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The purpose of this paper is to model how geometric errors of a machined surface (or manufacturing errors) are related to locators’ error, workpiece form error and machine tool volumetric error. A kinematic model is presented that puts into relationship the locator error, the workpiece form deviations and the machine tool volumetric error.

The paper presents a general and systematic approach for geometric error modelling in drilling because of the geometric errors of locators positioning, of workpiece datum surface and of machine tool. The model can be implemented in four steps: (1) calculation of the deviation in the workpiece reference frame because of deviations of locator positions; (2) evaluation of the deviation in the workpiece reference frame owing to form deviations in the datum surfaces of the workpiece; (3) formulation of the volumetric error of the machine tool; and (4) combination of those three models.

The advantage of this approach lies in that it enables the source errors affecting the drilling accuracy to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for accuracy improvement through suitable measures, i.e. component tolerancing in design, machining and so on. Two typical drilling operations are taken as examples to illustrate the generality and effectiveness of this approach.

Some source errors, such as the dynamic behaviour of the machine tool, are not taken into consideration, which will be modelled in practical applications.

The proposed kinematic model may be set by means of experimental tests, concerning the industrial specific application, to identify the values of the model parameters, such as standard deviation of the machine tool axes positioning and rotational errors. Then, it may be easily used to foresee the location deviation of a single or a pattern of holes.

The approaches present in the literature aim to model only one or at most two sources of machining error, such as fixturing, machine tool or workpiece datum. This paper goes beyond the state of the art because it considers the locator errors together with the form deviation on the datum surface into contact with the locators and, then, the volumetric error of the machine tool.

Relational thinking and spatial analyses have become highly relevant for higher education research. However, choices of research methods and specifically of statistical procedures do not often correspond to the epistemological underpinnings implied by relational perspectives. Against this background, this chapter illustrates the uses and challenges of geometric data analysis (GDA) for studying the complexities and dynamics of current spaces of higher education. GDA can be described as a set of statistical techniques that allow the identification, assessment and visualisation of complex relations in social science data. Using an investigation into the social topologies of first-year students as an example, we discuss the mathematical foundations, the step-by-step procedures of data analysis, the interpretation of results and strategies for integrating GDA into multimethod research designs. In sum, we argue that GDA does not only entail a comprehensive set of statistical instruments that permit visual analysis of relational structures, but also enables the systematic integration of qualitative and quantitative methods, hence supporting the development of innovative and coherent research designs and analytical strategies.

The virtual design environment offers users an opportunity to interact with a virtual prototyping rather than physical models and to build a fixture configuration in a realistic way. But the virtual reality (VR) environment tends to be inaccurate because humans have difficulty in performing precise positioning tasks. Therefore, it is necessary to implement precise object manipulation methods for assembly and disassembly activities, so that users can perform modular fixture configuration design efficiently in VE. The purpose of this paper is to develop a VR‐based modular fixture assembly design system, which supports the design and assembly of modular fixture configuration in a virtual environment.

Geometric constraint‐based method is utilized to represent and treat the assembly relationship between modular fixture elements. The paper presents a hybrid method of rule‐based reasoning and fuzzy comprehensive judgment to capture the user's operation intent and recognize geometric constraint. Through degrees of freedom based analysis, a mathematical matrix is presented for representing and reducing allowable motion of fixture elements, and a constraint‐based motion navigation approach is proposed to ensure that the manipulation of a fixture component not violate that the existing constraints.

The paper finds that the proposed techniques are applicable to the convenient manipulation and accurate positioning of fixture elements in a virtual environment.

Component manipulation plays a key role in interactive virtual assembly design. The proposed approach in this paper enables interactive assembly design of modular fixture in virtual environment.

This paper presents a geometric constraint‐based approach that realizes automatic assembly relationship recognition, constraint solving and motion navigation for interactive modular fixture assembly design in a virtual environment.

The three-sector framework (relating to agriculture, manufacturing and services) is one of the major concepts for studying the long-run change of the economic structure. This paper aims to discuss the system-theoretical classification of the structural change in the three-sector framework and, in particular, its predictability by the Poincaré–Bendixson theory.

This study compares the assumptions of the Poincaré–Bendixson theory to the typical axioms of structural change modeling, the empirical evidence on the geometrical properties of structural change trajectories and the methodological arguments referring to the laws of structural change.

The findings support the assumption that the structural change phenomenon is representable by a dynamical system that is predictable by the Poincaré–Bendixson theory. This result implies, among others, that in the long run, structural change is either transitory or cyclical and can be used in further geometrical/topological long-run structural change modeling and prediction.

Although widespread in mathematics, geometrical/topological modeling methods have not been used in modeling and prediction of long-run structural change, despite the fact that they seem to be predestined for this purpose owing to their global, system-theoretical nature, allowing for a reduction of ideology content of predictions and greater robustness of results.

A course of study on the philosophy of mathematics involved learning about Zeno's paradoxes and the solutions suggested for them by the ancient Greeks; the Eleatic and atomistic. The two schools were related to modern physics and the course students were asked which of the two approaches they preferred. They also participated in a test of the cerebral hemispheres. It was found that preference of the Eleatic solution over the atomistic is related to a dominance of the right hemisphere Over the left. The results are discussed in relation to the opposing views concerning Kant's theory of the a priori perception of physical phenomena.

The purpose of this paper is to propose a general model for locating and clamping workpieces of complex geometry with two skewed holes under multiple constraints.

Numerous constraints related to application of the proposed model are discussed as prerequisite to design of fixture solution. Based on theoretical model, a fixture was designed and successfully tested in experimental investigation. Experimental results were also verified using FEM simulations.

This study showed that, opposed to conventional approach, novel solution results in significantly smaller fixture dimensions, while providing greater stability. Insertion of mandrels and supports element sub-assemblies into the workpiece holes significantly increases workpiece stiffness through an increased moment of inertia, while the internal support elements largely diminish the problem of thin wall deformation in the workpiece.

The fixture designed in this case was actually used in industrial application to accommodate a thin-walled casting of gearbox housing, where it proved to be a very stable framework. It can be used in industry without any major readjustments.

According to available literature, this work is the first successful implementation of a fixture solution in which the problem of multiple constraints is solved by attaching centering elements, support sub-assemblies, and other fixture elements to the internal workpiece walls, and then locating them in the second part of the fixture.

In model‐based recognition the 3D models of objects are stored in a model library during an offline phase. During the online recognition phase, a view of the scene is matched with the model library to identify the location and pose of certain library objects in the scene. Aims to focus on the process of 3D modeling and model‐based recognition.

This paper discusses the process of 3D modeling and model‐based recognition along with their potential applications in industry with a particular emphasis on robot grasp analysis. The paper also emphasises the main challenges in these areas and give a brief literature review.

In order to develop an automatic 3D model‐based object recognition system it is necessary to automate the process of 3D modeling and recognition. The challenge in automating the 3D modeling process is to develop an automatic correspondence technique. The core of recognition is the representation scheme. Recognition is an online process. Therefore, representation and matching must be very fast in order to facilitate real time recognition.

There are numerous applications of 3D modeling in a variety of areas ranging from the entertainment industry to industrial automation. Some of its applications include computer graphics, virtual reality, medical imaging, reverse engineering, and 3D terrain construction.

Provides information on 3D modeling which constitutes an important part of computer vision or robot vision.

The purpose of this paper is to provide a comprehensive and unified presentation of recent developments in skid-steer wheeled mobile robots (SSWMR) with regard to its control, guidance and navigation for the researchers who wish to study in this field.

Most of the contemporary unmanned ground robot’s locomotion is based upon the wheels. For wheeled mobile robots (WMRs), one of the prominent and widely used driving schemes is skid steering. Because of mechanical simplicity and high maneuverability particularly in outdoor applications, SSWMR has an advantage over its counterparts. Different prospects of SSWMR have been discussed including its design, application, locomotion, control, navigation and guidance. The challenges pertaining to SSWMR have been pointed out in detail, which will seek the attention of the readers, who are interested to explore this area.

Relying on the recent literature on SSWMR, research gaps are identified that should be analyzed for the development of autonomous skid-steer wheeled robots.

An attempt to present a comprehensive review of recent advancements in the field of WMRs and providing references to the most intriguing studies.

The purpose of this paper is to present a novel method for integrating of chaotic exploration and thinning‐based topological mapping to deal with the “traverse targets and return” problem applied for robot navigation in unknown environments. This new strategy can guarantee the robot stronger ability of exploring unknown environments, as well as recording and selecting optimal trajectory to return.

The chaotic dynamic evolution of controlled multi‐scroll system is linked to the multi‐sensory perception and reactive behaviors of a mobile robot. The thinning‐based topological map (TTM), as the contextual layer of the cognitive system, is adopted to achieve the environmental recording in the process of robot exploration and navigation. Once the robot arrives at the terminal target via avoiding all the obstacles, the TTM has been built in real time. Based on the records in the topological map, a short and smooth point‐to‐point path is generated to achieve the exit from target and to move back to the starting point.

The simulation results confirmed that the proposed solution is suitable to resolve the robot's tasks of obstacle avoidance, target retrieving, and return, also has better performance than traditional strategies.

The presented novel method focuses integration of chaotic exploration and TTM self‐construction. The chaotic perception and control technique permits the robot to explore most of the environmental information within the smallest explored area. The introduced topological map, generated by applying a thinning algorithm, guarantees a short and smooth returning trajectory for the robot.

In this paper, we review the process of “3D modeling” and “model‐based recognition” along with their potential industrial applications. We put a particular emphasis on the case scenario of robot grasp analysis for which 3D model‐based object recognition seems to be a more palpable choice compared with the conventional tactile sensors solutions. We also put a particular emphasis on the main challenges in the areas of 3D modeling and model‐based recognition and give a brief literature review of the latest research that was carried out to respond to these challenges.