kiwifruit harvesting tasks are completed step by step so that the robot workspace covers the canopy completely. A two-arm, Cartesian kiwifruit harvesting robot system and several field experiments are developed for the investigation. The harvest cycle time of the Cartesian robot system is compared to that of an articulated robot system. The difference is analyzed based on the workspace geometries of these two robot configurations.

It is found that the kiwifruit harvesting productivity is increased by using a multiple robot system with Cartesian configuration owing to its regular workspace geometry.

An articulated robot is a common configuration for manufacturing because of its simple structure and the relatively static factory environment. Most of the agricultural robotics research studies use single articulated robot for their implementation. This paper pinpoints how the workspace of a multiple robot system affects the harvest cycle time for kiwifruit harvesting in a pergola style kiwifruit orchard.

In this study, a modeling method for a clamped deformable cable simulation based on Kirchhoff theory is proposed. This methodology can be used to describe the physical deformation configuration of any constrained flexible cable in a computer-aided design/manufacturing system. The modeling method, solution algorithm, simulation and experimental results are presented to prove the feasibility of the proposed methodology. The paper aims to discuss these issues.

First, Kirchhoff equations for deformable cables are proposed based on the nonlinear mechanics of thin elastic rods, and the general solution of the equations described by the Euler angles is given in the arc coordinate system. The parametric form solution of the Kirchhoff equations, which is easy to use, is then obtained in a cylindrical coordinate form based on Saint Venant’s theory. Finally, mathematical expressions that reflect the clamped cable configuration are given, and the deformable process is simulated based on an open source geometry kernel and is then tested by a 3D laser scanning technology.

The method presented in this paper can be adapted to any boundary condition for constrained cables as long as the external force and torque are known. The experimental results indicate that both the model and algorithm are efficient and accurate.

A more comprehensive study must be executed for the physical simulation of more complicated constrained cables, such as the helical spring and asymmetric constraint. The influence of the material properties of the cable on the calculation efficiency must be considered in future analysis.

The semi-analytical algorithm of the cable simulation in cylindrical coordinates is a novel topic and is more accurate and efficient than the common numerical solution.