Elementary Case Research Articles

Framework for the Machine Learning Based Wireless Sensing of the Electromagnetic Properties of Indoor Materials

Available digital maps of indoor environments are limited to a description of the geometrical environment, despite there being an urgent need for more accurate information, particularly data about the electromagnetic (EM) properties of the materials used for walls. Such data would enable new possibilities in the design and optimization of wireless networks and the development of new radio services. In this paper, we introduce, formalize, and evaluate a framework for machine learning (ML) based wireless sensing of indoor surface materials in the form of EM properties. We apply the radio-environment (RE) signatures of the wireless link, which inherently contains environmental information due to the interaction of the radio waves with the environment. We specify the content of the RE signature suitable for surface-material classification as a set of multipath components given by the received power, delay, phase shift, and angle of arrival. The proposed framework applies an ML approach to construct a classification model using RE signatures labeled with the environmental information. The ML method exploits the data obtained from measurements or simulations. The performance of the framework in different scenarios is evaluated based on standard ML performance metrics, such as classification accuracy and F-score. The results of the elementary case prove that the proposed approach can be applied for the classification of the surface material for a plain environment, and can be further extended for the classification of wall materials in more complex indoor environments.

A simple yet consistent constitutive law and mortar-based layer coupling schemes for thermomechanical macroscale simulations of metal additive manufacturing processes

This article proposes a coupled thermomechanical finite element model tailored to the macroscale simulation of metal additive manufacturing processes such as selective laser melting. A first focus lies on the derivation of a consistent constitutive law on basis of a Voigt-type spatial homogenization procedure across the relevant phases, powder, melt and solid. The proposed constitutive law accounts for the irreversibility of phase change and consistently represents thermally induced residual stresses. In particular, the incorporation of a reference strain term, formulated in rate form, allows to consistently enforce a stress-free configuration for newly solidifying material at melt temperature. Application to elementary test cases demonstrates the validity of the proposed constitutive law and allows for a comparison with analytical and reference solutions. Moreover, these elementary solidification scenarios give detailed insights and foster understanding of basic mechanisms of residual stress generation in melting and solidification problems with localized, moving heat sources. As a second methodological aspect, dual mortar mesh tying strategies are proposed for the coupling of successively applied powder layers. This approach allows for very flexible mesh generation for complex geometries. As compared to collocation-type coupling schemes, e.g., based on hanging nodes, these mortar methods enforce the coupling conditions between non-matching meshes in an L^2-optimal manner. The combination of the proposed constitutive law and mortar mesh tying approach is validated on realistic three-dimensional examples, representing a first step towards part-scale predictions.

Chiral magnetic effect in lattice models of tilted multi-Weyl semimetals

We study the chiral magnetic effect (CME) in tilted multi-Weyl semimetals (mWSMs) employing a two-band lattice model. We focus on the type-II phase of mWSMs, introduced by incorporating a Lorentz symmetry violating tilt term. Our work adds to the current understanding of the CME (and also the anomalous Hall effect) in the type-II phase of mWSMs and near the Lifshitz transition by varying tilt. Like the elementary Weyl semimetal case, our results also indicate that the Berry curvature drives the CME for higher monopole charges. We find a peak in the CME at the transition point and discuss its significance using the density of states. Along the way we also examine both observables as a function of the energy separation of the Weyl points.

Coupled continuous–discrete formulation based on microplane and strong discontinuity models for representing non-orthogonal intersecting cracks

Fracture processes in quasi-brittle materials are governed by the strain localization phenomenon, which involves the formation of localized damage zones and cohesive cracks. In this work, we present numerical tools to model strain localization from the onset of localized damage to the formation and propagation of multiple intersecting cracks. Two main ingredients are used for this purpose: (i) a microplane model to describe the initial anisotropic damage phase; (ii) the strong discontinuity method to introduce cracks as strong discontinuities in the damaged continuum using the Embedded Finite Element Method (E-FEM). Here, we formulate the microplane microdamage model within a thermodynamic framework by means of simple constitutive laws on each microplane. In order to describe intersecting cracks, we extend the standard E-FEM to accommodate two strong discontinuities. The coupling between the microplane microdamage model with the strong discontinuity model is achieved using a transition method based on the energy equivalence between both models. Exploiting the anisotropic description provided by the microplane model, transition criteria are formulated based on the quantities defined on each microplane. The proposed methodologies are illustrated using several elementary test cases involving both simple and complex stress-strain states.

Refinements of the integral Jensen\u2019s inequality generated by finite or infinite permutations

There are a lot of papers dealing with applications of the so-called cyclic refinement of the discrete Jensen’s inequality. A significant generalization of the cyclic refinement, based on combinatorial considerations, has recently been discovered by the author. In the present paper we give the integral versions of these results. On the one hand, a new method to refine the integral Jensen’s inequality is developed. On the other hand, the result contains some recent refinements of the integral Jensen’s inequality as elementary cases. Finally some applications to the Fejér inequality (especially the Hermite–Hadamard inequality), quasi-arithmetic means, and f-divergences are presented.

Spectral discrete dislocation dynamics with anisotropic short range interactions

Discrete dislocation dynamics models dislocation-mediated plastic deformation and microstructural evolution in solids whilst discretely representing and tracking all line defects present in the medium. Hybrid methodologies for evaluating mechanical fields using continuum approaches while retaining the discrete formalism for evaluating dislocation kinematics and interactions have greatly improved the numerical efficiency of the method. In the present work, we propose a spectrally-based continuum solution of the mechanical fields based on the field dislocation mechanics framework which produces highly accurate elastic fields near dislocation cores in both isotropic and anisotropic media. Application of the model to a few elementary cases (i.e. dislocation junction formation, dislocation migration) show that the model proposed predicts accurate elastic fields both on the short and long range.

On the Coupling of Power-Related and Inner Inverter Control Loops of Grid-Forming Converter Systems

In the last decade, different control concepts for the synchronisation of voltage-controlled power converters have been proposed in order to form converter-based power systems. The interoperability of these grid-forming power controls is often analysed based on reduced-order models covering only the slow controls or modes. In this article, the coupling of the outer, power-related and inner, inverter output-related control of multiple grid-forming power converter systems is analysed, based on a minimal working example. The elementary study cases each consist of a different grid-forming converter coupled with an external (and passive) grid. Here, the investigated stability problems are already manifested in the simplest possible setup. The analysis of these coupling effects is performed by modelling the system in impedance-based, state-space and phase portrait-based frameworks. In particular, small coupling impedances, like short transmission lines or small short circuit impedances, can be challenging for the controller stability of grid-forming converters while the inner controls can even enhance this issue. The impact of this phenomenon and the participating subsystems are identified in this work. Thus, recommendations concerning modelling techniques and their legitimate assumptions are given. Laboratory experiments validate the performed analysis by indicating a close correlation between analytical models and experimental results.

Self-organizing control systems for autonomous educational robotic complexes

Abstract The increasing social importance of educational robotics caused development not only a technical component of educational robots. But improvement of control algorithms is more important. At the same time the most important direction of development is the possibility of autonomous functioning at a solution of difficult tasks on dynamically changing external environment. Expansion of orbs of application of automatic control has caused development of intellectualization of control systems. One of the important directions is intelligent self-organizing of automatic control system (ISACS). They are capable to supply required capabilities of the purpose of control with change of environments and/or their parameters. It is attained by automatic synthesis of the control law, the most adequate a current situation. For this purpose the intelligent system of synthesis is used. The planning subsystem creates (in the elementary case selects from already known) the most adequate procedure of synthesis. However, existing approaches to planning actions have no property of mass parallelism. It do not allow applying them in control systems owing to the big costs of time for a solution of task. It is offered to use artificial neural planning networks (ANPN) within the planning subsystem of tasks solver. Features of planning of tasks solving with use ANPN are considered. These abilities become the urgent need for implementation of opportunities of autonomous functioning of socially important educational robots. Outcomes of simulation of control of a plants population with use ISACS are represented.

Solution of Thermal Conductivity Problem of a Finite Dimensions Plate with Two Heat Sources

Research in the basic sciences is a critical factor in the development of the civil engineering industry. Solving the problems of radiation-convective heat transfer from heated surfaces has always aroused interest from the point of view of science and practical engineering application of knowledge. However, analytical solutions to these problems are obtained for elementary cases, for example, for infinite plates heated uniformly, or the propagation of heat waves in them obeys certain laws. The solution of the coupled problem of radiation-convective transfer from the surface of these panels is complicated not only by the geometric shape, but also by the openness of the entire thermophysical system, which includes the transfer of thermal energy from the coolant (coolant for cooling systems) to the surface of the thermal panel, from the panel to the room air by convection, and radiation to surrounding bodies (enclosing structures, furniture, people). In turn, additional heat exchange by convection occurs between the air and the enclosing structures. This article considers the possibility of obtaining an analytical solution to the problem of temperature distribution on the surface of a plate with two heat sources. When deriving the formulas, the classical equations of thermodynamics (Newton-Richmann, Fourier’s law, Helmholtz equation) were used. The general solution of the differential equation, in this case, is a linear combination of the Infeld and MacDonald functions. The research results can be applied to various areas of technical sciences: cooling of microprocessors, renewable sources of thermal energy, thermal and cooling panels for industrial production, automotive, marine shipbuilding, and of course heating and air conditioning systems for buildings and transport.

"Trazar una bóveda cónica cuadrada" La trompa volada de Tomás Vicente Tosca

<div data-canvas-width="82.4750337835114"><p>The squinches isa very versatile construction type in the field of stonework. It is defined in its most elementary case as the covering of a triangular area with a conical surface, but, nevertheless, there are an infinite number of variants increasing the complexity of the layout and its execution.The studied case in this paper is the development of the layout of the "square conical vault" (actually, a cantilevered vault), in the treatise on stonework by Tomás Vicente Tosca, published in 1727. This author's work reflectsthe tradition of the local area (which comes mainly from the brilliant episode of the 15th century in Valencia), but it is also part of the pre-illustrated cultural trends of the time. The traces that appear are the result of combining ancient graphic habits with the development, to a certain extent, already scientific, of geometry and mathematics.All this leads, in the case of the "conical-square vault", to the development of a fundamentally descriptive trace, result of a mentality that is more analytical than practical, but that does not manage to emancipate itself from the old building tradition, as this study makes evident, and also the detected graphic habits.The research is also based on other examples of a documentary nature, such as the cantilevered domes of Vandelvira, Philibert de l'Orme, Gelabert, and on a built example; the squinch of the palace of the Generalitat de Valencia.</p></div><div data-canvas-width="145.94326164079826"> </div>

Exact distributional analysis of online algorithms with lookahead

In online optimization, input data is revealed sequentially. Optimization problems in practice often exhibit this type of information disclosure as opposed to standard offline optimization where all information is known in advance. We analyze the performance of algorithms for online optimization with lookahead using a holistic distributional approach. To this end, we first introduce the performance measurement method of counting distribution functions. Then, we derive analytical expressions for the counting distribution functions of the objective value and the performance ratio in elementary cases of the online bin packing and the online traveling salesman problem. For bin packing, we also establish a relation between algorithm processing and the Catalan numbers. The paper shows that an exact analysis is strongly interconnected to the combinatorial structure of the problem and algorithm under consideration. Results further indicate that the value of lookahead heavily relies on the problem itself. The analysis also shows that exact distributional analysis could be used in order to discover key effects and identify related root causes in relatively simple problem settings. These insights can then be transferred to the analysis of more complex settings where the introduced performance measurement approach has to be used on an approximative basis (e.g., in a simulation-based optimization).

An Application of Spherical Geometry to Hyperkähler Slices

AbstractThis work is concerned with Bielawski’s hyperkähler slices in the cotangent bundles of homogeneous affine varieties. One can associate such a slice with the data of a complex semisimple Lie group $G$, a reductive subgroup $H\subseteq G$, and a Slodowy slice $S\subseteq \mathfrak{g}:=\text{Lie}(G)$, defining it to be the hyperkähler quotient of $T^{\ast }(G/H)\times (G\times S)$ by a maximal compact subgroup of $G$. This hyperkähler slice is empty in some of the most elementary cases (e.g., when $S$ is regular and $(G,H)=(\text{SL}_{n+1},\text{GL}_{n})$, $n\geqslant 3$), prompting us to seek necessary and sufficient conditions for non-emptiness.We give a spherical-geometric characterization of the non-empty hyperkähler slices that arise when $S=S_{\text{reg}}$ is a regular Slodowy slice, proving that non-emptiness is equivalent to the so-called $\mathfrak{a}$-regularity of $(G,H)$. This $\mathfrak{a}$-regularity condition is formulated in several equivalent ways, one being a concrete condition on the rank and complexity of $G/H$. We also provide a classification of the $\mathfrak{a}$-regular pairs $(G,H)$ in which $H$ is a reductive spherical subgroup. Our arguments make essential use of Knop’s results on moment map images and Losev’s algorithm for computing Cartan spaces.

Time-asymptotic Dynamics of Hermitian Riccati Differential Equations

The matrix Riccati differential equation (RDE) raises in a wide variety of applications for science and applied mathematics. We are particularly interested in the Hermitian Riccati Differential Equation (HRDE). Radon's lemma gives a solution representation to HRDE. Although solutions of HRDE may show the finite escape time phenomenon, we can investigate the time asymptotic dynamical behavior of HRDE by its extended solutions. In this paper, we adapt the Hamiltonian Jordan canonical form to characterize the time asymptotic phenomena of the extended solutions for HRDE in four elementary cases. The extended solutions of HRDE exhibit the dynamics of heteroclinic, homoclinic and periodic orbits in the elementary cases under some conditions.

Effect of non-uniform temperature distribution on entropy generation and enthalpy for the laminar developing pipe flow of a high Prandtl number fluid

In this article, Entropy generation and enthalpy are investigated on the pipe wall in developed laminar flow for 7 cases. Variation of entropy generation and enthalpy are shown along the radius. Entropy generation and enthalpy along the radius are obtained. Heat transfer is increased with the flow of fluid through the pipe, in inlet of pipe points to the output. The amount of entropy generation in the pipes of higher temperature is more than other points. Enthalpy is proportional to temperature in surface variation of 7 cases. In the points of higher temperature in elementary cases, the enthalpy value is increasing and it is increasing in other cases. Fluctuations of enthalpy and entropy generation are producted in interface points of pipe surfaces. The diagram data can be used to measure the minimum entropy generation in pipe heat transfer. Minimum entropy generation is in surface whit high temperature. The enthalpy in centerline is constant and inlet enthalpy of the tube is greater than other point with higher temperatures in radial flow. The lowest enthalpy is obtained in tubes with lowest initial temperature (case 7). Minimum entropy generation is presented in surface whit high temperature at the beginning (case 1-3) or high at the ending (case 5-7).

Televacuna: ¿a qué estás esperando?

Discrete dislocation dynamics models dislocation-mediated plastic deformation and microstructural evolution in solids whilst discretely representing and tracking all line defects present in the medium. Hybrid methodologies for evaluating mechanical fields using continuum approaches while retaining the discrete formalism for evaluating dislocation kinematics and interactions have greatly improved the numerical efficiency of the method. In the present work, we propose a spectrally-based continuum solution of the mechanical fields based on the field dislocation mechanics framework which produces highly accurate elastic fields near dislocation cores in both isotropic and anisotropic media. Application of the model to a few elementary cases (i.e. dislocation junction formation, dislocation migration) show that the model proposed predicts accurate elastic fields both on the short and long range.

Motion of a disk in contact with a parametric 2D curve and Painlevé’s paradox

This paper addresses the modeling and simulation of a homogeneous disk that undergoes plane motion constrained to be in permanent contact with and in the same plane as a two-dimensional curve described by a parametric equation. Except for the elementary cases in which the curve is a straight line or an arc of circumference, the investigated problem presents significant challenges to both modeling and simulation. In addition to the necessity of using differential geometry methods to calculate local geometrical properties of the motion, this system exhibits typical difficulties of non-smooth dynamics. Different modes of operation require the synthesis of suitable rules for switching systems of differential equations and, due to the discontinuities caused by the exchange of dynamic models, numerical integration methods suitable for solving stiff problems are necessary. It should also be emphasized that the dynamic model here developed shows the Painleve’s paradox, caused by the application of a simplified law of friction (Coulomb’s law) to a rigid body subjected to an unilateral constraint. Among the results obtained in this work, we would like to highlight the following: (i) the realization that both the geometry of the contact curve and that followed by the center of mass of the disk must be considered to construct a correct dynamic model for the motion; (ii) a detailed procedure to identify the instant the disk stops sliding and initiates a pure rolling motion on the two-dimensional track represented by a $\mathfrak{C}_{2}$ class curve $C$ in parametric form; (iii) the realization that, for arbitrary geometries of flat two-dimensional curves of class $\mathfrak{C}_{2}$ and simplified models of friction, it is not possible to establish an arbitrary initial kinematic condition (a necessity for integrating the equations of motion) without incurring in a paradoxical result, known in the literature as Painleve’s paradox. We consider that the approach adopted in this work might contribute to building dynamic models of hybrid systems, especially those with non-elementary geometric characteristics.

Regularization of the Lagrangian point force approximation for deterministic discrete particle simulations

The current article presents a regularization procedure of the Lagrangian point-force approach commonly used to account for the perturbation of a fluid phase by a dispersed particle phase. The regularization procedure is based on a nonlinear diffusion equation to naturally ensure parallel efficiency when the regularization length scale extends over several grid cells. The diffusion coefficient thus becomes a function of the particle source term gradient and expressions allowing to approximately adjust the regularization length scale according to the local particle to mesh size ratio are proposed, so that mesh refinement or polydisperse sprays may be handled. Elementary numerical test cases confirm the convergence of the present procedure under mesh refinement and its ability to locally adapt the regularization length scale. Furthermore, the chosen regularization length scale allows to match the leading order term of the perturbation flow field set by the particle beyond approximately two particle diameters in the Stokes regime.When applying the presented source term regularization procedure, the terminal velocity of a particle settling under gravity in the Stokes regime becomes relatively insensitive to mesh refinement. However, errors with respect to the theoretical settling velocity remain substantial and removal of the particle’s self induced velocity appears necessary to recover the undisturbed fluid velocity at the particle location and correctly evaluate the drag force. As the current regularization procedure yields source terms that are close to Gaussian, an analytic expression from the literature is used to estimate the particle’s self induced velocity. When combining source term regularization and removal of the particle’s self induced velocity, good results are obtained for the terminal settling speed in the Stokes regime. Results obtained for horizontally separated particle pairs settling under gravity in the Stokes regime show equally good agreement with theoretical results. Because analytic expressions for the particle’s self-induced velocity are no longer available at finite particle Reynolds numbers, correlations recently proposed in the literature are used to obtain correct settling velocities beyond the Stokes regime.

A Study on Review about Person of Disability of mind & spirit -Focusing on analysis of criminal judgment in 2018-

본 연구는 2018년에 법원이 공개한 심신장애인 판단과 관련된 판례 2건의 사건을 개관하고 관련 정신장애와 심신장애의 판단 제도를 고찰한 후 사건별로 심신장애인 판단 요인에 대한 분석을 통해 구체적인 쟁점을 검토하였다. 「형법」제10조의 심신장애인은 심신상실자와 심신미약자로 구분할 수 있고, 이는 심신장애로 인하여 사물변별능력 또는 의사결정능력이 결여되거나 미약한 사람을 의미한다. 생물학적 요소인 심신장애는 정신적 장애로 보아 정신병, 비정상적 정신상태로 분류하고, 일반적으로「형사소송법」에 따라 정신감정을 통해 확인한다. 심리적 요소는 공판 과정을 통해 법원이 심신장애로 인하여 사물변별능력과 의사결정능력의 정도에 따라 법률적으로 판단한다. 법원이 공개한 각각의 판결은 다음과 같이 검토하였다. 먼저, 교도소 수용자상해사건의 피고인은 ‘충동조절장애와 불안장애 등의 정신장애 내지 그 치료를 위하여 복용한 약물의 부작용’으로 인하여 심신미약을 주장하였고, 법원은 ‘1. 정신장애로 인하여 범행 당시 심신미약 상태에 있었는지’와 ‘2. 약물부작용으로 범행 당시 심신미약 상태에 있었는지’를 심리하여 심신미약 주장을 배척하였다. 이 판결에서 피고인이 주장한 충동조절장애를 대분류 차원에서 판단한 점과 전문가의 감정을 실시하지 않고 심신미약 주장을 배척한 점에 대하여 주목하였다. 또한 인천 초등학생 살해사건의 피고인은 ‘아스퍼거 증후군’ 으로 인한 심신미약을 주장하였고, 이를 심리한 법원은 ‘1. 아스퍼거 증후군을 갖고 있는지 불확실하다는 요인’과 ‘2. 아스퍼거 증후군이 있다는 것만으로 사물변별능력이나 의사결정능력에 어떠한 영향을 미쳤다고 볼 수 없다는 요인’을 제시하며 심신미약 주장을 배척하였다. 이 판결에서 법원이 생물학적 요소의 존부에 대하여 판단한 점과 심신장애 판단 법리와 모순된 감정인의 법률적 의견 제시에 대한 사항을 분석하였다. 판결을 통해 살펴본 바에 따라 도출되는 심신장애인 판단에 대한 제언은 다음과 같다. 첫째, 충동조절장애와 같은 정신장애는 세부 진단기준을 통해 확정된 진단명을 통해 심리가 이루어져야 한다. 둘째, 충동조절장애 등 두 가지 이 상의 정신장애가 주장된 경우에 전문가의 감정을 실시하여 생물학적 요소를 확정하여야 한다. 셋째, 생물학적 요소의 존부에 대한 법원의 판단은 자제되어야 한다. 넷째, 정신감정의 전문가는 법률적 판단에 대하여 의학적 범위에서 의견을 제시하여야 한다.In this study analyzed the factors of judgment of the Person of Disability of mind and spirit based on two cases related to judgment of the person with a disability released by the court in 2018. In Article 10 of the「Criminal Act」, Person of Disability of mind and spirit who lacks or is weak because of Disability of mind and spirit , In general, it is confirmed through mental emotions according to the 「Criminal Procedure Act」. And The court shall make its own judgment by combining the evidence by a mixed method. Each court s decision was reviewed as follows. The defendant in prison inmate injury case insisted on the mental weakness due to Side effects of drugs taken for the treatment of mental disorders such as impulse control disorders and anxiety disorders , The court rejected the mental weakness by examining 1. When a crime is caused by mental and 2. When you commit a crime for drug side effects . In this judgment case, the defendant s impulse control disorder was analyzed in terms of the major category and the mental and mental claims were rejected without the expert s Mental Examination. Also, The defendant in the Incheon elementary school student murder case, The court rejected the mental weakness by examining 1. Factor of uncertainty about having Asperger s syndrome and 2. Asperger s syndrome is the only factor that can not be considered to have any effect on the ability to discriminate or make decisions . In this judgment case, the Court considers he judgment of the defendant on biological factors and the controversial legal opinion of the expert. I examined the case and suggested the following suggestions. First, Mental disorders such as impulse control disorders should be judged through a diagnosis that is confirmed by detailed criteria, Second, If two or more mental disorders such as impulse control disorder are claimed, the examination of the expert should be performed, Third, The court s judgment on the presence of biological factors should be refrained, Fourth, The psychiatric specialist must provide medical opinion on legal judgment.

The Academic and Behavioral Implications of Robotics In the Classroom: an Elementary Case Study

The Academic and Behavioral Implications of Robotics In the Classroom: an Elementary Case Study

A CAD/CAE integration framework for analyzing and designing spatial compliant mechanisms via pseudo-rigid-body methods

Abstract Compliant Mechanisms (CMs) are currently employed in several engineering applications requiring high precision and reduced number of parts. For a given mechanism topology, CM analysis and synthesis may be developed resorting to the Pseudo–Rigid Body (PRB) method, in which the behavior of flexible members is approximated via a series of rigid links connected by spring-loaded kinematic pairs. From a CM analysis standpoint, the applicability of a generic PRB model requires the determination of the kinematic pairs’ location and the stiffness of a set of generalized springs. In parallel, from a design standpoint, a PRB model representing the kinetostatic behavior of a flexible system should allow to compute the flexures’ characteristics providing the desired compliance. In light of these considerations, this paper describes a Computer-Aided Design/Engineering (CAD/CAE) framework for the automatic derivation of accurate PRB model parameters, on one hand, and for the shape optimization of complex-shape flexures comprising out-of-plane displacements and distributed compliance. The method leverages on the modelling and simulation capabilities of a parametric CAD (i.e. PTC Creo) seamlessly connected to a CAE tool (i.e. RecurDyn), which provides built-in functions for modelling the motion of flexible members. The method is initially validated on an elementary case study taken from the literature. Then, an industrial case study, which consists of a spatial crank mechanism connected to a fully-compliant four-bar linkage is discussed. At first, an initial sub-optimal design is considered and its PRB representation is automatically determined. Secondly, on the basis of the PRB model, several improved design alternatives are simulated. Finally, the most promising design solution is selected and the dimensions of a flexure with non-trivial shape (i.e. hybrid flexure) is computed. This technique, which combines reliable numerical results to the visual insight of CAD/CAE tools, may be particularly useful for analyzing/designing spatial CMs composed of complex flexure topologies.