Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Using passive techniques for vibration damping in mechanical systems

This paper examines two passive techniques for vibration reduction in mechanical systems: the first one is based on dynamic vibration absorbers (DVAs) and the second uses resonant circuit shunted (RCS) piezoceramics. Genetic algorithms are used to determine the optimal design parameters with respect to performance indexes, which are associated with the dynamical behavior of the system over selected frequency bands. The calculation of the frequency response functions (FRFs) of the composite structure (primary system + DVAs) is performed through a substructure coupling technique. A modal technique is used to determine the frequency response function of the structure containing shunted piezoceramics which are bonded to the primary structure. The use of both techniques simultaneously on the same structure is investigated. The methodology developed is illustrated by numerical applications in which the primary structure is represented by simple Euler-Bernoulli beams. However, the design aspects of vibration control devices presented in this paper can be extended to more complex structures.

Identification of Mechanical Systems through Kautz Filter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Abductive reasoning, information, and mechanical systems

We investigate, from a philosophical perspective, the relation between abductive reasoning and information in the context of biological systems. Emphasis is given to the organizational role played by abductive reasoning in practical activities of embodied embedded agency that involve meaningful information. From this perspective, meaningful information is provisionally characterized as a selforganizing process of pattern generation that constrains coherent action. We argue that this process can be considered as a part of evolutionarily developed learning abilities of organisms in order to help with their survival. We investigate the case of inorganic mechanical systems (like robots), which deal only with stable forms of habits, rather than with evolving learning abilities. Some difficulties are considered concerning the hypothesis that mechanical systems may operate with meaningful information, present in abductive reasoning. Finally, an example of hypotheses creation in the domain of medical sciences is presented in order to illustrate the complexity of abduction in practical reasoning concerning human activities. © 2007 Springer-Verlag Berlin Heidelberg.

Design of a state observer using decay rate LMI constraints for fault detection in mechanical systems

Nowadays, one of the most important concerns for many companies is to maintain the operation of their systems without sudden equipment break down. Because of this, new techniques for fault detection and location in mechanical systems subject to dynamic loads have been developed. This paper studies of the influence of the decay rate in the design of state observers using LMI for fault detection in mechanical systems. This influence is analyzed by the performance index proposed by Huh and Stein for the condition of a state observer. An example is presented to illustrate the methodology discussed.

Modeling, design and experimental characterization of Micro-Electro-Mechanical-Systems for gas chromatographic applications

Design parameters, process flows, electro-thermal-fluidic simulations and experimental characterizations of Micro-Electro-Mechanical-Systems (MEMS) suited for gas-chromatographic (GC) applications are presented and thoroughly described in this thesis, whose topic belongs to the research activities the Institute for Microelectronics and Microsystems (IMM)-Bologna is involved since several years, i.e. the development of micro-systems for chemical analysis, based on silicon micro-machining techniques and able to perform analysis of complex gaseous mixtures, especially in the field of environmental monitoring. In this regard, attention has been focused on the development of micro-fabricated devices to be employed in a portable mini-GC system for the analysis of aromatic Volatile Organic Compounds (VOC) like Benzene, Toluene, Ethyl-benzene and Xylene (BTEX), i.e. chemical compounds which can significantly affect environment and human health because of their demonstrated carcinogenicity (benzene) or toxicity (toluene, xylene) even at parts per billion (ppb) concentrations. The most significant results achieved through the laboratory functional characterization of the mini-GC system have been reported, together with in-field analysis results carried out in a station of the Bologna air monitoring network and compared with those provided by a commercial GC system. The development of more advanced prototypes of micro-fabricated devices specifically suited for FAST-GC have been also presented (silicon capillary columns, Ultra-Low-Power (ULP) Metal OXide (MOX) sensor, Thermal Conductivity Detector (TCD)), together with the technological processes for their fabrication. The experimentally demonstrated very high sensitivity of ULP-MOX sensors to VOCs, coupled with the extremely low power consumption, makes the developed ULP-MOX sensor the most performing metal oxide sensor reported up to now in literature, while preliminary test results proved that the developed silicon capillary columns are capable of performances comparable to those of the best fused silica capillary columns. Finally, the development and the validation of a coupled electro-thermal Finite Element Model suited for both steady-state and transient analysis of the micro-devices has been described, and subsequently implemented with a fluidic part to investigate devices behaviour in presence of a gas flowing with certain volumetric flow rates.

Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Engineering design handbook : computer aided design of mechanical systems.

Cover title.

Design and fabrication of two switched superconductivity microstrip hairpin filters using series micro-electro-mechanical systems (MEMS) switches

Series Micro-Electro-Mechanical System (MEMS) switches based on superconductor are utilized to switch between two bandpass hairpin filters with bandwidths of 365 MHz and nominal center frequencies of 2.1 GHz and 2.6 GHz. This was accomplished with 4 switches actuated in pairs, one pair at a time. When one pair was actuated the first bandpass filter was coupled to the input and output ports. When the other pair was actuated the second bandpass filter was coupled to the input and output ports. The device is made of a YBa2Cu 3O7 thin film deposited on a 20 mm x 20 mm LaAlO3 substrate by pulsed laser deposition. BaTiO3 deposited by RF magnetron sputtering in utilized as the insulation layer at the switching points of contact. These results obtained assured great performance showing a switchable device at 68 V with temperature of 40 K for the 2.1 GHz filter and 75 V with temperature of 30 K for the 2.6 GHz hairpin filter. ^

Mars delivery service - development of the electro-mechanical systems of the Sample Fetch Rover for the Mars Sample Return Campaign

This thesis describes the development of the Sample Fetch Rover (SFR), studied for Mars Sample Return (MSR), an international campaign carried out in cooperation between the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The focus of this document is the design of the electro-mechanical systems of the rover. After placing this work into the general context of robotic planetary exploration and summarising the state of the art for what concerns Mars rovers, the architecture of the Mars Sample Return Campaign is presented. A complete overview of the current SFR architecture is provided, touching upon all the main subsystems of the spacecraft. For each area, it is discussed what are the design drivers, the chosen solutions and whether they use heritage technology (in particular from the ExoMars Rover) or new developments. This research focuses on two topics of particular interest, due to their relevance for the mission and the novelty of their design: locomotion and sample acquisition, which are discussed in depth. The early SFR locomotion concepts are summarised, covering the initial trade-offs and discarded designs for higher traverse performance. Once a consolidated architecture was reached, the locomotion subsystem was developed further, defining the details of the suspension, actuators, deployment mechanisms and wheels. This technology is presented here in detail, including some key analysis and test results that support the design and demonstrate how it responds to the mission requirements. Another major electro-mechanical system developed as part of this work is the one dedicated to sample tube acquisition. The concept of operations of this machinery was defined to be robust against the unknown conditions that characterise the mission. The design process led to a highly automated robotic system which is described here in its main components: vision system, robotic arm and tube storage.

Multibody systems formulation

"Series: Solid mechanics and its applications, vol. 226"